├── .gitattributes ├── .gitignore ├── LICENSE ├── README.md ├── data ├── airlines.dat ├── airports.json ├── covid_data │ ├── X.pkl │ ├── from_state_to_id.pkl │ ├── g.pkl │ ├── y_cases.pkl │ ├── y_cases_normalized.pkl │ ├── y_deaths.pkl │ └── y_deaths_normalized.pkl ├── gp_on_graphs_teaser.png ├── heat_distribution │ ├── 1d.json │ ├── 1d.pkl │ └── 2d.pkl ├── hungary_chicken_pox │ ├── hungary_chickenpox.csv │ ├── hungary_county_edges.csv │ └── nn_dataset.json ├── st99_d00.dbf ├── st99_d00.shp ├── st99_d00.shx ├── us-states.csv ├── wave │ ├── X.pkl │ ├── graph.pkl │ └── y.pkl └── weather │ ├── X.pkl │ ├── g.pkl │ ├── g_100.pkl │ ├── weekly │ ├── X.pkl │ ├── g.pkl │ ├── g_100.pkl │ ├── g_50.pkl │ └── y_temprature.pkl │ └── y_temprature.pkl ├── experiments ├── 1d_experiments.py ├── 1d_wave_experiments.ipynb ├── run_chicken_pox.py └── run_covid_experiments.py ├── graph_kernels ├── __init__.py ├── data_utils.py ├── kernels.py ├── time_kernels.py ├── utils.py ├── utils_opt.py └── utils_postproc.py ├── requirements.txt └── setup.py /.gitattributes: -------------------------------------------------------------------------------- 1 | data/** filter=lfs diff=lfs merge=lfs -text 2 | *.ipynb linguist-detectable=false 3 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | *$py.class 5 | 6 | # C extensions 7 | *.so 8 | 9 | # Distribution / packaging 10 | .Python 11 | build/ 12 | develop-eggs/ 13 | dist/ 14 | downloads/ 15 | eggs/ 16 | .eggs/ 17 | lib/ 18 | lib64/ 19 | parts/ 20 | sdist/ 21 | var/ 22 | wheels/ 23 | pip-wheel-metadata/ 24 | share/python-wheels/ 25 | *.egg-info/ 26 | .installed.cfg 27 | *.egg 28 | MANIFEST 29 | 30 | # PyInstaller 31 | # Usually these files are written by a python script from a template 32 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 33 | *.manifest 34 | *.spec 35 | 36 | # Installer logs 37 | pip-log.txt 38 | pip-delete-this-directory.txt 39 | 40 | # Unit test / coverage reports 41 | htmlcov/ 42 | .tox/ 43 | .nox/ 44 | .coverage 45 | .coverage.* 46 | .cache 47 | nosetests.xml 48 | coverage.xml 49 | *.cover 50 | *.py,cover 51 | .hypothesis/ 52 | .pytest_cache/ 53 | 54 | # Translations 55 | *.mo 56 | *.pot 57 | 58 | # Django stuff: 59 | *.log 60 | local_settings.py 61 | db.sqlite3 62 | db.sqlite3-journal 63 | 64 | # Flask stuff: 65 | instance/ 66 | .webassets-cache 67 | 68 | # Scrapy stuff: 69 | .scrapy 70 | 71 | # Sphinx documentation 72 | docs/_build/ 73 | 74 | # PyBuilder 75 | target/ 76 | 77 | # Jupyter Notebook 78 | .ipynb_checkpoints 79 | 80 | # IPython 81 | profile_default/ 82 | ipython_config.py 83 | 84 | # pyenv 85 | .python-version 86 | 87 | # pipenv 88 | # According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control. 89 | # However, in case of collaboration, if having platform-specific dependencies or dependencies 90 | # having no cross-platform support, pipenv may install dependencies that don't work, or not 91 | # install all needed dependencies. 92 | #Pipfile.lock 93 | 94 | # PEP 582; used by e.g. github.com/David-OConnor/pyflow 95 | __pypackages__/ 96 | 97 | # Celery stuff 98 | celerybeat-schedule 99 | celerybeat.pid 100 | 101 | # SageMath parsed files 102 | *.sage.py 103 | 104 | # Environments 105 | .env 106 | .venv 107 | env/ 108 | venv/ 109 | ENV/ 110 | env.bak/ 111 | venv.bak/ 112 | 113 | # Spyder project settings 114 | .spyderproject 115 | .spyproject 116 | 117 | # Rope project settings 118 | .ropeproject 119 | 120 | # mkdocs documentation 121 | /site 122 | 123 | # mypy 124 | .mypy_cache/ 125 | .dmypy.json 126 | dmypy.json 127 | 128 | # Pyre type checker 129 | .pyre/ 130 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | Apache License 2 | Version 2.0, January 2004 3 | http://www.apache.org/licenses/ 4 | 5 | TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 6 | 7 | 1. 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We also recommend that a 185 | file or class name and description of purpose be included on the 186 | same "printed page" as the copyright notice for easier 187 | identification within third-party archives. 188 | 189 | Copyright [yyyy] [name of copyright owner] 190 | 191 | Licensed under the Apache License, Version 2.0 (the "License"); 192 | you may not use this file except in compliance with the License. 193 | You may obtain a copy of the License at 194 | 195 | http://www.apache.org/licenses/LICENSE-2.0 196 | 197 | Unless required by applicable law or agreed to in writing, software 198 | distributed under the License is distributed on an "AS IS" BASIS, 199 | WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 200 | See the License for the specific language governing permissions and 201 | limitations under the License. 202 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Non-separable Spatio-temporal Graph Kernels via SPDEs 2 | 3 | This repository is the official implementation of the methods in the publication 4 | * Alexander Nikitin, ST John, Arno Solin, and Samuel Kaski (2022). **Non-separable spatio-temporal graph kernels via SPDEs**. In *Proceedings of the 25th International Conference on Artificial Intelligence and Statistics (AISTATS)*. [[arXiv]](https://arxiv.org/abs/2111.08524) 5 | 6 |

7 | 8 |

9 | 10 | 11 | We leverage an explicit link between stochastic partial differential equations (SPDEs) and Gaussian processes on graphs and derive non-separable spatio-temporal graph kernels that capture interaction across space and time. We formulate the graph kernels for the stochastic heat equation and wave equation. We show that by providing novel tools for spatio-temporal GP modelling on graphs, we outperform pre-existing graph kernels in real-world applications that feature diffusion, oscillation, and other complicated interactions. 12 | 13 | ## Use 14 | The repo uses [git-lfs](https://git-lfs.github.com/) to store datasets. To fetch the data use: 15 | ```bash 16 | git lfs fetch 17 | ``` 18 | 19 | The code was tested with `python==3.6` and should work for `python>=3.6`. 20 | 21 | To install the required packages, run: 22 | ```bash 23 | pip install -r requirements.txt 24 | pip install -e . 25 | ``` 26 | 27 | ## Structure 28 | The repository contains two sets of kernels for time-independent and temporal processes on graphs. 29 | * Time-independent kernels are stored in `graph_kernels/kernels.py`. 30 | * Temporal kernels are stored in `graph_kernels/time_kernels.py`. 31 | * SHEK and SWEK are implemented in `graph_kernels/time_kernels.py:StochasticHeatEquation` and `graph_kernels/time_kernels.py:StochasticWaveEquationKernel`. 32 | 33 | ## Experiments. 34 | We provide an experimental evaluation of the proposed kernels on several datasets. 35 | 36 | ### Heat Transfer Dataset 37 | #### Interpolation: 38 | ```bash 39 | python experiments/1d_experiments.py --interpolation --dump_directory=$PATH_TO_RESULTS 40 | ``` 41 | 42 | #### Extrapolation: 43 | ```bash 44 | python experiments/1d_experiments.py --extrapolation --dump_directory=$PATH_TO_RESULTS 45 | ``` 46 | 47 | ### Chickenpox experiments 48 | #### Interpolation (103 + num_test_weeks): 49 | ```bash 50 | python experiments/run_chicken_pox.py --num_test_weeks=2 --interpolation --dump_directory=$PATH_TO_RESULTS 51 | ``` 52 | 53 | #### Extrapolation: 54 | ```bash 55 | python experiments/run_chicken_pox.py --num_test_weeks=2 --extrapolation --dump_directory=$PATH_TO_RESULTS 56 | ``` 57 | 58 | 59 | ### Covid19 Experiments 60 | #### Interpolation (33 + num_test_weeks): 61 | ```bash 62 | python experiments/run_covid_experiments.py --log_target --no-use_flight_graph \ 63 | --no-use_normalized_target --num_test_weeks=2 --interpolation --dump_directory=$PATH_TO_RESULTS 64 | ``` 65 | 66 | #### Extrapolation: 67 | ```bash 68 | python experiments/run_covid_experiments.py --log_target --no-use_flight_graph \ 69 | --no-use_normalized_target --num_test_weeks=2 --interpolation --dump_directory=$PATH_TO_RESULTS 70 | ``` 71 | 72 | 73 | ### Wave Experiments: 74 | Open with jupyter-notebook: 75 | ```bash 76 | ./experiments/1d_wave_experiments.ipynb 77 | ``` 78 | 79 | ## Citation 80 | If you use the code in this repository for your research, please cite the paper as follows: 81 | ```bibtex 82 | @inproceedings{nikitin2022non, 83 | title={Non-separable spatio-temporal graph kernels via SPDEs}, 84 | author={Nikitin, Alexander V and John, ST and Solin, Arno and Kaski, Samuel}, 85 | booktitle={International Conference on Artificial Intelligence and Statistics}, 86 | pages={10640--10660}, 87 | year={2022}, 88 | organization={PMLR} 89 | } 90 | ``` 91 | 92 | ## Contributing 93 | For all correspondence, please contact alexander.nikitin@aalto.fi. 94 | 95 | ## License 96 | This software is provided under the [Apache License 2.0](LICENSE). 97 | -------------------------------------------------------------------------------- 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-------------------------------------------------------------------------------- /experiments/1d_experiments.py: -------------------------------------------------------------------------------- 1 | import argparse 2 | import os 3 | import json 4 | import copy 5 | 6 | import numpy as np 7 | from tqdm import tqdm 8 | 9 | import sklearn 10 | import sklearn.metrics 11 | 12 | import gpflow 13 | from gpflow import Parameter 14 | import tensorflow as tf 15 | 16 | from graph_kernels import data_utils 17 | from graph_kernels import time_kernels 18 | from graph_kernels import utils_opt 19 | from graph_kernels import utils 20 | 21 | 22 | def parse_arguments(): 23 | parser = argparse.ArgumentParser(description='Heat distribution over a 1d line.') 24 | 25 | group = parser.add_mutually_exclusive_group() 26 | group.add_argument('--interpolation', action='store_true', default=False, 27 | help='Evaluate the models on the interpolation task.') 28 | group.add_argument('--extrapolation', dest='interpolation', action='store_false') 29 | 30 | parser.add_argument('--dump_directory', type=str, help='Path to directory with results.', 31 | default="dump_directory") 32 | return parser.parse_args() 33 | 34 | 35 | args = parse_arguments() 36 | INTERPOLATION = args.interpolation 37 | DUMP_DIRECTORY = args.dump_directory 38 | if not os.path.exists(DUMP_DIRECTORY): 39 | os.makedirs(DUMP_DIRECTORY) 40 | 41 | 42 | DATASET_PATH_1d = os.path.join( 43 | os.path.dirname(os.path.abspath(__file__)), "../data/heat_distribution/1d.pkl") 44 | DATASET_PATH_2s = os.path.join( 45 | os.path.dirname(os.path.abspath(__file__)), "../data/heat_distribution/2d.pkl") 46 | 47 | N_ITER = 2000 48 | RANDOM_SEEDS = [23, 42, 82, 100, 2 * 23, 2 * 42, 2 * 82, 2 * 100] 49 | NUM_TRAIN = 50 # number of training timestamps 50 | NUM_TEST = 10 51 | 52 | gpflow.config.set_default_jitter(1e-8) 53 | 54 | 55 | class ConstantArray(gpflow.mean_functions.MeanFunction): 56 | def __init__(self, shape): 57 | super().__init__() 58 | c = tf.zeros(shape) 59 | self.c = Parameter(c) 60 | 61 | def __call__(self, X): 62 | return tf.reshape( 63 | tf.gather(self.c, tf.cast(X[:, 0], dtype=tf.int32)), 64 | (X.shape[0], 1) 65 | ) 66 | 67 | 68 | def convert_dataset_to_nodes(data): 69 | new_data = [] 70 | for row in data: 71 | new_data.append([from_x_to_nodes[row[0]], row[1]]) 72 | return np.array(new_data) 73 | 74 | 75 | def extract_ml_dataset(dataset_1d, times): 76 | data = [] 77 | target = [] 78 | for t in times: 79 | for i, el in enumerate(dataset_1d[t]["x"]): 80 | data.append(np.append(el, np.array(t))) 81 | target.append(dataset_1d[t]["y"][i]) 82 | data = np.array(data) 83 | target = np.array(target)[:, np.newaxis] 84 | return data, target 85 | 86 | 87 | def evaluate_kernel(kernel, kernel_name): 88 | results = {} 89 | for random_seed in tqdm(RANDOM_SEEDS): 90 | utils.set_all_random_seeds(random_seed) 91 | 92 | train_data, train_target, test_data, test_target = datasets[random_seed] 93 | if kernel_name != "td_exponential": 94 | train_data = convert_dataset_to_nodes(train_data) 95 | test_data = convert_dataset_to_nodes(test_data) 96 | mean_function = ConstantArray(num_nodes) 97 | else: 98 | mean_function = gpflow.mean_functions.Constant() 99 | print("Shape: ", train_data.shape, test_data.shape) 100 | result, gprocess = utils_opt.evaluate_kernel_mcmc( 101 | copy.deepcopy(kernel), train_data, train_target, 102 | test_data, test_target, graph, mean_function=copy.deepcopy(mean_function), n_iter=N_ITER, 103 | optimizer_name="LBFGS") 104 | 105 | results[random_seed] = result 106 | return results, gprocess 107 | 108 | 109 | dataset_1d = data_utils.read_heat_1d(DATASET_PATH_1d) 110 | 111 | t = list(dataset_1d.keys())[0] 112 | graph = data_utils.build_graph_from_1d_points(dataset_1d[t]["x"]) 113 | 114 | num_nodes = len(graph.nodes()) 115 | 116 | from_x_to_nodes = {data["point"]: node for node, data in graph.nodes(data=True)} 117 | 118 | times = sorted(dataset_1d.keys())[1:] 119 | 120 | datasets = {} 121 | for i, rs in enumerate(RANDOM_SEEDS): 122 | start = i 123 | start_testing = start + NUM_TRAIN 124 | train_times = times[start:start_testing] 125 | test_times = times[start_testing:start_testing + NUM_TEST] 126 | 127 | train_data, train_target = extract_ml_dataset(dataset_1d, train_times) 128 | test_data, test_target = extract_ml_dataset(dataset_1d, test_times) 129 | if INTERPOLATION: 130 | train_data, test_data, train_target, test_target = \ 131 | sklearn.model_selection.train_test_split( 132 | np.concatenate((train_data, test_data)), 133 | np.concatenate((train_target, test_target)), test_size=0.1, random_state=rs) 134 | 135 | datasets[rs] = (train_data, train_target, test_data, test_target) 136 | 137 | 138 | kernels = { 139 | "td_exponential": time_kernels.TimeDistributed1dExponentialKernel(graph), 140 | # "td_laplacian": time_kernels.TimeDistributedLaplacianKernel(graph), 141 | "td_matern_nu_52_d_1": time_kernels.TimeDistributedMaternKernel(graph, nu=5 / 2, kappa=1), 142 | "td_matern_nu_32_d_1": time_kernels.TimeDistributedMaternKernel(graph, nu=3 / 2, kappa=1), 143 | "td_matern_nu_12_d_1": time_kernels.TimeDistributedMaternKernel(graph, nu=1 / 2, kappa=1), 144 | "stoch_heat_vector_pseudo_diff_1": time_kernels.StochasticHeatEquation( 145 | graph, c=0.1, use_pseudodifferential=True, nu=5 / 2, 146 | kappa=1, variance=[1.] * len(graph.nodes())), 147 | "stoch_heat_vector_pseudo_diff_2": time_kernels.StochasticHeatEquation( 148 | graph, c=0.1, use_pseudodifferential=True, nu=3 / 2, 149 | kappa=1, variance=[1.] * len(graph.nodes())), 150 | "stoch_heat_vector_pseudo_diff_3": time_kernels.StochasticHeatEquation( 151 | graph, c=0.1, use_pseudodifferential=True, nu=1 / 2, 152 | kappa=1, variance=[1.] * len(graph.nodes())), 153 | } 154 | 155 | for kernel_name, kernel in kernels.items(): 156 | print("Evaluating {}".format(kernel_name)) 157 | result, gprocess = evaluate_kernel( 158 | copy.deepcopy(kernel), kernel_name) 159 | folder = os.path.join(DUMP_DIRECTORY, kernel_name) 160 | os.makedirs(folder, exist_ok=True) 161 | # pickle.dump(gprocess, open(os.path.join(folder, "gprocess.pkl"), "wb")) 162 | json.dump(result, open(os.path.join(folder, "result.json"), "w")) 163 | -------------------------------------------------------------------------------- /experiments/1d_wave_experiments.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 1, 6 | "metadata": {}, 7 | "outputs": [ 8 | { 9 | "data": { 10 | "text/plain": [ 11 | "
" 12 | ] 13 | }, 14 | "metadata": {}, 15 | "output_type": "display_data" 16 | } 17 | ], 18 | "source": [ 19 | "%load_ext autoreload\n", 20 | "%autoreload 2\n", 21 | "\n", 22 | "from IPython.display import HTML\n", 23 | "\n", 24 | "import pickle\n", 25 | "\n", 26 | "import seaborn as sns\n", 27 | "import collections\n", 28 | "import networkx as nx\n", 29 | "import copy\n", 30 | "import time\n", 31 | "import os\n", 32 | "\n", 33 | "import numpy as np\n", 34 | "import matplotlib.pyplot as plt\n", 35 | "\n", 36 | "from matplotlib.pyplot import figure\n", 37 | "\n", 38 | "import gpflow\n", 39 | "\n", 40 | "from graph_kernels import data_utils\n", 41 | "from graph_kernels import utils\n", 42 | "from graph_kernels import time_kernels\n", 43 | "from graph_kernels import utils_opt\n", 44 | "from graph_kernels import utils_postproc\n", 45 | "\n", 46 | "figure(num=None, figsize=(28, 28), dpi=80, facecolor='w', edgecolor='k')\n", 47 | "\n", 48 | "gpflow.config.set_default_jitter(1e-4)" 49 | ] 50 | }, 51 | { 52 | "cell_type": "code", 53 | "execution_count": 13, 54 | "metadata": {}, 55 | "outputs": [], 56 | "source": [ 57 | "PATH_TO_DATA_FOLDER = (\"../data/wave/\")\n", 58 | "PATH_X = os.path.join(PATH_TO_DATA_FOLDER, \"X.pkl\")\n", 59 | "PATH_Y = os.path.join(PATH_TO_DATA_FOLDER, \"y.pkl\")\n", 60 | "PATH_GRAPH = os.path.join(PATH_TO_DATA_FOLDER, \"graph.pkl\")\n", 61 | "graph = pickle.load(open(PATH_GRAPH, \"rb\"))\n", 62 | "N_NODES = len(graph.nodes())\n", 63 | "\n", 64 | "DUMP_DIRECTORY = \"dump_directory\"\n", 65 | "os.makedirs(DUMP_DIRECTORY, exist_ok=True)\n", 66 | "os.makedirs(\"images\", exist_ok=True)" 67 | ] 68 | }, 69 | { 70 | "cell_type": "code", 71 | "execution_count": 3, 72 | "metadata": {}, 73 | "outputs": [], 74 | "source": [ 75 | "NUM_TEST_WEEKS = 2\n", 76 | "NUM_TRAIN = 50 * N_NODES\n", 77 | "NUM_TEST = NUM_TEST_WEEKS * N_NODES\n", 78 | "START = 4 * N_NODES * 2\n", 79 | "N_ITER = 5_000\n", 80 | "RANDOM_SEEDS = [23, 42, 82, 100, 123, 223,\n", 81 | " 2 * 23, 2 * 42, 2 * 82, 2 * 100, 2 * 123, 2 * 223]" 82 | ] 83 | }, 84 | { 85 | "cell_type": "code", 86 | "execution_count": 4, 87 | "metadata": {}, 88 | "outputs": [], 89 | "source": [ 90 | "X = pickle.load(open(PATH_X, \"rb\"))\n", 91 | "y = pickle.load(open(PATH_Y, \"rb\"))" 92 | ] 93 | }, 94 | { 95 | "cell_type": "code", 96 | "execution_count": 5, 97 | "metadata": {}, 98 | "outputs": [], 99 | "source": [ 100 | "kernels = {\n", 101 | " \"td_laplacian\": time_kernels.TimeDistributedLaplacianKernel(graph),\n", 102 | " \"td_matern_nu_52_k_1\": time_kernels.TimeDistributedMaternKernel(graph, nu=5/2, kappa=1),\n", 103 | " \"td_matern_nu_32_k_1\": time_kernels.TimeDistributedMaternKernel(graph, nu=3/2, kappa=1),\n", 104 | " \"td_matern_nu_12_k_1\": time_kernels.TimeDistributedMaternKernel(graph, nu=1/2, kappa=1),\n", 105 | " \"stoch_heat_vector_pseudo_diff_1\": time_kernels.StochasticHeatEquation(graph,\n", 106 | " c=0.1, use_pseudodifferential=True, nu=5/2,\n", 107 | " kappa=1, variance=[1.]*len(graph.nodes())),\n", 108 | " \"stoch_heat_vector_pseudo_diff_2\": time_kernels.StochasticHeatEquation(graph,\n", 109 | " c=0.1, use_pseudodifferential=True, nu=3/2,\n", 110 | " kappa=1, variance=[1.]*len(graph.nodes())),\n", 111 | " \"stoch_heat_vector_pseudo_diff_3\": time_kernels.StochasticHeatEquation(graph,\n", 112 | " c=0.1, use_pseudodifferential=True, nu=1/2,\n", 113 | " kappa=1, variance=1.),\n", 114 | " \"stoch_wave_kernel_nu_12\": time_kernels.StochasticWaveEquationKernel(\n", 115 | " graph, c=0.1, use_pseudodifferential=True, nu=1 / 2, kappa=10,\n", 116 | " variance=1.0),\n", 117 | " \"stoch_wave_kernel_nu_32\": time_kernels.StochasticWaveEquationKernel(\n", 118 | " graph, c=0.1, use_pseudodifferential=True, nu=3 / 2, kappa=1,\n", 119 | " variance=1.0),\n", 120 | " \"stoch_wave_kernel_nu_52\": time_kernels.StochasticWaveEquationKernel(\n", 121 | " graph, c=0.1, use_pseudodifferential=True, nu=5 / 2, kappa=10,\n", 122 | " variance=1.0),\n", 123 | "}" 124 | ] 125 | }, 126 | { 127 | "cell_type": "code", 128 | "execution_count": 6, 129 | "metadata": {}, 130 | "outputs": [], 131 | "source": [ 132 | "results = collections.defaultdict(dict)" 133 | ] 134 | }, 135 | { 136 | "cell_type": "code", 137 | "execution_count": 7, 138 | "metadata": {}, 139 | "outputs": [ 140 | { 141 | "name": "stdout", 142 | "output_type": "stream", 143 | "text": [ 144 | "0:\tELBO: -522.78695\tMAPE: 49411083745101.2500000000\tMAE: 0.0494760289\n", 145 | "1:\tELBO: -649.60072\tMAPE: 87218169830742.5468750000\tMAE: 0.0515282197\n", 146 | "2:\tELBO: -824.59367\tMAPE: 90807941555610.4375000000\tMAE: 0.0511540748\n", 147 | "3:\tELBO: -955.31851\tMAPE: 68342742878235.9453125000\tMAE: 0.0404082756\n", 148 | "4:\tELBO: -1152.45533\tMAPE: 35426937814843.6562500000\tMAE: 0.0236137586\n", 149 | "5:\tELBO: -1193.72487\tMAPE: 41640826968279.1250000000\tMAE: 0.0249512851\n", 150 | "6:\tELBO: -1221.01163\tMAPE: 47917634274505.5546875000\tMAE: 0.0315043598\n", 151 | "7:\tELBO: -1256.06121\tMAPE: 40104203824625.6015625000\tMAE: 0.0250922668\n", 152 | "8:\tELBO: -1260.73102\tMAPE: 39114375409547.6875000000\tMAE: 0.0243952481\n", 153 | "9:\tELBO: -1266.31820\tMAPE: 38759128574627.7812500000\tMAE: 0.0245500426\n", 154 | "10:\tELBO: -1271.73075\tMAPE: 37424899169070.4375000000\tMAE: 0.0247418769\n", 155 | "11:\tELBO: -1276.20968\tMAPE: 37220355215276.4453125000\tMAE: 0.0242883255\n", 156 | "12:\tELBO: -1283.45992\tMAPE: 36377933381502.3750000000\tMAE: 0.0246828267\n", 157 | "13:\tELBO: -1288.13708\tMAPE: 36276255408576.1562500000\tMAE: 0.0249266317\n", 158 | "14:\tELBO: -1289.39792\tMAPE: 37828748534609.7421875000\tMAE: 0.0252464624\n", 159 | "15:\tELBO: -1289.72658\tMAPE: 37351560268436.4765625000\tMAE: 0.0250686593\n", 160 | "16:\tELBO: -1289.78160\tMAPE: 37590105937283.8828125000\tMAE: 0.0250816727\n", 161 | "17:\tELBO: -1289.81950\tMAPE: 37718362948373.6171875000\tMAE: 0.0250789229\n", 162 | "18:\tELBO: -1289.91168\tMAPE: 37912337725456.7109375000\tMAE: 0.0250336248\n", 163 | "19:\tELBO: -1290.00858\tMAPE: 37990765436280.9062500000\tMAE: 0.0250376842\n", 164 | "20:\tELBO: -1290.04343\tMAPE: 37811904701063.3671875000\tMAE: 0.0248566383\n", 165 | "21:\tELBO: -1290.14220\tMAPE: 37726453581146.7812500000\tMAE: 0.0249401615\n", 166 | "22:\tELBO: -1290.22413\tMAPE: 37456102859620.1328125000\tMAE: 0.0249979521\n", 167 | "23:\tELBO: -1290.26739\tMAPE: 37203011272484.7031250000\tMAE: 0.0250672947\n", 168 | "24:\tELBO: -1290.28505\tMAPE: 37021202556996.2734375000\tMAE: 0.0250241352\n", 169 | "25:\tELBO: -1290.31220\tMAPE: 36875243251738.9921875000\tMAE: 0.0250548885\n", 170 | "26:\tELBO: -1290.33380\tMAPE: 36670146296457.4687500000\tMAE: 0.0250621257\n", 171 | "27:\tELBO: -1290.33825\tMAPE: 36638160318912.6953125000\tMAE: 0.0251000477\n", 172 | "28:\tELBO: -1290.34270\tMAPE: 36533621588011.8671875000\tMAE: 0.0250764243\n", 173 | "29:\tELBO: -1290.34484\tMAPE: 36458184152902.2968750000\tMAE: 0.0250685636\n", 174 | "30:\tELBO: -1290.34591\tMAPE: 36417236830188.9843750000\tMAE: 0.0250725603\n", 175 | "31:\tELBO: -1290.34686\tMAPE: 36405260022223.0078125000\tMAE: 0.0250828099\n", 176 | "32:\tELBO: -1290.34896\tMAPE: 36391605242716.1328125000\tMAE: 0.0251038633\n", 177 | "33:\tELBO: -1290.35328\tMAPE: 36386873986147.7343750000\tMAE: 0.0251220274\n", 178 | "34:\tELBO: -1290.36344\tMAPE: 36396310676440.8515625000\tMAE: 0.0251853621\n", 179 | "35:\tELBO: -1290.37104\tMAPE: 36215908826574.3515625000\tMAE: 0.0251737857\n", 180 | "36:\tELBO: -1290.38026\tMAPE: 36275447139535.4062500000\tMAE: 0.0253036889\n", 181 | "37:\tELBO: -1290.38255\tMAPE: 36275886204780.6015625000\tMAE: 0.0252891037\n", 182 | "38:\tELBO: -1290.38327\tMAPE: 36260072099426.7500000000\tMAE: 0.0252777955\n", 183 | "39:\tELBO: -1290.38367\tMAPE: 36258613944832.1015625000\tMAE: 0.0252740860\n", 184 | "40:\tELBO: -1290.38400\tMAPE: 36229128932267.3359375000\tMAE: 0.0252708193\n", 185 | "41:\tELBO: -1290.38459\tMAPE: 36234916872106.7187500000\tMAE: 0.0252716454\n", 186 | "42:\tELBO: -1290.38487\tMAPE: 36233358363031.0937500000\tMAE: 0.0252738838\n", 187 | "43:\tELBO: -1290.38496\tMAPE: 36232455782840.6718750000\tMAE: 0.0252780025\n", 188 | "44:\tELBO: -1290.38506\tMAPE: 36231895072822.7343750000\tMAE: 0.0252793214\n", 189 | "45:\tELBO: -1290.38515\tMAPE: 36231788775926.3593750000\tMAE: 0.0252803320\n", 190 | "46:\tELBO: -1290.38525\tMAPE: 36233244305607.2265625000\tMAE: 0.0252819269\n", 191 | "47:\tELBO: -1290.38535\tMAPE: 36239829064610.5390625000\tMAE: 0.0252764902\n", 192 | "48:\tELBO: -1290.38547\tMAPE: 36259148400086.1250000000\tMAE: 0.0252774194\n", 193 | "49:\tELBO: -1290.38555\tMAPE: 36278348998613.0468750000\tMAE: 0.0252769212\n", 194 | "50:\tELBO: -1290.38560\tMAPE: 36298055148564.8750000000\tMAE: 0.0252764348\n", 195 | "51:\tELBO: -1290.38560\tMAPE: 36302075428952.1171875000\tMAE: 0.0252772613\n", 196 | "52:\tELBO: -1290.38560\tMAPE: 36300656613550.1796875000\tMAE: 0.0252769210\n", 197 | "0:\tELBO: -521.07341\tMAPE: 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0.0200879649\n", 705 | "21:\tELBO: -1290.28437\tMAPE: 12363286338668.9394531250\tMAE: 0.0201714460\n", 706 | "22:\tELBO: -1290.29538\tMAPE: 12351073774798.8535156250\tMAE: 0.0202223645\n", 707 | "23:\tELBO: -1290.30312\tMAPE: 12297003809169.9199218750\tMAE: 0.0202626254\n", 708 | "24:\tELBO: -1290.31552\tMAPE: 12319553555632.9140625000\tMAE: 0.0202842205\n", 709 | "25:\tELBO: -1290.35182\tMAPE: 12649195622623.8671875000\tMAE: 0.0204453022\n", 710 | "26:\tELBO: -1290.39222\tMAPE: 12908211477452.8984375000\tMAE: 0.0204750693\n", 711 | "27:\tELBO: -1290.42443\tMAPE: 13179198280345.8457031250\tMAE: 0.0204980342\n", 712 | "28:\tELBO: -1290.43947\tMAPE: 13332886561229.6386718750\tMAE: 0.0205425863\n", 713 | "29:\tELBO: -1290.44995\tMAPE: 13329311279487.5566406250\tMAE: 0.0205595732\n", 714 | "30:\tELBO: -1290.45561\tMAPE: 13179505627532.2324218750\tMAE: 0.0206054121\n", 715 | "31:\tELBO: -1290.46224\tMAPE: 13047510318376.0332031250\tMAE: 0.0205803832\n", 716 | "32:\tELBO: -1290.46537\tMAPE: 12947857177494.5625000000\tMAE: 0.0205791208\n", 717 | "33:\tELBO: -1290.46669\tMAPE: 12860256844218.4199218750\tMAE: 0.0205846158\n", 718 | "34:\tELBO: -1290.46707\tMAPE: 12825879176747.0566406250\tMAE: 0.0205932140\n", 719 | "35:\tELBO: -1290.46800\tMAPE: 12756483685447.3164062500\tMAE: 0.0206013891\n", 720 | "36:\tELBO: -1290.46977\tMAPE: 12624324553345.8730468750\tMAE: 0.0206052735\n", 721 | "37:\tELBO: -1290.47259\tMAPE: 12264485492440.3300781250\tMAE: 0.0205518417\n", 722 | "38:\tELBO: -1290.47297\tMAPE: 12207938794877.0761718750\tMAE: 0.0205460684\n", 723 | "39:\tELBO: -1290.47369\tMAPE: 12110260250434.9199218750\tMAE: 0.0205136369\n", 724 | "40:\tELBO: -1290.47382\tMAPE: 12114724619568.5546875000\tMAE: 0.0205012369\n", 725 | "41:\tELBO: -1290.47387\tMAPE: 12133582674304.8105468750\tMAE: 0.0205032890\n", 726 | "42:\tELBO: -1290.47393\tMAPE: 12154391564985.3164062500\tMAE: 0.0205068143\n", 727 | "43:\tELBO: -1290.47403\tMAPE: 12170550383214.6328125000\tMAE: 0.0205120134\n", 728 | "44:\tELBO: -1290.47405\tMAPE: 12163216194653.5332031250\tMAE: 0.0205112301\n", 729 | "45:\tELBO: -1290.47409\tMAPE: 12152212241121.8808593750\tMAE: 0.0205119486\n", 730 | "46:\tELBO: -1290.47410\tMAPE: 12138552001941.0253906250\tMAE: 0.0205098486\n", 731 | "47:\tELBO: -1290.47410\tMAPE: 12136147824151.6816406250\tMAE: 0.0205101848\n" 732 | ] 733 | } 734 | ], 735 | "source": [ 736 | "#kernel_name = \"stoch_heat_vector_pseudo_diff_3\"\n", 737 | "kernel_name = \"stoch_wave_kernel_nu_52\"\n", 738 | "\n", 739 | "for i, rs in enumerate(RANDOM_SEEDS):\n", 740 | " kernel = copy.deepcopy(kernels[kernel_name])\n", 741 | " utils.set_all_random_seeds(rs)\n", 742 | "\n", 743 | " utils.set_all_random_seeds(rs)\n", 744 | " train_X, train_y, test_X, test_y, qt = data_utils.generate_dataset(\n", 745 | " X, y, NUM_TRAIN, NUM_TEST,\n", 746 | " start=START + 10 * len(graph.nodes()) + i * len(graph.nodes()), log_target=False, rs=rs,\n", 747 | " interpolation=False)\n", 748 | " start = time.time()\n", 749 | " result, gprocess = utils_opt.evaluate_kernel_mcmc(\n", 750 | " kernel, train_X, train_y, test_X, test_y, graph,\n", 751 | " n_iter=N_ITER, dump_everything=False, dump_directory=DUMP_DIRECTORY)\n", 752 | " results[kernel_name][rs] = result" 753 | ] 754 | }, 755 | { 756 | "cell_type": "code", 757 | "execution_count": 8, 758 | "metadata": {}, 759 | "outputs": [], 760 | "source": [ 761 | "agg_kernel_results = utils_postproc.parse_results(results)" 762 | ] 763 | }, 764 | { 765 | "cell_type": "code", 766 | "execution_count": 9, 767 | "metadata": {}, 768 | "outputs": [ 769 | { 770 | "name": "stdout", 771 | "output_type": "stream", 772 | "text": [ 773 | "stoch_wave_kernel_nu_52\n", 774 | "Mean: 0.0189 $\\pm$ 0.0028\n", 775 | "Confidence Interval 95%%: 0.01610405905604751, 0.021731816631653467\n", 776 | "(0.01610405905604751, 0.021731816631653467)\n", 777 | "Data: [0.025276921027308018, 0.019689531058666873, 0.01286791425585474, 0.015034357473585053, 0.01436047199927747, 0.015805523963914877, 0.01709513207841518, 0.016351642022197983, 0.019562474216397095, 0.02513599117882034, 0.02532511004077812, 0.02051018481099016]\n", 778 | "====================================\n" 779 | ] 780 | } 781 | ], 782 | "source": [ 783 | "for kernel_name in results.keys():\n", 784 | " print(kernel_name)\n", 785 | " utils_postproc.stats_array([r[\"MAE\"] for r in results[kernel_name].values()])\n", 786 | " print(\"====================================\")" 787 | ] 788 | }, 789 | { 790 | "cell_type": "markdown", 791 | "metadata": {}, 792 | "source": [ 793 | "## Interpolation (2)\n", 794 | "stoch_wave_kernel_nu_52\n", 795 | "Mean: 0.0028 $\\pm$ 0.0006\n", 796 | "Confidence Interval 95%%: 0.0022401338710728927, 0.003451229086341565\n", 797 | "(0.0022401338710728927, 0.003451229086341565)\n", 798 | "\n", 799 | "Data: [0.0017450406668729596, 0.004414391742788683, 0.004453214111611686, 0.0021427154657830167, 0.001821253925833599, 0.0024079721248159744, 0.0025783857412016963, 0.0022940820372391252, 0.0031607236224262952, 0.0022596849189193305, 0.003928416917940637, 0.0029422964690537417]\n", 800 | "\n", 801 | "====================================\n", 802 | "\n", 803 | "stoch_heat_vector_pseudo_diff_3\n", 804 | "Mean: 0.0047 $\\pm$ 0.0014\n", 805 | "Confidence Interval 95%%: 0.003322288909083467, 0.0060250689146361955\n", 806 | "(0.0033222889090834666, 0.006025068914636196)\n", 807 | "\n", 808 | "Data: [0.0039073701859408975, 0.00502979652575883, 0.007811263104709524, 0.002084047933587993, 0.004071909169771604, 0.0025462248547979053, 0.004087074038491602, 0.003633725543103668, 0.006207459554040093, 0.0028253794905910993, 0.009191976295210859, 0.004687920246313\n", 809 | "\n", 810 | "\n", 811 | "## Extrapolation \n", 812 | "stoch_heat_vector_pseudo_diff_3\n", 813 | "Mean: 0.0274 $\\pm$ 0.0067\n", 814 | "Confidence Interval 95%%: 0.020609731103628355, 0.03410758679848596\n", 815 | "(0.020609731103628355, 0.03410758679848596)\n", 816 | "\n", 817 | "Data: [0.03236539513724462, 0.022677598991751556, 0.01165332385894794, 0.007914633900852069, 0.01911465579315055, 0.028778972004901007, 0.03587617517178525, 0.039150246636727705, 0.039725863943984634, 0.03717489520129039, 0.03130447329271192, 0.022567673479338222]\n", 818 | "\n", 819 | "====================================\n", 820 | "\n", 821 | "stoch_wave_kernel_nu_52\n", 822 | "Mean: 0.0189 $\\pm$ 0.0028\n", 823 | "Confidence Interval 95%%: 0.01610405905604751, 0.021731816631653467\n", 824 | "(0.01610405905604751, 0.021731816631653467)\n", 825 | "\n", 826 | "Data: [0.025276921027308018, 0.019689531058666873, 0.01286791425585474, 0.015034357473585053, 0.01436047199927747, 0.015805523963914877, 0.01709513207841518, 0.016351642022197983, 0.019562474216397095, 0.02513599117882034, 0.02532511004077812, 0.02051018481099016]\n", 827 | "\n", 828 | "====================================\n", 829 | "\n" 830 | ] 831 | }, 832 | { 833 | "cell_type": "code", 834 | "execution_count": 10, 835 | "metadata": {}, 836 | "outputs": [ 837 | { 838 | "name": "stdout", 839 | "output_type": "stream", 840 | "text": [ 841 | "0:\tELBO: -474.96614\tMAPE: 24645810085517.2578125000\tMAE: 0.0296326765\n", 842 | "1:\tELBO: -576.02563\tMAPE: 19003437695932.1757812500\tMAE: 0.0259727013\n", 843 | "2:\tELBO: -713.54835\tMAPE: 12498801157852.0820312500\tMAE: 0.0201895766\n", 844 | "3:\tELBO: -822.26806\tMAPE: 13805302588245.2500000000\tMAE: 0.0130924225\n", 845 | "4:\tELBO: -1022.18304\tMAPE: 7525847832508.3515625000\tMAE: 0.0059436819\n", 846 | "5:\tELBO: -1048.62851\tMAPE: 6051768189694.6757812500\tMAE: 0.0051288084\n", 847 | "6:\tELBO: -1076.66693\tMAPE: 4967651560894.9482421875\tMAE: 0.0042977134\n", 848 | "7:\tELBO: -1087.22058\tMAPE: 3988782965217.1567382812\tMAE: 0.0040269194\n", 849 | "8:\tELBO: -1094.16457\tMAPE: 4297801887967.3291015625\tMAE: 0.0039813612\n", 850 | "9:\tELBO: -1098.30482\tMAPE: 4165111177225.1972656250\tMAE: 0.0038234018\n", 851 | "10:\tELBO: -1107.26751\tMAPE: 3840882090748.3291015625\tMAE: 0.0034909915\n", 852 | "11:\tELBO: -1113.32152\tMAPE: 3623277855807.8310546875\tMAE: 0.0033348642\n", 853 | "12:\tELBO: -1120.58866\tMAPE: 3591378790111.0405273438\tMAE: 0.0032380606\n", 854 | "13:\tELBO: -1124.32423\tMAPE: 3654870613543.1000976562\tMAE: 0.0032316609\n", 855 | "14:\tELBO: -1128.08389\tMAPE: 3345362973381.7099609375\tMAE: 0.0030733673\n", 856 | "15:\tELBO: -1130.62344\tMAPE: 3197316655935.5991210938\tMAE: 0.0029438184\n", 857 | "16:\tELBO: -1131.27964\tMAPE: 2958687740761.7348632812\tMAE: 0.0028542106\n", 858 | "17:\tELBO: -1131.36479\tMAPE: 2970904410209.6284179688\tMAE: 0.0028589393\n", 859 | "18:\tELBO: -1131.48152\tMAPE: 2979031013072.9394531250\tMAE: 0.0028658297\n", 860 | "19:\tELBO: -1131.64123\tMAPE: 2959802652426.6679687500\tMAE: 0.0028606358\n", 861 | "20:\tELBO: -1131.75535\tMAPE: 3073073396650.7685546875\tMAE: 0.0028898361\n", 862 | "21:\tELBO: -1132.08893\tMAPE: 3011894854709.0009765625\tMAE: 0.0028749672\n", 863 | "22:\tELBO: -1132.51635\tMAPE: 2959290561555.9931640625\tMAE: 0.0028619974\n", 864 | "23:\tELBO: -1132.75207\tMAPE: 2967361042712.6123046875\tMAE: 0.0028700259\n", 865 | "24:\tELBO: -1132.76807\tMAPE: 2971788132412.2812500000\tMAE: 0.0028652019\n", 866 | "25:\tELBO: -1132.89897\tMAPE: 2999267443088.4072265625\tMAE: 0.0028788519\n", 867 | "26:\tELBO: -1132.95688\tMAPE: 3015906129854.9882812500\tMAE: 0.0028875495\n", 868 | "27:\tELBO: -1132.97280\tMAPE: 3032049941358.5253906250\tMAE: 0.0028907912\n", 869 | "28:\tELBO: -1133.00444\tMAPE: 3017220500193.0249023438\tMAE: 0.0028850949\n", 870 | "29:\tELBO: -1133.02348\tMAPE: 3012677241533.1938476562\tMAE: 0.0028815979\n", 871 | "30:\tELBO: -1133.03020\tMAPE: 2997158793964.4775390625\tMAE: 0.0028736042\n", 872 | "31:\tELBO: -1133.03664\tMAPE: 3002187990900.9667968750\tMAE: 0.0028734929\n", 873 | "32:\tELBO: -1133.03756\tMAPE: 3003889222497.9687500000\tMAE: 0.0028734281\n", 874 | "33:\tELBO: -1133.04032\tMAPE: 3004968020183.5976562500\tMAE: 0.0028721141\n", 875 | "34:\tELBO: -1133.04306\tMAPE: 3004327370774.7822265625\tMAE: 0.0028695747\n", 876 | "35:\tELBO: -1133.04705\tMAPE: 2997328580704.2617187500\tMAE: 0.0028673854\n", 877 | "36:\tELBO: -1133.05083\tMAPE: 2996620623659.6010742188\tMAE: 0.0028663415\n", 878 | "37:\tELBO: -1133.05592\tMAPE: 2990269737402.7709960938\tMAE: 0.0028667763\n", 879 | "38:\tELBO: -1133.06188\tMAPE: 2990675070556.4233398438\tMAE: 0.0028690704\n", 880 | "39:\tELBO: -1133.06948\tMAPE: 2988114790390.9287109375\tMAE: 0.0028703060\n", 881 | "40:\tELBO: -1133.07193\tMAPE: 3007199425001.3310546875\tMAE: 0.0028773070\n", 882 | "41:\tELBO: -1133.07755\tMAPE: 2998259084262.6542968750\tMAE: 0.0028723819\n", 883 | "42:\tELBO: -1133.07892\tMAPE: 2995706175100.3784179688\tMAE: 0.0028700472\n", 884 | "43:\tELBO: -1133.07947\tMAPE: 2995147920854.4750976562\tMAE: 0.0028692143\n", 885 | "44:\tELBO: -1133.07960\tMAPE: 3001760103112.0590820312\tMAE: 0.0028715120\n", 886 | "45:\tELBO: -1133.07983\tMAPE: 2999767305004.9653320312\tMAE: 0.0028713374\n", 887 | "46:\tELBO: -1133.07985\tMAPE: 2999859591215.7187500000\tMAE: 0.0028713858\n", 888 | "47:\tELBO: -1133.07986\tMAPE: 3000046286209.7587890625\tMAE: 0.0028715826\n", 889 | "48:\tELBO: -1133.07986\tMAPE: 3000302612850.5224609375\tMAE: 0.0028717173\n", 890 | "49:\tELBO: -1133.07986\tMAPE: 3000170185181.0400390625\tMAE: 0.0028717180\n" 891 | ] 892 | } 893 | ], 894 | "source": [ 895 | "kernel = copy.deepcopy(kernels[\"stoch_wave_kernel_nu_52\"])\n", 896 | "#kernel = copy.deepcopy(kernels[\"stoch_heat_vector_pseudo_diff_3\"])\n", 897 | "utils.set_all_random_seeds(rs)\n", 898 | "\n", 899 | "utils.set_all_random_seeds(rs)\n", 900 | "train_X, train_y, test_X, test_y, qt = data_utils.generate_dataset(\n", 901 | " X, y, NUM_TRAIN, NUM_TEST,\n", 902 | " start=START + 10 * len(graph.nodes()), log_target=False, rs=rs,\n", 903 | " interpolation=True)\n", 904 | "start = time.time()\n", 905 | "result, gprocess = utils_opt.evaluate_kernel_mcmc(\n", 906 | " kernel, train_X, train_y, test_X, test_y, graph,\n", 907 | " n_iter=N_ITER, dump_everything=False, dump_directory=DUMP_DIRECTORY)\n", 908 | "results[kernel_name][rs] = result" 909 | ] 910 | }, 911 | { 912 | "cell_type": "code", 913 | "execution_count": 14, 914 | "metadata": {}, 915 | "outputs": [], 916 | "source": [ 917 | "def filter_ds(X, y, node_id):\n", 918 | " inds = [i for i in range(X.shape[0]) if X[i, 0] == node_id]\n", 919 | " return X[inds], np.array(y)[inds][:]\n", 920 | "\n", 921 | "\n", 922 | "def plot(m, X_train, signal, node_id):\n", 923 | " xmin, xmax = 0.5, 5\n", 924 | " xx = np.linspace(xmin, xmax, 100)\n", 925 | " xx = np.array([[node_id, x] for x in xx])\n", 926 | " \n", 927 | " mean, var = m.predict_y(xx)\n", 928 | " plt.figure(figsize=(12, 6))\n", 929 | " X_train, signal = filter_ds(X_train, signal, node_id)\n", 930 | " plt.plot(X_train[:, 1], signal, 'kx', mew=2)\n", 931 | " plt.plot(xx[:, 1], mean, 'b', lw=2)\n", 932 | " plt.fill_between(xx[:, 1], mean[:, 0] - 2 * np.sqrt(var[:, 0]), mean[:, 0] + 2 * np.sqrt(var[:, 0]), color='blue', alpha=0.2)\n", 933 | " plt.xlim(xmin, xmax)\n", 934 | " plt.title(\"Fit of GP (SWEK) model to synthetic wave dataset (node: {})\".format(node_id), fontsize=24)\n", 935 | " plt.savefig(\"images/swek_fit_wave_{}.pdf\".format(node_id))" 936 | ] 937 | }, 938 | { 939 | "cell_type": "code", 940 | "execution_count": 15, 941 | "metadata": {}, 942 | "outputs": [ 943 | { 944 | "data": { 945 | "image/png": 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\n", 946 | "text/plain": [ 947 | "
" 948 | ] 949 | }, 950 | "metadata": { 951 | "needs_background": "light" 952 | }, 953 | "output_type": "display_data" 954 | } 955 | ], 956 | "source": [ 957 | "plot(gprocess, train_X, train_y, 2)" 958 | ] 959 | }, 960 | { 961 | "cell_type": "code", 962 | "execution_count": null, 963 | "metadata": {}, 964 | "outputs": [], 965 | "source": [] 966 | } 967 | ], 968 | "metadata": { 969 | "kernelspec": { 970 | "display_name": "Python 3", 971 | "language": "python", 972 | "name": "python3" 973 | }, 974 | "language_info": { 975 | "codemirror_mode": { 976 | "name": "ipython", 977 | "version": 3 978 | }, 979 | "file_extension": ".py", 980 | "mimetype": "text/x-python", 981 | "name": "python", 982 | "nbconvert_exporter": "python", 983 | "pygments_lexer": "ipython3", 984 | "version": "3.6.5" 985 | } 986 | }, 987 | "nbformat": 4, 988 | "nbformat_minor": 4 989 | } 990 | -------------------------------------------------------------------------------- /experiments/run_chicken_pox.py: -------------------------------------------------------------------------------- 1 | import os 2 | 3 | import json 4 | import time 5 | import argparse 6 | import copy 7 | import sklearn 8 | 9 | import networkx as nx 10 | from tqdm import tqdm 11 | 12 | import gpflow 13 | import tensorflow as tf 14 | 15 | from graph_kernels import utils 16 | from graph_kernels import data_utils 17 | from graph_kernels import utils_opt 18 | from graph_kernels import time_kernels 19 | 20 | gpflow.config.set_default_jitter(1e-4) 21 | gpflow.config.set_default_float(tf.float64) 22 | f64 = gpflow.utilities.to_default_float 23 | 24 | 25 | def parse_arguments(): 26 | parser = argparse.ArgumentParser(description='Toy epidemiological dataset.') 27 | parser.add_argument('--dump_directory', type=str, 28 | help='Path to directory with results.', 29 | default="dump_directory") 30 | 31 | parser.add_argument('--num_test_weeks', type=int, help='Number of test weeks.', default=2) 32 | 33 | group = parser.add_mutually_exclusive_group() 34 | group.add_argument('--interpolation', action='store_true', default=False, 35 | help='Evaluate the models on the interpolation task.') 36 | group.add_argument('--extrapolation', dest='interpolation', action='store_false') 37 | 38 | return parser.parse_args() 39 | 40 | 41 | args = parse_arguments() 42 | 43 | INTERPOLATION = args.interpolation 44 | DATA_FOLDER = os.path.join( 45 | os.path.dirname(os.path.abspath(__file__)), "../data/hungary_chicken_pox/") 46 | 47 | GRAPH_PATH = os.path.join(DATA_FOLDER, "hungary_county_edges.csv") 48 | graph = data_utils.load_hungary_graph(GRAPH_PATH) 49 | graph.remove_edges_from(nx.selfloop_edges(graph)) 50 | 51 | NUM_TEST_WEEKS = args.num_test_weeks 52 | NUM_TRAIN = 103 * len(graph.nodes()) 53 | NUM_TEST = len(graph.nodes()) * NUM_TEST_WEEKS 54 | N_ITER = 2_000 55 | 56 | RANDOM_SEEDS = [23, 42, 82, 100, 123, 223, 57 | 2 * 23, 2 * 42, 2 * 82, 2 * 100, 2 * 123, 2 * 223] 58 | 59 | DUMP_DIRECTORY = args.dump_directory 60 | DUMP_EVERYTHING = False 61 | os.makedirs(DUMP_DIRECTORY, exist_ok=True) 62 | 63 | 64 | X, y, graph, _ = data_utils.load_hungary_dataset( 65 | graph, path_to_csv=os.path.join(DATA_FOLDER, "hungary_chickenpox.csv")) 66 | 67 | 68 | exp_kernels = { 69 | #"td_laplacian": time_kernels.TimeDistributedLaplacianKernel(graph), 70 | "stoch_heat_vector_pseudo_diff_1_scalar": time_kernels.StochasticHeatEquation( 71 | graph, c=0.1, use_pseudodifferential=True, nu=1 / 2, 72 | kappa=1, variance=1.), 73 | "td_matern_nu_52_d_1": time_kernels.TimeDistributedMaternKernel(graph, nu=5 / 2, kappa=1), 74 | "td_matern_nu_32_d_1": time_kernels.TimeDistributedMaternKernel(graph, nu=3 / 2, kappa=1), 75 | "td_matern_nu_12_d_1": time_kernels.TimeDistributedMaternKernel(graph, nu=1 / 2, kappa=1), 76 | "stoch_heat_vector_pseudo_diff_1": time_kernels.StochasticHeatEquation( 77 | graph, c=0.1, use_pseudodifferential=True, nu=5 / 2, 78 | kappa=1, variance=[1.] * len(graph.nodes())), 79 | "stoch_heat_vector_pseudo_diff_2": time_kernels.StochasticHeatEquation( 80 | graph, c=0.1, use_pseudodifferential=True, nu=3 / 2, 81 | kappa=1, variance=[1.] * len(graph.nodes())), 82 | "stoch_heat_vector_pseudo_diff_3": time_kernels.StochasticHeatEquation( 83 | graph, c=0.1, use_pseudodifferential=True, nu=1 / 2, 84 | kappa=1, variance=[1.] * len(graph.nodes())), 85 | } 86 | 87 | 88 | if __name__ == "__main__": 89 | results = {} 90 | for kernel_name, kernel in exp_kernels.items(): 91 | print("Evaluating kernel ", kernel_name) 92 | results[kernel_name] = {} 93 | for i, rs in tqdm(enumerate(RANDOM_SEEDS), total=len(RANDOM_SEEDS)): 94 | utils.set_all_random_seeds(rs) 95 | train_X, train_y, test_X, test_y, qt = data_utils.generate_dataset( 96 | X, y.ravel(), 97 | num_training_data=NUM_TRAIN, num_testing_data=NUM_TEST, 98 | start=i * len(graph.nodes()), 99 | log_target=True, rs=rs) 100 | if INTERPOLATION: 101 | train_X, test_X, train_y, test_y = \ 102 | sklearn.model_selection.train_test_split( 103 | train_X, train_y, test_size=0.1, random_state=rs) 104 | train_y = tf.cast(train_y, tf.float64) 105 | test_y = tf.cast(test_y, tf.float64) 106 | 107 | start = time.time() 108 | result, gprocess = utils_opt.evaluate_kernel_mcmc( 109 | copy.deepcopy(kernel), train_X, train_y, test_X, test_y, graph, 110 | transformer=qt, 111 | n_iter=N_ITER, optimizer_name="LBFGS") 112 | results[kernel_name][rs] = result 113 | results[kernel_name][rs]["time"] = time.time() - start 114 | json.dump(results, open(os.path.join(DUMP_DIRECTORY, "results.json"), "w")) 115 | -------------------------------------------------------------------------------- /experiments/run_covid_experiments.py: -------------------------------------------------------------------------------- 1 | import os 2 | import pickle 3 | import json 4 | import time 5 | import argparse 6 | import copy 7 | 8 | from tqdm import tqdm 9 | 10 | import gpflow 11 | 12 | from graph_kernels import utils 13 | from graph_kernels import time_kernels 14 | from graph_kernels import data_utils 15 | from graph_kernels import utils_opt 16 | 17 | 18 | def parse_arguments(): 19 | parser = argparse.ArgumentParser(description='COVID-19 across the US') 20 | parser.add_argument('--log_target', action='store_true', default=False, 21 | help='Apply log transform to the target.') 22 | parser.add_argument('--no-log_target', dest='log_target', action='store_false') 23 | 24 | parser.add_argument('--use_flight_graph', action='store_true', default=False, 25 | help='Use graph that contains information about the flights.') 26 | parser.add_argument('--no-use_flight_graph', dest='use_flight_graph', action='store_false') 27 | 28 | group = parser.add_mutually_exclusive_group() 29 | group.add_argument('--use_normalized_target', action='store_true', default=False, 30 | help='Normalize the target by population in a state.') 31 | group.add_argument('--no-use_normalized_target', dest='use_normalized_target', action='store_false') 32 | 33 | group = parser.add_mutually_exclusive_group() 34 | group.add_argument('--interpolation', action='store_true', default=False, 35 | help='Evaluate the models on the interpolation task.') 36 | group.add_argument('--extrapolation', dest='interpolation', action='store_false') 37 | 38 | parser.add_argument('--dump_directory', type=str, help='Path to directory with results.', 39 | default="dump_directory") 40 | 41 | parser.add_argument('--num_test_weeks', type=int, help='Number of test weeks.', default=2) 42 | 43 | return parser.parse_args() 44 | 45 | 46 | args = parse_arguments() 47 | 48 | gpflow.config.set_default_jitter(1e-4) 49 | 50 | DATA_FOLDER = os.path.join( 51 | os.path.dirname(os.path.abspath(__file__)), "../data/covid_data/") 52 | 53 | INTERPOLATION = args.interpolation 54 | USE_FLIGHT_GRAPH = args.use_flight_graph 55 | if USE_FLIGHT_GRAPH: 56 | GRAPH_PATH = os.path.join(DATA_FOLDER, "state_graph.pkl") 57 | else: 58 | GRAPH_PATH = os.path.join(DATA_FOLDER, "g.pkl") 59 | graph = pickle.load(open(GRAPH_PATH, "rb")) 60 | N_NODES = len(graph.nodes()) 61 | 62 | NUM_TEST_WEEKS = args.num_test_weeks 63 | NUM_TRAIN = 33 * N_NODES 64 | NUM_TEST = NUM_TEST_WEEKS * N_NODES 65 | START = 4 * N_NODES * 2 66 | N_ITER = 5_000 67 | 68 | IS_PREDICT_CASES = True 69 | LOG_TARGET = args.log_target 70 | USE_NORMALIZED_TARGET = args.use_normalized_target 71 | 72 | 73 | RANDOM_SEEDS = [23, 42, 82, 100, 123, 74 | 2 * 23, 2 * 42, 2 * 82, 2 * 100, 2 * 123] 75 | 76 | X_PATH = os.path.join(DATA_FOLDER, "X.pkl") 77 | if USE_NORMALIZED_TARGET: 78 | Y_CASES_PATH = os.path.join(DATA_FOLDER, "y_cases_normalized.pkl") 79 | Y_DEATHS_PATH = os.path.join(DATA_FOLDER, "y_deaths_normalized.pkl") 80 | else: 81 | Y_CASES_PATH = os.path.join(DATA_FOLDER, "y_cases.pkl") 82 | Y_DEATHS_PATH = os.path.join(DATA_FOLDER, "y_deaths.pkl") 83 | 84 | 85 | FROM_STATE_TO_ID_PATH = os.path.join(DATA_FOLDER, "from_state_to_id.pkl") 86 | DUMP_DIRECTORY = args.dump_directory 87 | DUMP_EVERYTHING = False 88 | os.makedirs(DUMP_DIRECTORY, exist_ok=True) 89 | 90 | 91 | X = pickle.load(open(X_PATH, "rb")) 92 | y_cases = pickle.load(open(Y_CASES_PATH, "rb")) 93 | y_deaths = pickle.load(open(Y_DEATHS_PATH, "rb")) 94 | from_state_to_id = pickle.load(open(FROM_STATE_TO_ID_PATH, "rb")) 95 | 96 | 97 | if IS_PREDICT_CASES: 98 | y = y_cases 99 | else: 100 | y = y_deaths 101 | 102 | 103 | y[y < 0] = 0 104 | 105 | exp_kernels = { 106 | "td_matern_nu_52_k_1": time_kernels.TimeDistributedMaternKernel(graph, nu=5 / 2, kappa=1), 107 | "td_matern_nu_32_k_1": time_kernels.TimeDistributedMaternKernel(graph, nu=3 / 2, kappa=1), 108 | "td_matern_nu_12_k_1": time_kernels.TimeDistributedMaternKernel(graph, nu=1 / 2, kappa=1), 109 | "stoch_heat_vector_pseudo_diff_1": time_kernels.StochasticHeatEquation( 110 | graph, c=0.1, use_pseudodifferential=True, nu=5 / 2, kappa=1, variance=[1.] * len(graph.nodes())), 111 | "stoch_heat_vector_pseudo_diff_2": time_kernels.StochasticHeatEquation( 112 | graph, c=0.1, use_pseudodifferential=True, nu=3 / 2, kappa=1, variance=[1.] * len(graph.nodes())), 113 | "stoch_heat_vector_pseudo_diff_3": time_kernels.StochasticHeatEquation( 114 | graph, c=0.1, use_pseudodifferential=True, nu=1 / 2, kappa=1, variance=[1.] * len(graph.nodes())), 115 | } 116 | 117 | 118 | if __name__ == "__main__": 119 | results = {} 120 | for kernel_name, kernel in exp_kernels.items(): 121 | results[kernel_name] = {} 122 | for i, rs in tqdm(enumerate(RANDOM_SEEDS), total=len(RANDOM_SEEDS)): 123 | utils.set_all_random_seeds(rs) 124 | train_X, train_y, test_X, test_y, qt = data_utils.generate_dataset( 125 | X, y, NUM_TRAIN, NUM_TEST, 126 | start=START + i * len(graph.nodes()), log_target=LOG_TARGET, rs=rs, 127 | interpolation=INTERPOLATION) 128 | print("Evaluating kernel ", kernel_name) 129 | start = time.time() 130 | result, gprocess = utils_opt.evaluate_kernel_mcmc( 131 | copy.deepcopy(kernel), train_X, train_y, test_X, test_y, graph, 132 | transformer=qt, 133 | n_iter=N_ITER, dump_directory=DUMP_DIRECTORY, 134 | dump_everything=DUMP_EVERYTHING, optimizer_name="LBFGS") 135 | results[kernel_name][rs] = result 136 | results[kernel_name][rs]["time"] = time.time() - start 137 | json.dump(results, open(os.path.join(DUMP_DIRECTORY, "results.json"), "w")) 138 | -------------------------------------------------------------------------------- /graph_kernels/__init__.py: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/AaltoPML/spatiotemporal-graph-kernels/b82529b6a1dfeb4ff06fb9ea0952ec926f0d7ae0/graph_kernels/__init__.py -------------------------------------------------------------------------------- /graph_kernels/data_utils.py: -------------------------------------------------------------------------------- 1 | import os 2 | 3 | import numpy as np 4 | import pandas as pd 5 | import networkx as nx 6 | import pickle 7 | 8 | import sklearn 9 | from sklearn.preprocessing import FunctionTransformer 10 | 11 | import matplotlib.pyplot as plt 12 | 13 | 14 | HEAT_DATASET_1d = "./data/heat_distribution/1d.pkl" 15 | HEAT_DATASET_2d = "./data/heat_distribution/2d.pkl" 16 | 17 | 18 | def same_component(v1, v2, N): 19 | return v1 < N / 2 and v2 < N / 2 or v1 > N / 2 and v2 > N / 2 20 | 21 | 22 | def get_noisy_signal(N, variance=0.1): 23 | signal = [] 24 | for i in range(N // 2): 25 | signal.append(np.random.normal(-1, variance)) 26 | 27 | signal.append(0) 28 | 29 | for i in range(N // 2): 30 | signal.append(np.random.normal(1, variance)) 31 | return np.array(signal) 32 | 33 | 34 | def generate_graph_n_comp(N, n_comp=3): 35 | raise NotImplementedError 36 | 37 | 38 | def generate_graph(N, p): 39 | covariances = np.zeros((N, N)) 40 | G = nx.Graph() 41 | for v1 in range(0, N): 42 | G.add_node(v1) 43 | for v2 in range(0, N): 44 | if v1 == v2: 45 | covariances[v1, v2] = 1 46 | continue 47 | else: 48 | if same_component(v1, v2, N) and np.random.rand() < p or v1 == N // 2 or v2 == N // 2: 49 | G.add_edge(v1, v2) 50 | covariances[v1, v2] = p 51 | return G, get_noisy_signal(N), covariances 52 | 53 | 54 | def generate_ring_graph(N): 55 | graph = nx.Graph() 56 | graph.add_nodes_from(range(N)) 57 | graph.add_edges_from([(i, (i + 1) % N) for i in range(N)]) 58 | signal = [-1 + i * (2 / (N - 1)) for i in range(N)] 59 | return graph, np.array(signal) 60 | 61 | 62 | def generate_lattice(n): 63 | G = nx.Graph() 64 | for v1 in range(0, n - 1): 65 | G.add_node(v1) 66 | G.add_node(v1 + 1) 67 | G.add_edge(v1, v1 + 1) 68 | return G 69 | 70 | 71 | def generate_2d_lattice(n, m=None): 72 | if n is None: 73 | n = m 74 | return nx.generators.lattice.grid_2d_graph(m, n) 75 | 76 | 77 | def draw_2d_lattice(G, signal=None): 78 | pos = dict((n, n) for n in G.nodes()) 79 | labels = dict(((i, j), i * 10 + j) for i, j in G.nodes()) 80 | nx.draw_networkx(G, pos=pos, labels=labels, node_color=signal) 81 | 82 | 83 | def plot_nodes_with_colors(g, signal, title="2 component graph", layout=nx.spring_layout, ax=None): 84 | if layout is None: 85 | layout = nx.spring_layout 86 | 87 | nodes = g.nodes() 88 | assert len(nodes) == len(signal) 89 | 90 | # drawing nodes and edges separately so we can capture collection for colobar 91 | pos = layout(g) 92 | nx.draw_networkx_edges(g, pos, alpha=0.2) 93 | nc = nx.draw_networkx_nodes(g, pos, nodelist=nodes, node_color=signal, 94 | node_size=100, cmap=plt.cm.jet, ax=ax) 95 | plt.title(title) 96 | plt.colorbar(nc) 97 | plt.axis('off') 98 | 99 | 100 | def visualize_kernel_for_graph(gprocess, G, node=0, title=None): 101 | all_nodes = sorted(list(G.nodes())) 102 | covariance_train = gprocess.kernel.K(all_nodes) 103 | plot_nodes_with_colors( 104 | G, 105 | covariance_train[0], 106 | layout=nx.layout.circular_layout, 107 | title=title) 108 | 109 | 110 | def read_heat_1d(path=HEAT_DATASET_1d): 111 | return pickle.load(open(path, "rb")) 112 | 113 | 114 | def read_heat_2d(path=HEAT_DATASET_2d): 115 | return pickle.load(open(path, "rb")) 116 | 117 | 118 | def build_graph_from_1d_points(x_lin): 119 | G = nx.Graph() 120 | for i in range(x_lin.shape[0]): 121 | G.add_node(i, point=x_lin[i]) 122 | 123 | for i in range(1, x_lin.shape[0]): 124 | G.add_node(i, point=x_lin[i]) 125 | G.add_edge(i - 1, i) 126 | if i + 1 < x_lin.shape[0]: 127 | G.add_edge(i, i + 1) 128 | 129 | return G 130 | 131 | 132 | def build_graph_from_2d_points(X, Y): 133 | G = nx.Graph() 134 | for i in range(X.shape[0]): 135 | for j in range(X.shape[1]): 136 | G.add_node((i, j)) 137 | if i - 1 >= 0: 138 | G.add_edge((i - 1, j), (i, j)) 139 | if j - 1 >= 0: 140 | G.add_edge((i, j - 1), (i, j)) 141 | return G 142 | 143 | 144 | def generate_dataset(X, y, num_training_data, num_testing_data, start=0, log_target=False, rs=42, 145 | interpolation=False): 146 | start_test = start + num_training_data 147 | end_test = start_test + num_testing_data 148 | 149 | if interpolation: 150 | train_X, test_X, train_y, test_y = sklearn.model_selection.train_test_split( 151 | X[start:end_test], y[start:end_test], 152 | test_size=0.1, random_state=rs) 153 | train_y, test_y = train_y[:, np.newaxis], test_y[:, np.newaxis] 154 | else: 155 | train_X, train_y = X[start:start_test], y[start:start_test, np.newaxis] 156 | test_X, test_y = X[start_test:end_test], y[start_test:end_test, np.newaxis] 157 | 158 | if log_target: 159 | qt = FunctionTransformer(func=np.log1p, inverse_func=np.expm1) 160 | train_y = qt.fit_transform(train_y) 161 | test_y = qt.transform(test_y) 162 | else: 163 | qt = None 164 | 165 | return train_X, train_y, test_X, test_y, qt 166 | 167 | 168 | def load_hungary_graph(path_to_csv="../data/hungary_chicken_pox/hungary_county_edges.csv"): 169 | df = pd.read_csv(path_to_csv) 170 | g = nx.from_pandas_edgelist(df, source="name_1", target="name_2") 171 | return g 172 | 173 | 174 | def load_hungary_dataset(g, path_to_csv="../data/hungary_chicken_pox/hungary_chickenpox.csv"): 175 | df = pd.read_csv(path_to_csv) 176 | from_node_to_id = dict(zip(g.nodes(), range(len(g.nodes())))) 177 | X, y = [], [] 178 | for t, row_dict in enumerate(df.to_dict(orient="records")): 179 | for v in g.nodes(): 180 | X.append([from_node_to_id[v], t]) 181 | y.append(row_dict[v]) 182 | 183 | g = nx.relabel_nodes(g, from_node_to_id) 184 | return np.array(X), np.array(y), g, from_node_to_id 185 | 186 | 187 | def generate_new_chickenpox_dataset(start=0): 188 | g = load_hungary_graph() 189 | X, y, g, node_ids = load_hungary_dataset(g) 190 | new_dataset = {} 191 | new_dataset["edges"] = list(g.edges()) 192 | # new_dataset["node_ids"] = list(g.edges()) 193 | new_dataset["FX"] = y[start * len(g.nodes()):].reshape((-1, len(g.nodes()))).tolist() 194 | return new_dataset 195 | 196 | 197 | def generate_new_covid19_dataset(start=0): 198 | DATA_FOLDER = "../data/covid_data/" 199 | GRAPH_PATH = os.path.join(DATA_FOLDER, "g.pkl") 200 | 201 | g = pickle.load(open(GRAPH_PATH, "rb")) 202 | g = nx.relabel.convert_node_labels_to_integers(g) 203 | X_PATH = os.path.join(DATA_FOLDER, "X.pkl") 204 | Y_CASES_PATH = os.path.join(DATA_FOLDER, "y_cases.pkl") 205 | X = pickle.load(open(X_PATH, "rb")) 206 | y_cases = pickle.load(open(Y_CASES_PATH, "rb")) 207 | y_cases[y_cases < 0] = 0 208 | 209 | new_dataset = {} 210 | new_dataset["edges"] = list(g.edges()) 211 | y_cases_reordered = [] 212 | for i in range(start * len(g.nodes()), y_cases.shape[0], len(g.nodes())): 213 | cur = y_cases[i:i + len(g.nodes())] 214 | new_row = np.zeros(len(g.nodes())) 215 | for j, x in enumerate(X[i:i + len(g.nodes())]): 216 | new_row[int(x[0])] = cur[j] 217 | y_cases_reordered.append(new_row) 218 | y_cases_reordered = np.array(y_cases_reordered) 219 | new_dataset["FX"] = y_cases_reordered.tolist() 220 | return new_dataset 221 | -------------------------------------------------------------------------------- /graph_kernels/kernels.py: -------------------------------------------------------------------------------- 1 | import gpflow 2 | from gpflow import Parameter 3 | import tensorflow as tf 4 | 5 | import scipy.linalg 6 | import numpy as np 7 | 8 | from . import utils 9 | 10 | 11 | def get_matern_kernel(L, nu, kappa): 12 | N = L.shape[0] 13 | alpha = nu 14 | Id = np.eye(N) 15 | A = ((2 * nu / kappa**2) * Id + L) 16 | A = scipy.linalg.fractional_matrix_power(A, alpha / 2) 17 | A = tf.cast(A, dtype=tf.float64) 18 | kern = tf.matmul(A, A, adjoint_a=True) 19 | kern = tf.linalg.pinv(kern) 20 | return kern 21 | 22 | 23 | class LaplacianKernel(gpflow.kernels.base.Kernel): 24 | def __init__(self, sparse_adj_mat, variance=1.0, normalized_laplacian=True): 25 | super().__init__() 26 | self.variance = Parameter(variance, transform=gpflow.utilities.positive(), name="variance") 27 | self.sparse_adj_mat = sparse_adj_mat 28 | self.laplacian = utils.get_laplacian(sparse_adj_mat, normalized_laplacian) 29 | self.cov = tf.matmul(self.laplacian, self.laplacian, adjoint_a=True) 30 | self.cov = tf.linalg.pinv(self.cov) 31 | 32 | def K(self, X, Y=None, presliced=False): 33 | X = tf.reshape(tf.cast(X, tf.int32), [-1]) 34 | X2 = tf.reshape(tf.cast(Y, tf.int32), [-1]) if Y is not None else X 35 | 36 | cov = self.variance * self.cov 37 | cov = tf.gather(tf.gather(cov, X, axis=0), X2, axis=1) 38 | return cov 39 | 40 | def K_diag(self, X, presliced=False): 41 | return tf.linalg.diag_part(self.K(X, presliced=presliced)) 42 | 43 | 44 | class DiffusionKernel(gpflow.kernels.base.Kernel): 45 | def __init__(self, sparse_adj_mat, variance=1.0, beta=0.1, normalized_laplacian=True): 46 | super().__init__() 47 | self.variance = Parameter(variance, transform=gpflow.utilities.positive(), name="variance") 48 | self.beta = beta 49 | 50 | self.sparse_adj_mat = sparse_adj_mat 51 | self.laplacian = utils.get_laplacian(sparse_adj_mat, normalized_laplacian) 52 | self.cov = tf.linalg.expm(-self.beta * self.laplacian) 53 | 54 | def K(self, X, Y=None, presliced=False): 55 | X = tf.reshape(tf.cast(X, tf.int32), [-1]) 56 | X2 = tf.reshape(tf.cast(Y, tf.int32), [-1]) if Y is not None else X 57 | 58 | cov = self.variance * self.cov 59 | cov = tf.gather(tf.gather(cov, X, axis=0), X2, axis=1) 60 | 61 | return cov 62 | 63 | def K_diag(self, X, presliced=False): 64 | return tf.linalg.diag_part(self.K(X, presliced=presliced)) 65 | 66 | 67 | class RandomWalkKernel(gpflow.kernels.base.Kernel): 68 | def __init__(self, sparse_adj_mat, variance=1.0): 69 | super().__init__() 70 | self.variance = Parameter(variance, transform=gpflow.utilities.positive(), name="variance") 71 | sparse_adj_mat[np.diag_indices(sparse_adj_mat.shape[0])] = 1.0 72 | self.sparse_P = utils.sparse_mat_to_sparse_tensor(sparse_adj_mat) 73 | self.sparse_P = self.sparse_P / sparse_adj_mat.sum(axis=1) 74 | self.cov = tf.sparse.sparse_dense_matmul(self.sparse_P, tf.sparse.to_dense(self.sparse_P), adjoint_b=True) 75 | 76 | def K(self, X, Y=None, presliced=False): 77 | X = tf.reshape(tf.cast(X, tf.int32), [-1]) 78 | X2 = tf.reshape(tf.cast(Y, tf.int32), [-1]) if Y is not None else X 79 | cov = self.variance * self.cov 80 | cov = tf.gather(tf.gather(cov, X, axis=0), X2, axis=1) 81 | return cov 82 | 83 | def K_diag(self, X, presliced=False): 84 | return tf.linalg.diag_part(self.K(X, presliced=presliced)) 85 | 86 | 87 | class MaternKernel(gpflow.kernels.base.Kernel): 88 | def __init__(self, sparse_adj_mat, nu, kappa, variance=1.0, normalized_laplacian=True): 89 | super().__init__() 90 | self.variance = Parameter(variance, transform=gpflow.utilities.positive(), name="variance") 91 | self.nu = nu 92 | self.kappa = kappa 93 | 94 | self.normalized_laplacian = normalized_laplacian 95 | self.laplacian = utils.get_laplacian(sparse_adj_mat=sparse_adj_mat, normalized_laplacian=normalized_laplacian) 96 | 97 | self.matern_kernel = get_matern_kernel(self.laplacian, self.nu, self.kappa) 98 | 99 | def K(self, X, Y=None, presliced=False): 100 | X = tf.reshape(tf.cast(X, tf.int32), [-1]) 101 | X2 = tf.reshape(tf.cast(Y, tf.int32), [-1]) if Y is not None else X 102 | 103 | cov = self.variance * self.matern_kernel 104 | cov = tf.gather(tf.gather(cov, X, axis=0), X2, axis=1) 105 | return cov 106 | 107 | def K_diag(self, X, presliced=False): 108 | return tf.linalg.diag_part(self.K(X, presliced=presliced)) 109 | 110 | 111 | class WaveKernel(gpflow.kernels.base.Kernel): 112 | def __init__(self, sparse_adj_mat, variance=1.0, beta=0.1, c1=1, c2=1): 113 | super().__init__() 114 | self.variance = Parameter(variance, transform=gpflow.utilities.positive(), 115 | name="variance") 116 | self.c1 = Parameter(c1, transform=gpflow.utilities.positive(), 117 | name="c1") 118 | self.c2 = Parameter(c2, transform=gpflow.utilities.positive(), 119 | name="c2") 120 | 121 | self.beta = beta 122 | 123 | self.laplacian = utils.get_normalized_laplacian(sparse_adj_mat) 124 | self.sqrt_lapl = tf.constant(scipy.linalg.sqrtm(self.laplacian.numpy()), dtype=tf.float64) 125 | 126 | self.sqrt_inv_lapl = tf.constant( 127 | np.linalg.pinv(self.sqrt_lapl), dtype=tf.float64) 128 | self.sin = self.sqrt_inv_lapl @ scipy.linalg.sinm(self.sqrt_lapl * self.beta) 129 | self.cov = None 130 | 131 | def K(self, X, Y=None, presliced=False): 132 | X = tf.reshape(tf.cast(X, tf.int32), [-1]) 133 | X2 = tf.reshape(tf.cast(Y, tf.int32), [-1]) if Y is not None else X 134 | self.sin = self.sqrt_inv_lapl @ scipy.linalg.sinm(self.sqrt_lapl * self.c1) 135 | self.cov = self.variance * self.sin 136 | self.cov = tf.gather(tf.gather(self.cov, X, axis=0), X2, axis=1) 137 | return self.cov 138 | 139 | def K_diag(self, X, presliced=False): 140 | return tf.linalg.diag_part(self.K(X, presliced=presliced)) 141 | -------------------------------------------------------------------------------- /graph_kernels/time_kernels.py: -------------------------------------------------------------------------------- 1 | import gpflow 2 | from gpflow import Parameter 3 | import tensorflow as tf 4 | 5 | import scipy 6 | from scipy import sparse 7 | 8 | import networkx as nx 9 | 10 | from . import utils 11 | from . import kernels 12 | 13 | 14 | def get_adj_matrix(graph): 15 | element = list(graph.nodes())[0] 16 | if nx.is_weighted(graph): 17 | return sparse.csr_matrix(nx.linalg.attrmatrix.attr_matrix(graph, "weight", rc_order=graph.nodes())) 18 | else: 19 | if isinstance(element, int): 20 | return nx.adjacency_matrix(graph, nodelist=range(len(graph.nodes()))) 21 | else: 22 | return nx.adjacency_matrix(graph, nodelist=graph.nodes()) 23 | 24 | 25 | class TimeDistributed1dExponentialKernel(gpflow.kernels.base.Kernel): 26 | def __init__(self, graph, variance=1.0): 27 | super().__init__() 28 | self.variance = Parameter(variance, transform=gpflow.utilities.positive(), name="variance") 29 | self.graph = graph 30 | self.time_kernel = gpflow.kernels.Exponential() 31 | self.graph_kernel = gpflow.kernels.Exponential() 32 | gpflow.set_trainable(self.graph_kernel.variance, False) 33 | gpflow.set_trainable(self.time_kernel.variance, False) 34 | 35 | def K(self, X, Y=None, presliced=False): 36 | t = tf.reshape(tf.cast(X[:, -1], tf.float64), [X.shape[0], 1]) 37 | X = tf.cast(X[:, :-1], tf.float64) 38 | 39 | if Y is not None: 40 | t2 = tf.reshape(tf.cast(Y[:, -1], tf.float64), [Y.shape[0], 1]) 41 | X2 = tf.cast(Y[:, :-1], tf.float64) 42 | else: 43 | t2 = t 44 | X2 = X 45 | 46 | cov = self.variance * self.time_kernel(t, t2) * self.graph_kernel(X, X2) 47 | return cov 48 | 49 | def K_diag(self, X, presliced=False): 50 | return tf.linalg.diag_part(self.K(X, presliced=presliced)) 51 | 52 | 53 | class TimeDistributedGraphKernel(gpflow.kernels.base.Kernel): 54 | def __init__(self, graph, graph_kernel, variance=1.0, time_kernel_class=None): 55 | super().__init__() 56 | self.variance = Parameter(variance, transform=gpflow.utilities.positive(), name="variance") 57 | self.graph = graph 58 | self.time_kernel = time_kernel_class() if time_kernel_class is not None else gpflow.kernels.RBF() 59 | self.graph_kernel = graph_kernel 60 | gpflow.set_trainable(self.graph_kernel.variance, False) 61 | gpflow.set_trainable(self.time_kernel.variance, False) 62 | 63 | # Input: (node_id, time) 64 | def K(self, X, Y=None, presliced=False): 65 | t = tf.reshape(tf.cast(X[:, -1], tf.float64), [X.shape[0], 1]) 66 | X = tf.cast(X[:, :-1], tf.float64) 67 | 68 | if Y is not None: 69 | t2 = tf.reshape(tf.cast(Y[:, -1], tf.float64), [Y.shape[0], 1]) 70 | X2 = tf.cast(Y[:, :-1], tf.float64) 71 | else: 72 | t2 = t 73 | X2 = X 74 | 75 | cov = self.variance * self.time_kernel(t, t2) * self.graph_kernel(X, X2) 76 | return cov 77 | 78 | def K_diag(self, X, presliced=False): 79 | return tf.linalg.diag_part(self.K(X, presliced=presliced)) 80 | 81 | 82 | class TimeDistributedLaplacianKernel(TimeDistributedGraphKernel): 83 | def __init__(self, graph, variance=1.0, time_kernel_class=None, normalized_laplacian=True): 84 | sparse_adj_matrix = get_adj_matrix(graph) 85 | graph_kernel = kernels.LaplacianKernel(sparse_adj_matrix, normalized_laplacian=normalized_laplacian) 86 | super().__init__(graph, graph_kernel, variance, time_kernel_class) 87 | 88 | 89 | class TimeDistributedMaternKernel(TimeDistributedGraphKernel): 90 | def __init__(self, graph, nu, kappa, variance=1.0, normalized_laplacian=True, time_kernel_class=None): 91 | sparse_adj_matrix = get_adj_matrix(graph) 92 | graph_kernel = kernels.MaternKernel( 93 | sparse_adj_matrix, 94 | nu, kappa, normalized_laplacian=normalized_laplacian) 95 | super().__init__(graph, graph_kernel, variance, time_kernel_class) 96 | 97 | 98 | class TimeDistributedDiffusionKernel(TimeDistributedGraphKernel): 99 | def __init__(self, graph, variance=1.0, normalized_laplacian=True, time_kernel_class=None): 100 | sparse_adj_matrix = get_adj_matrix(graph) 101 | graph_kernel = kernels.DiffusionKernel( 102 | sparse_adj_matrix, normalized_laplacian=normalized_laplacian) 103 | super().__init__(graph, graph_kernel, variance, time_kernel_class) 104 | 105 | 106 | class TimeDistributedRandomWalkKernel(TimeDistributedGraphKernel): 107 | def __init__(self, graph, variance=1.0, time_kernel_class=None): 108 | sparse_adj_matrix = get_adj_matrix(graph) 109 | graph_kernel = kernels.RandomWalkKernel(sparse_adj_matrix) 110 | super().__init__(graph, graph_kernel, variance, time_kernel_class) 111 | 112 | 113 | def get_inds(t_indices, t2_indices, X, X2): 114 | # returns [(t1, t2, x1, x2)] 115 | left = tf.concat([t_indices, tf.cast(X, dtype=tf.int64)], axis=-1) 116 | right = tf.concat([t2_indices, tf.cast(X2, dtype=tf.int64)], axis=-1) 117 | inds = utils.cartesian_product(left, right) 118 | inds = tf.gather(inds, [0, 2, 1, 3], axis=2) 119 | return inds 120 | 121 | 122 | def get_exponents_tf(vals, Gamma): 123 | return tf.linalg.expm(tf.tensordot(vals, -Gamma, axes=0)) 124 | 125 | 126 | def get_exponents(vals, Gamma): 127 | unique_vals = tf.sort(tf.unique(tf.reshape(vals, [-1]))[0]) 128 | int_dist = tf.reshape( 129 | tf.where( 130 | tf.equal(tf.reshape(vals, [-1])[:, tf.newaxis], unique_vals[tf.newaxis, :]))[:, 1], vals.shape) 131 | unique_vals = tf.constant(unique_vals, dtype=tf.float64) 132 | return tf.gather(tf.linalg.expm(tf.tensordot(unique_vals, -Gamma, axes=0)), int_dist) 133 | 134 | 135 | def get_exponents_scalar_tf(vals, lambdas): 136 | return tf.math.exp(tf.tensordot(-lambdas, vals, axes=0)) 137 | 138 | 139 | def get_exponents_scalar(vals, lambdas): 140 | unique_vals = tf.sort(tf.unique(tf.reshape(vals, [-1]))[0]) 141 | int_dist = tf.reshape( 142 | tf.where( 143 | tf.equal(tf.reshape(vals, [-1])[:, tf.newaxis], unique_vals[tf.newaxis, :]))[:, 1], vals.shape) 144 | unique_vals = tf.constant(unique_vals, dtype=tf.float64) 145 | return tf.gather(tf.math.exp(tf.tensordot(-lambdas, unique_vals, axes=0)), int_dist, axis=1) 146 | 147 | 148 | # calculating exp(-lambda (t + s)) 149 | def get_sums_exps(unique_t, unique_t2, lambdas): 150 | # we use only diagonal elements because consider diagonal matrix \Sigma 151 | unique_t, unique_t2 = tf.squeeze(unique_t), tf.squeeze(unique_t2) 152 | time_pairwise_sums = unique_t[:, None] + unique_t2[None, :] 153 | time_pairwise_sums = tf.tensordot(-lambdas, time_pairwise_sums, axes=0) 154 | return tf.math.exp(time_pairwise_sums) 155 | 156 | 157 | # calculating a solution for stochastic heat equation 158 | # for diagonal variance 159 | def get_covariance_solution(dists_exps, sums_exps, variance, u, gamma_s): 160 | mult = tf.math.pow(tf.linalg.diag(variance), 2) 161 | pair_sums = utils.replace_small_values(gamma_s[None, :] + gamma_s[:, None], 1e-7) 162 | G = tf.linalg.diag_part(tf.math.divide(mult, pair_sums))[:, tf.newaxis, tf.newaxis, ] *\ 163 | (dists_exps - sums_exps) 164 | G = tf.linalg.diag(tf.transpose(G, [1, 2, 0])) 165 | return u @ G @ tf.transpose(u) 166 | 167 | 168 | def get_covariance_solution_fixed(t, s, u, variance, lambdas): 169 | sigma = tf.linalg.diag(variance) 170 | mult = tf.transpose(u) @ sigma @ tf.transpose(sigma) @ u 171 | pair_sums = lambdas[None, :] + lambdas[:, None] 172 | mult = tf.math.divide(mult, pair_sums) 173 | 174 | lt = lambdas[:, None] @ t[None, :] 175 | ls = lambdas[:, None] @ s[None, :] 176 | pairwise_sums = lt[:, :, None, None] + ls[None, None, :, :] 177 | pairwise_sums = tf.transpose(pairwise_sums, [0, 2, 1, 3]) 178 | 179 | mins = tf.math.minimum(t[:, None], s[None, :]) 180 | left = tf.math.exp(pair_sums[:, :, None, None] * mins[None, None, :, :] - pairwise_sums) 181 | 182 | right = tf.math.exp(-pairwise_sums) 183 | G = mult[:, :, None, None] * (left - right) 184 | G = tf.transpose(G, [2, 3, 0, 1]) 185 | return u @ G @ tf.transpose(u) 186 | 187 | 188 | class StochasticHeatEquation(gpflow.kernels.base.Kernel): 189 | def __init__(self, graph, variance=1.0, c=1, normalized_laplacian=True, 190 | use_pseudodifferential=False, nu=None, kappa=None): 191 | super().__init__() 192 | self.variance = Parameter(variance, transform=gpflow.utilities.positive(1e-4), name="variance") 193 | self.c = Parameter(c, transform=gpflow.utilities.positive(1e-4), name="diffusion") 194 | self.graph = graph 195 | if nx.is_weighted(graph): 196 | self.laplacian = utils.get_laplacian( 197 | sparse.csr_matrix(nx.linalg.attrmatrix.attr_matrix(graph, "weight", rc_order=graph.nodes())), 198 | normalized_laplacian) 199 | else: 200 | self.laplacian = utils.get_laplacian(nx.adjacency_matrix(graph), normalized_laplacian) 201 | 202 | self.use_pseudodifferential = use_pseudodifferential 203 | if use_pseudodifferential: 204 | self.nu = nu 205 | self.kappa = kappa 206 | else: 207 | self.nu = None 208 | self.kappa = None 209 | 210 | # laplacian = self.u @ tf.linalg.diag(self.laplacian_s) @ tf.transpose(self.v) 211 | self.laplacian_s, self.u, self.v = tf.linalg.svd(self.laplacian) 212 | 213 | def get_scaled_differential_s(self): 214 | if self.use_pseudodifferential: 215 | return self.c * ((2 * self.nu) / (self.kappa ** 2) + self.laplacian_s) ** (self.nu / 2) 216 | else: 217 | return self.c * self.laplacian_s 218 | 219 | def get_scaled_differential(self): 220 | if self.use_pseudodifferential: 221 | return self.u @ tf.linalg.diag(self.get_scaled_differential_s()) @ tf.transpose(self.u) 222 | else: 223 | return self.c * self.laplacian 224 | 225 | # Input: (node_id, time) 226 | def K(self, X, Y=None, presliced=False): 227 | t = tf.reshape(tf.cast(X[:, -1], tf.float64), [X.shape[0]]) 228 | X = tf.cast(X[:, :-1], tf.float64) 229 | if Y is not None: 230 | t2 = tf.reshape(tf.cast(Y[:, -1], tf.float64), [Y.shape[0]]) 231 | X2 = tf.cast(Y[:, :-1], tf.float64) 232 | else: 233 | t2 = t 234 | X2 = X 235 | 236 | unique_t = tf.sort(tf.unique(t)[0])[:, tf.newaxis] 237 | unique_t2 = tf.sort(tf.unique(t2)[0])[:, tf.newaxis] 238 | 239 | self.time_pairwise_distances = tf.abs(unique_t - tf.transpose(unique_t2)) 240 | self.time_pairwise_sums = (unique_t + tf.transpose(unique_t2)) 241 | Gamma = self.get_scaled_differential() 242 | 243 | gamma_s = self.get_scaled_differential_s() 244 | if len(self.variance.shape) > 0: 245 | cov = get_covariance_solution_fixed( 246 | tf.squeeze(unique_t), tf.squeeze(unique_t2), self.u, self.variance, gamma_s) 247 | else: 248 | left_part = get_exponents(self.time_pairwise_distances, Gamma) 249 | right_part = get_exponents(self.time_pairwise_sums, Gamma) 250 | cov = self.variance * (left_part - right_part) @ tf.linalg.pinv(Gamma) 251 | t_indices = tf.where(tf.transpose(tf.equal(t, unique_t)))[:, 1] 252 | t2_indices = tf.where(tf.transpose(tf.equal(t2, unique_t2)))[:, 1] 253 | 254 | t_indices = tf.expand_dims(t_indices, 1) 255 | t2_indices = tf.expand_dims(t2_indices, 1) 256 | 257 | inds = get_inds(t_indices, t2_indices, X, X2) 258 | cov = tf.gather_nd(cov, inds) 259 | return cov 260 | 261 | def K_diag(self, X, presliced=False): 262 | return tf.linalg.diag_part(self.K(X, presliced=presliced)) 263 | 264 | 265 | def get_cosines(vals, Gamma): 266 | unique_vals = tf.sort(tf.unique(tf.reshape(vals, [-1]))[0]) 267 | int_dist = tf.reshape( 268 | tf.where( 269 | tf.equal(tf.reshape(vals, [-1])[:, tf.newaxis], unique_vals[tf.newaxis, :]))[:, 1], vals.shape) 270 | result = utils.tf_cosm(tf.tensordot(unique_vals, Gamma, axes=0)) 271 | return tf.gather(result, int_dist) 272 | 273 | 274 | def get_sines(vals, Gamma): 275 | unique_vals = tf.sort(tf.unique(tf.reshape(vals, [-1]))[0]) 276 | int_dist = tf.reshape( 277 | tf.where( 278 | tf.equal(tf.reshape(vals, [-1])[:, tf.newaxis], unique_vals[tf.newaxis, :]))[:, 1], vals.shape) 279 | result = utils.tf_sinm(tf.tensordot(unique_vals, Gamma, axes=0)) 280 | return tf.gather(result, int_dist) 281 | 282 | 283 | def get_cosines_tf(vals, Gamma): 284 | return utils.tf_cosm(tf.tensordot(vals, Gamma, axes=0)) 285 | 286 | 287 | def get_sines_tf(vals, Gamma): 288 | return utils.tf_sinm(tf.tensordot(vals, Gamma, axes=0)) 289 | 290 | 291 | class StochasticWaveEquationKernel(gpflow.kernels.base.Kernel): 292 | def __init__(self, graph, variance=1.0, c=1., normalized_laplacian=True, use_pseudodifferential=False, 293 | nu=None, kappa=None): 294 | super().__init__() 295 | self.variance = Parameter(variance, transform=gpflow.utilities.positive(), name="variance") 296 | self.c = Parameter(c, transform=gpflow.utilities.positive(1e-2), name="propagation speed") 297 | self.graph = graph 298 | self.laplacian = utils.get_laplacian(nx.adjacency_matrix(graph), normalized_laplacian) 299 | if use_pseudodifferential: 300 | self.nu = nu 301 | self.kappa = kappa 302 | self.laplacian_s, self.u, self.v = tf.linalg.svd(self.laplacian) 303 | else: 304 | self.nu = None 305 | self.kappa = None 306 | self.id_l = tf.eye(self.laplacian.shape[0], dtype=tf.float64) 307 | 308 | # Input: (node_id, time) 309 | def K(self, X, Y=None, presliced=False): 310 | s = ((2 * self.nu) / (self.kappa ** 2) + self.laplacian_s) ** (self.nu / 2) 311 | self.laplacian = self.u @ tf.linalg.diag(s) @ tf.transpose(self.u) 312 | s = ((2 * self.nu) / (self.kappa ** 2) + self.laplacian_s) ** (self.nu / 4) 313 | self.sqrt_lapl = self.u @ tf.linalg.diag(s) @ tf.transpose(self.u) 314 | self.laplacian_inv = tf.linalg.pinv(self.laplacian) 315 | 316 | t = tf.reshape(tf.cast(X[:, -1], tf.float64), [X.shape[0]]) 317 | X = tf.cast(X[:, :-1], tf.float64) 318 | if Y is not None: 319 | t2 = tf.reshape(tf.cast(Y[:, -1], tf.float64), [Y.shape[0]]) 320 | X2 = tf.cast(Y[:, :-1], tf.float64) 321 | else: 322 | t2 = t 323 | X2 = X 324 | unique_t = tf.sort(tf.unique(t)[0])[:, tf.newaxis] 325 | unique_t2 = tf.sort(tf.unique(t2)[0])[:, tf.newaxis] 326 | time_pairwise_distances = tf.abs(unique_t - tf.transpose(unique_t2)) 327 | 328 | theta = self.c * self.sqrt_lapl 329 | # Gamma = (self.c**2) * self.laplacian 330 | mins = tf.math.minimum(unique_t, tf.transpose(unique_t2)) 331 | maxs = tf.math.maximum(unique_t, tf.transpose(unique_t2)) 332 | # gamma_inv = tf.linalg.pinv(Gamma) 333 | gamma_inv = (1 / self.c**2) * self.laplacian_inv 334 | if len(self.variance.shape) > 0: 335 | raise Exception("Not implemented for matrix variance") 336 | else: 337 | gamma_inv = self.variance * gamma_inv 338 | cov = gamma_inv @ get_cosines(time_pairwise_distances, theta) 339 | cov = tf.tensordot(mins, self.id_l, axes=0) @ cov - 0.5 *\ 340 | gamma_inv @ get_cosines(maxs, theta) @ get_sines(mins, theta) @ tf.linalg.inv(theta) 341 | 342 | t_indices = tf.where(tf.transpose(tf.equal(t, unique_t)))[:, 1] 343 | t2_indices = tf.where(tf.transpose(tf.equal(t2, unique_t2)))[:, 1] 344 | 345 | t_indices = tf.expand_dims(t_indices, 1) 346 | t2_indices = tf.expand_dims(t2_indices, 1) 347 | 348 | inds = get_inds(t_indices, t2_indices, X, X2) 349 | cov = tf.gather_nd(cov, inds) 350 | return cov 351 | 352 | def K_diag(self, X, presliced=False): 353 | return tf.linalg.diag_part(self.K(X, presliced=presliced)) 354 | -------------------------------------------------------------------------------- /graph_kernels/utils.py: -------------------------------------------------------------------------------- 1 | import os 2 | import json 3 | import random 4 | import pickle 5 | import networkx as nx 6 | import tensorflow as tf 7 | import numpy as np 8 | 9 | from matplotlib import pyplot as plt 10 | import seaborn as sns 11 | 12 | import sklearn.metrics 13 | from sklearn.utils import shuffle 14 | from sklearn.decomposition import PCA 15 | from sklearn.manifold import TSNE 16 | 17 | import gpflow 18 | from gpflow import Parameter 19 | 20 | from . import data_utils 21 | 22 | 23 | def sparse_mat_to_sparse_tensor(sparse_mat): 24 | """ 25 | Converts a scipy csr_matrix to a tensorflow SparseTensor. 26 | """ 27 | coo = sparse_mat.tocoo() 28 | indices = np.stack([coo.row, coo.col], axis=-1) 29 | tensor = tf.sparse.SparseTensor(indices, sparse_mat.data, sparse_mat.shape) 30 | return tensor 31 | 32 | 33 | def normalize_laplacian(laplacian, d): 34 | inv_d = tf.linalg.diag([1. / float(el) if el != 0 else 0 for el in tf.linalg.diag_part(d)]) 35 | inv_d = tf.cast(inv_d, dtype=tf.float64) 36 | inv_sqrt_d = tf.pow(inv_d, 0.5) 37 | laplacian_normalized = tf.linalg.matmul(inv_sqrt_d, laplacian) 38 | laplacian_normalized = tf.linalg.matmul(laplacian_normalized, inv_sqrt_d) 39 | return laplacian_normalized 40 | 41 | 42 | def get_non_normalized_laplacian(sparse_adj_mat): 43 | sparse_adj_mat = sparse_mat_to_sparse_tensor(sparse_adj_mat) 44 | sparse_adj_mat = tf.cast(sparse_adj_mat, tf.float64) 45 | 46 | d_dense = tf.sparse.to_dense(tf.sparse.SparseTensor( 47 | indices=list(zip(*np.diag_indices(sparse_adj_mat.shape[0]))), 48 | values=tf.math.reduce_sum(tf.sparse.to_dense(sparse_adj_mat), axis=1), 49 | dense_shape=sparse_adj_mat.shape, 50 | )) 51 | laplacian_sparse = tf.math.subtract( 52 | d_dense, tf.sparse.to_dense(sparse_adj_mat)) 53 | 54 | return laplacian_sparse, d_dense 55 | 56 | 57 | def get_normalized_laplacian(sparse_adj_mat): 58 | laplacian_sparse, d_dense = get_non_normalized_laplacian(sparse_adj_mat) 59 | return normalize_laplacian(laplacian_sparse, d_dense) 60 | 61 | 62 | def get_normalized_laplacian_from_graph(graph): 63 | return get_normalized_laplacian( 64 | nx.adjacency_matrix(graph, nodelist=range(len(graph.nodes()))) 65 | ) 66 | 67 | 68 | def get_non_normalized_laplacian_from_graph(graph): 69 | return get_non_normalized_laplacian( 70 | nx.adjacency_matrix(graph, nodelist=range(len(graph.nodes()))) 71 | )[0] 72 | 73 | 74 | def get_laplacian(sparse_adj_mat, normalized_laplacian): 75 | if normalized_laplacian: 76 | return get_normalized_laplacian(sparse_adj_mat) 77 | else: 78 | return get_non_normalized_laplacian(sparse_adj_mat)[0] 79 | 80 | 81 | def get_dataset_ids_from_graph(G, tr_ratio, random_seed=42): 82 | N = len(G.nodes()) 83 | ids = np.array(list(range(N))) 84 | ids = shuffle(ids, random_state=random_seed) 85 | tr_id = int(N * tr_ratio) 86 | A = nx.to_scipy_sparse_matrix(G) 87 | idx_train, idx_test = ids[:tr_id, np.newaxis], ids[tr_id:, np.newaxis] 88 | return A, idx_train, idx_test 89 | 90 | 91 | def evaluate_mse(X_val, y_val, gprocess): 92 | pred_y, pred_y_var = gprocess.predict_y(X_val) 93 | return sklearn.metrics.mean_squared_error(pred_y, y_val) 94 | 95 | 96 | def evaluate_mape_predictions(pred_y, y_val, transformer=None): 97 | if transformer is not None: 98 | pred_y = transformer.inverse_transform(pred_y) 99 | y_val = transformer.inverse_transform(y_val) 100 | return sklearn.metrics.mean_absolute_percentage_error(y_val, pred_y) 101 | 102 | 103 | def evaluate_mape(X_val, y_val, gprocess, transformer=None): 104 | pred_y, pred_y_var = gprocess.predict_y(X_val) 105 | return evaluate_mape_predictions(pred_y, y_val, transformer) 106 | 107 | 108 | def evaluate_mae_predictions(pred_y, y_val, transformer=None): 109 | if transformer is not None: 110 | pred_y = transformer.inverse_transform(pred_y) 111 | y_val = transformer.inverse_transform(y_val) 112 | return sklearn.metrics.mean_absolute_error(y_val, pred_y) 113 | 114 | 115 | def evaluate_mae(X_val, y_val, gprocess, transformer=None): 116 | pred_y, pred_y_var = gprocess.predict_y(X_val) 117 | return evaluate_mae_predictions(pred_y, y_val, transformer) 118 | 119 | 120 | def smape(y_pred, y_true): 121 | return 100 / len(y_pred) * np.sum(2 * np.abs(y_true - y_pred) / (np.abs(y_pred) + np.abs(y_true))) 122 | 123 | 124 | def plot(m, X_train, signal): 125 | xmin, xmax = 0.0, 30 126 | xx = np.linspace(xmin, xmax, 100)[:, None] 127 | mean, var = m.predict_y(xx) 128 | var = np.array([max(float(var[i]), 1e-3) for i in range(var.shape[0])])[:, np.newaxis] 129 | plt.figure(figsize=(12, 6)) 130 | plt.plot(X_train, signal[[int(el) for el in X_train[:, 0]]], 'kx', mew=2) 131 | plt.plot(xx, mean, 'b', lw=2) 132 | plt.fill_between(xx[:, 0], mean[:, 0] - 2 * np.sqrt(var[:, 0]), mean[:, 0] + 2 * np.sqrt(var[:, 0]), color='blue', alpha=0.2) 133 | plt.xlim(xmin, xmax) 134 | plt.title("Adjacency matrix covariance function") 135 | 136 | 137 | def visualize_gprocess(gprocess, X_train, X_test, G, signal, layout=None): 138 | X_all = tf.concat((X_train, X_test), axis=0) 139 | y_pred, var = gprocess.predict_y(X_all) 140 | 141 | y_pred_unshuffle = [0] * len(G.nodes()) 142 | for i, y in zip(X_all, y_pred): 143 | y_pred_unshuffle[int(i)] = float(y) 144 | data_utils.plot_nodes_with_colors(G, y_pred_unshuffle, layout=layout) 145 | plot(gprocess, X_train, signal) 146 | 147 | 148 | def training_step(X_train, y_train, optimizer, gprocess, natgrad=None): 149 | loss_fn = gprocess.training_loss_closure((X_train, y_train), compile=False) 150 | optimizer.minimize(loss_fn, var_list=gprocess.trainable_variables) 151 | if natgrad is not None: 152 | natgrad.minimize(loss_fn, var_list=[(gprocess.q_mu, gprocess.q_sqrt)]) 153 | 154 | return -gprocess.elbo((X_train, y_train)) 155 | 156 | 157 | def cartesian_product(a, b): 158 | a_ = tf.reshape(tf.tile(a, [1, b.shape[0]]), (a.shape[0] * b.shape[0], a.shape[1])) 159 | b_ = tf.tile(b, [a.shape[0], 1]) 160 | 161 | return tf.reshape(tf.concat([a_, b_], 1), [a.shape[0], b.shape[0], 4]) 162 | 163 | 164 | def is_pos_semi_def(x): 165 | return np.all(np.array(np.linalg.eigvals(x), dtype=np.float64) >= -1e-7) 166 | 167 | 168 | def save_model_to_hyperparameters(model, save_path="gprocess_hyperparams.pkl"): 169 | pickle.dump(gpflow.utilities.parameter_dict(model), open(save_path, "wb")) 170 | 171 | 172 | # loaded_result = loaded_model.predict_f_compiled(samples_input) 173 | def load_model(model, path): 174 | params = pickle.load(open(path, "rb")) 175 | gpflow.utilities.multiple_assign(model, params) 176 | return model 177 | 178 | 179 | def set_all_random_seeds(random_seed): 180 | tf.compat.v1.reset_default_graph() 181 | tf.keras.backend.clear_session() 182 | 183 | tf.random.set_seed(random_seed) 184 | random.seed(random_seed) 185 | np.random.seed(random_seed) 186 | 187 | 188 | class ConstantArray(gpflow.mean_functions.MeanFunction): 189 | def __init__(self, shape): 190 | super().__init__() 191 | c = tf.zeros(shape) 192 | self.c = Parameter(c, name="constant array mean") 193 | 194 | def __call__(self, X): 195 | return tf.reshape(tf.gather(self.c, tf.cast(X[:, 0], dtype=tf.int32)), (X.shape[0], 1)) 196 | 197 | 198 | def tf_cosm(A): 199 | return tf.math.real(tf.linalg.expm(1j * tf.cast(A, dtype=tf.complex128))) 200 | 201 | 202 | def tf_sinm(matrix): 203 | if matrix.dtype.is_complex: 204 | j_matrix = 1j * matrix 205 | return -0.5j * (tf.linalg.expm(j_matrix) - tf.linalg.expm(-j_matrix)) 206 | else: 207 | j_matrix = tf.complex(tf.zeros_like(matrix), matrix) 208 | return tf.math.imag(tf.linalg.expm(j_matrix)) 209 | 210 | 211 | class Callback: 212 | def __init__(self, model, Xtrain, Ytrain, Xtest, Ytest, loss_fn=None, transformer=None): 213 | self.model = model 214 | self.Xtrain = Xtrain 215 | self.Ytrain = Ytrain 216 | self.Xtest = Xtest 217 | self.Ytest = Ytest 218 | self.transformer = transformer 219 | self.epoch = 0 220 | self.loss_fn = loss_fn 221 | 222 | def __call__(self, step=None, variables=None, values=None): 223 | mape = evaluate_mape(self.Xtest, self.Ytest, self.model, transformer=self.transformer) 224 | mae = evaluate_mae(self.Xtest, self.Ytest, self.model, transformer=self.transformer) 225 | if self.loss_fn is None: 226 | elbo = self.model.elbo((self.Xtrain, self.Ytrain)).numpy() 227 | else: 228 | elbo = self.loss_fn() 229 | 230 | print(f"{self.epoch}:\tELBO: {elbo:.5f}\tMAPE: {mape:.10f}\tMAE: {mae:.10f}") 231 | self.epoch += 1 232 | 233 | 234 | def replace_small_values(tensor, eps=1e-7): 235 | return tf.where( 236 | tf.abs(tensor) < eps, 237 | tf.ones_like(tensor), tensor) 238 | 239 | 240 | def get_hmc_sample(num_samples, samples, hmc_helper, model, test_X): 241 | f_samples = [] 242 | for i in range(num_samples): 243 | if i % 10 == 0: 244 | print(i) 245 | # Note that hmc_helper.current_state contains the unconstrained variables 246 | for var, var_samples in zip(hmc_helper.current_state, samples): 247 | var.assign(var_samples[i]) 248 | f = model.predict_f_samples(test_X, 5) 249 | f_samples.append(f) 250 | f_samples = np.vstack(f_samples) 251 | return f_samples 252 | -------------------------------------------------------------------------------- /graph_kernels/utils_opt.py: -------------------------------------------------------------------------------- 1 | import gpflow 2 | import tensorflow as tf 3 | import tensorflow_probability as tfp 4 | from tensorflow_probability import distributions as tfd 5 | import numpy as np 6 | 7 | from . import utils 8 | 9 | 10 | gpflow.config.set_default_float(tf.float64) 11 | f64 = gpflow.utilities.to_default_float 12 | 13 | 14 | def optimize_ada_natgrad(gprocess, train_X, train_y, test_X, test_y, n_iter, learning_rate=1e-2, 15 | transformer=None): 16 | decayed_lr = tf.keras.optimizers.schedules.ExponentialDecay( 17 | learning_rate, 5000, 0.5, staircase=False, name=None 18 | ) 19 | optimizer = tf.optimizers.Adam(decayed_lr) 20 | 21 | gpflow.set_trainable(gprocess.q_mu, False) 22 | gpflow.set_trainable(gprocess.q_sqrt, False) 23 | natgrad_opt = gpflow.optimizers.NaturalGradient(gamma=0.1) 24 | 25 | result = {} 26 | for epoch in range(n_iter): 27 | elbo = -utils.training_step( 28 | train_X, train_y, optimizer, gprocess, natgrad_opt).numpy() 29 | 30 | mape = utils.evaluate_mape(test_X, test_y, gprocess, transformer) 31 | mae = utils.evaluate_mae(test_X, test_y, gprocess, transformer) 32 | result[epoch] = { 33 | "ELBO": elbo, 34 | "MAPE": mape, 35 | "MAE": mae, 36 | } 37 | print(f"{epoch}:\tELBO: {elbo:.5f}\tMAPE: {mape:.10f}\tMAE: {mae:.10f}") 38 | 39 | return result, gprocess 40 | 41 | 42 | def optimize_lbfgs_b(gprocess, train_X, train_y, test_X, test_y, n_iter, transformer=None, compile=False): 43 | optimizer = gpflow.optimizers.Scipy() 44 | loss_fn = gprocess.training_loss_closure((train_X, train_y), compile=compile) 45 | callback = utils.Callback( 46 | gprocess, train_X, train_y, test_X, test_y, 47 | transformer=transformer) 48 | optimizer.minimize( 49 | loss_fn, 50 | variables=gprocess.trainable_variables, 51 | compile=compile, 52 | options=dict(disp=True, maxiter=n_iter), 53 | step_callback=callback, 54 | ) 55 | 56 | mape = utils.evaluate_mape(test_X, test_y, gprocess, transformer=transformer) 57 | mae = utils.evaluate_mae(test_X, test_y, gprocess, transformer=transformer) 58 | elbo = loss_fn() 59 | result = {"ELBO": elbo.numpy(), "MAPE": mape, "MAE": mae} 60 | return result, gprocess 61 | 62 | 63 | def evaluate_kernel_svgp(kernel, train_X, train_y, test_X, test_y, graph, transformer=None, 64 | dump_everything=False, dump_directory=None, optimizer_name="Adam", n_iter=2000, 65 | mean_function=None, compile=False): 66 | # Optimizer = Adam or LBFGS 67 | if mean_function is None: 68 | mean_function = utils.ConstantArray(len(graph.nodes())) 69 | 70 | gprocess = gpflow.models.SVGP( 71 | kernel, gpflow.likelihoods.Gaussian(), 72 | inducing_variable=train_X, mean_function=mean_function, whiten=True, q_diag=False) 73 | gpflow.set_trainable(gprocess.inducing_variable, False) 74 | gprocess.likelihood.variance.assign(1e-2) 75 | if optimizer_name == "Adam": 76 | result, gprocess = optimize_ada_natgrad( 77 | gprocess, train_X, train_y, 78 | test_X, test_y, n_iter=n_iter, transformer=transformer) 79 | elif optimizer_name == "LBFGS": 80 | result, gprocess = optimize_lbfgs_b( 81 | gprocess, train_X, train_y, test_X, test_y, n_iter=n_iter, transformer=transformer, 82 | compile=compile) 83 | else: 84 | raise ValueError("Supported optimizers: Adam & LBFGS") 85 | return result, gprocess 86 | 87 | 88 | def initialize_hmc_helpers(model): 89 | hmc_helper = gpflow.optimizers.SamplingHelper( 90 | model.log_posterior_density, model.trainable_parameters, 91 | ) 92 | hmc = tfp.mcmc.HamiltonianMonteCarlo( 93 | target_log_prob_fn=hmc_helper.target_log_prob_fn, 94 | num_leapfrog_steps=10, step_size=0.01 95 | ) 96 | adaptive_hmc = tfp.mcmc.SimpleStepSizeAdaptation( 97 | hmc, num_adaptation_steps=10, target_accept_prob=0.75, adaptation_rate=0.1 98 | ) 99 | return hmc_helper, hmc, adaptive_hmc 100 | 101 | 102 | def evaluate_kernel_mcmc(kernel, train_X, train_y, test_X, test_y, graph, 103 | mean_function=None, transformer=None, 104 | dump_everything=False, dump_directory=None, optimizer_name="Adam", n_iter=2000, 105 | num_burnin_steps=300, num_samples=500, full_mcmc=False): 106 | if mean_function is None: 107 | mean_function = utils.ConstantArray(len(graph.nodes())) 108 | model = gpflow.models.GPR((train_X, train_y), kernel, mean_function, noise_variance=0.01) 109 | 110 | model.likelihood.variance.prior = tfd.Normal(f64(0.0), f64(1e-2)) 111 | for var in kernel.trainable_parameters: 112 | var.prior = tfd.Gamma(f64(1.0), f64(1.0)) 113 | optimizer = gpflow.optimizers.Scipy() 114 | loss_fn = model.training_loss_closure(compile=False) 115 | callback = utils.Callback( 116 | model, train_X, train_y, test_X, test_y, 117 | loss_fn=loss_fn, transformer=transformer) 118 | optimizer.minimize( 119 | loss_fn, model.trainable_variables, compile=False, 120 | options=dict(disp=True, maxiter=n_iter), callback=callback) 121 | if full_mcmc: 122 | hmc_helper, hmc, adaptive_hmc = initialize_hmc_helpers(model) 123 | samples, traces = tfp.mcmc.sample_chain( 124 | num_results=num_samples, 125 | num_burnin_steps=num_burnin_steps, 126 | current_state=hmc_helper.current_state, 127 | kernel=adaptive_hmc, 128 | trace_fn=lambda _, pkr: pkr.inner_results.is_accepted, 129 | ) 130 | print("Acceptance rate:", traces.is_accepted.numpy().mean()) 131 | 132 | r_hat = tfp.mcmc.potential_scale_reduction(samples) 133 | print("R-hat diagnostic (per latent variable):", r_hat.numpy()) 134 | 135 | #parameter_samples = hmc_helper.convert_to_constrained_values(samples) 136 | f_samples = utils.get_hmc_sample(num_samples, samples, hmc_helper, model, test_X) 137 | y_pred = np.median(f_samples, 0) 138 | mape = utils.evaluate_mape_predictions(y_pred, test_y, transformer) 139 | mae = utils.evaluate_mae_predictions(y_pred, test_y, transformer) 140 | elbo = loss_fn() 141 | else: 142 | mape = utils.evaluate_mape(test_X, test_y, model, transformer) 143 | mae = utils.evaluate_mae(test_X, test_y, model, transformer) 144 | elbo = loss_fn() 145 | return {"ELBO": elbo.numpy(), "MAPE": mape, "MAE": mae}, model 146 | -------------------------------------------------------------------------------- /graph_kernels/utils_postproc.py: -------------------------------------------------------------------------------- 1 | import os 2 | import collections 3 | import json 4 | import numpy as np 5 | import scipy 6 | import scipy.stats 7 | 8 | 9 | def load_result(path, filename="result.json"): 10 | path = os.path.join(path, filename) 11 | result = json.load(open(path, "rb")) 12 | return {int(k): v for k, v in result.items()} 13 | 14 | 15 | def separate_results(result): 16 | all_iterations = [] 17 | all_elbos = [] 18 | all_mses = [] 19 | for random_seed in result: 20 | cur_result = {int(k): v for k, v in result[random_seed].items()} 21 | iterations = sorted([int(i) for i in cur_result.keys()]) 22 | 23 | all_iterations.extend(iterations) 24 | all_elbos.extend([cur_result[i]["ELBO"] for i in iterations]) 25 | all_mses.extend([cur_result[i]["MSE"] for i in iterations]) 26 | return all_iterations, all_elbos, all_mses 27 | 28 | 29 | def separate_results_all_with_iter(result): 30 | all_metrics = collections.defaultdict(list) 31 | for random_seed in result: 32 | if "time" in result[random_seed]: 33 | del result[random_seed]["time"] 34 | cur_result = {int(k): v for k, v in result[random_seed].items()} 35 | iterations = sorted([int(i) for i in cur_result.keys()]) 36 | 37 | all_metrics["iterations"].extend(iterations) 38 | for k in cur_result[0].keys(): 39 | all_metrics[k].extend([cur_result[i][k] for i in iterations]) 40 | return all_metrics 41 | 42 | 43 | def separate_results_all(result): 44 | all_metrics = collections.defaultdict(list) 45 | for random_seed in result: 46 | for k in result[random_seed].keys(): 47 | all_metrics[k].append(result[random_seed][k]) 48 | return all_metrics 49 | 50 | 51 | def stats_array(data): 52 | mean = np.mean(data) 53 | # evaluate sample variance by setting delta degrees of freedom (ddof) to 54 | # 1. The degree used in calculations is N - ddof 55 | stddev = np.std(data, ddof=1) 56 | # Get the endpoints of the range that contains 95% of the distribution 57 | t_bounds = scipy.stats.t.interval(0.95, len(data) - 1) 58 | # sum mean to the confidence interval 59 | ci = [mean + critval * stddev / (len(data)**0.5) for critval in t_bounds] 60 | print("Mean: {:.4f} $\\pm$ {:.4f}".format(mean, ci[1] - mean)) 61 | print("Confidence Interval 95%%: {}, {}".format(ci[0], ci[1])) 62 | print(scipy.stats.t.interval(0.95, len(data) - 1, loc=np.mean(data), scale=scipy.stats.sem(data))) 63 | print("Data: ", data) 64 | 65 | 66 | def print_statistics(result, n=2000): 67 | data = [] 68 | for i, m in zip(result[0], result[2]): 69 | if i == n - 1: 70 | data.append(m) 71 | stats_array(data) 72 | 73 | 74 | def from_folder_to_results(folder): 75 | results_dict = {} 76 | for dir_name in os.listdir(folder): 77 | results_dict[dir_name] = load_result(os.path.join(folder, dir_name)) 78 | return results_dict 79 | 80 | 81 | def parse_results(results): 82 | parsed_result = {} 83 | for k, v in results.items(): 84 | parsed_result[k] = separate_results_all(v) 85 | return parsed_result 86 | -------------------------------------------------------------------------------- /requirements.txt: -------------------------------------------------------------------------------- 1 | gpflow==2.1.4 2 | networkx==2.5 3 | tensorflow==2.5.1 4 | tensorflow-datasets==4.3.0 5 | tensorflow-hub==0.12.0 6 | tensorflow-probability==0.12.0 7 | gast==0.4.0 8 | scikit-learn==0.24.2 9 | numpy==1.19.5 10 | seaborn==0.11.0 11 | matplotlib==3.3.4 12 | scipy==1.5.4 13 | tqdm==4.62.3 14 | jupyter==1.0.0 15 | -------------------------------------------------------------------------------- /setup.py: -------------------------------------------------------------------------------- 1 | from setuptools import setup 2 | from setuptools import find_packages 3 | 4 | setup(name='graph_kernels', 5 | version='0.0', 6 | description='Graph Kernels with GPFlow', 7 | author='', 8 | author_email='', 9 | url='', 10 | download_url='', 11 | license='Apache-2.0', 12 | install_requires=[], 13 | package_data={'graph_kernels': ['README.md']}, 14 | packages=find_packages()) 15 | --------------------------------------------------------------------------------