├── .gitignore
├── README.md
├── Training Latent ODE Model.ipynb
├── autograd_extended.py
├── data.csv
└── requirements.txt
/.gitignore:
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1 | __pycache__/
2 | .ipynb_checkpoints/
3 |
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/README.md:
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1 | # Neural Ordinary Differential Equations
2 | ## Overview and Summary
3 | I try to implement the findings in the paper in this repo. Here's a summary of what I think is significant information.
4 |
5 | Neural Ordinary Differential Equations introduces an interesting way of specifiying a neural network. Instead of treating the neural network as a sequence of discrete states, the approach parameterizes the derivative of the hidden state using a neural network. This parameterizing of the hidden state provides a continuous depth model provides a bunch of useful properties.
6 |
7 | ### Useful Properties I Understand
8 | 1. Memory Efficiency: The specifications give a constant memory costs wrt to depth
9 | 2. Adaptive Computation: Adapt level of error for efficiency, useful for real-time or low-power applications
10 | 3. Scalable and Invertible Normalizing Flows: Continuous transformation allows for easier computation of change of variables. The paper derives a new fclass of invertible density models that avoids the bottleneck of normalizing flows, allowing the model to be trained directly by max-likelihood.
11 | 4. Scalable and invertible normalizing flows: The continuous transformation makes the change of variables formula easier to compute. This allows the constructuion of a new class of invertible density models that avoids previous bottlenecks.
12 |
13 | 5. Continuous Time-series Models: Able to model time-series data that arrive at arbitrary times unlike RNNs.
14 |
15 | ### What Are Normalizing Flows? I am confused.
16 | I got stumped on this one for a while. My reaction irl the whole time -> ( ・◇・)？
17 |
18 | If you're a noob like me you would probably get stumped too. Here's what I understand without the math.
19 |
20 | Imagine if you were in a conference and someone asked the presenter something really difficult. Making the presenter go ( ・◇・)？ The presenter
21 | doesn't want to cop out and look stupid so he/she tries to answer the question. The presenter then simplifies the question and answers that simpified question instead. Not satisfactory, but it should gets the point across. This is essentially the idea behind Variational Inference. The quantity that describes this is termed as the posterior distribution.
22 |
23 | What happens if this explanation seemed to hand wavy or oversimplistic? We need to find a slightly more detailed way of explaning the same thing. How should we tune the complexity of the explanation? This method of tuning the complexity is the idea behind Normalizing Flows. By using these normalizing flows, we can apply a sequence of invertible transformation (we can back and forth and not lose information) to transform that simple posterior distribution (ie. the explanation) into something more complex that captures the idea we want to describe.
24 |
25 | This paper essentially provides a continuous formulation of the normalizing flow concept. While an elegant concept, it can get hard to compute terms, like the change of variables. Using the continuous formulation, the paper offers a method of using the trace of the mapping function, which is more efficient. Check the maths in the paper for a clearer picture.
26 |
27 |
28 | #### Useful links
29 | 1. [Quora explanation by Sam Wang](https://www.quora.com/What-is-variational-inference) I used his analogy
30 | 2. [Variational Inference by David M. Blei](https://www.cs.princeton.edu/courses/archive/fall11/cos597C/lectures/variational-inference-i.pdf)
31 | 3. [Variational Inference with Normalizing Flows Paper](https://arxiv.org/abs/1505.05770)
32 | 4. [Normalizing Flows](http://akosiorek.github.io/ml/2018/04/03/norm_flows.html) as suggested by zdhNarsil
33 |
34 | ### Limitations
35 | 1. Unstraightforward Minibatching: Though minibatching can still be achieved by concatenating the states of each batch elements together to form an ODE.
36 | 2. Uniqueness: A unique solution only exists if the neural netowrk has finate weights and Lipshitz nonlinearities like tanh or relu.
37 | 3. Reversibility: Forward trajectory of the network is invertible in principle, but numerical errors will emerge in forward ODE solver and reverse ODE solver (though this can be reduce at the cost of more computation). Information is lost due to multiple initial value mapping to the final state, this is expected to be a problem if the system dynamics encoded optimization-like, convergent dynamics.
38 |
39 |
40 | ## Link To Arxiv Paper
41 | https://arxiv.org/abs/1806.07366
42 |
43 | ## TODOS
44 | To look into JJFORD link to Arxiv Paper
45 | https://arxiv.org/abs/1810.01367
46 |
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/Training Latent ODE Model.ipynb:
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1 | {
2 | "cells": [
3 | {
4 | "cell_type": "code",
5 | "execution_count": 44,
6 | "metadata": {},
7 | "outputs": [],
8 | "source": [
9 | "%matplotlib inline\n",
10 | "\n",
11 | "# import\n",
12 | "import numpy\n",
13 | "import pandas as pd\n",
14 | "import autograd_extended\n",
15 | "import tensorflow as tf\n",
16 | "import matplotlib.pyplot as plt\n",
17 | "\n",
18 | "from keras.models import Model\n",
19 | "from keras.layers import LSTM, Input, Lambda, Dense, RepeatVector\n",
20 | "from keras import backend as K\n",
21 | "from keras import objectives\n",
22 | "\n",
23 | "import scipy.integrate\n",
24 | "\n",
25 | "import autograd.numpy as np\n",
26 | "from autograd import make_vjp, grad\n",
27 | "from autograd.extend import primitive, defvjp_argnums\n",
28 | "from autograd.misc import flatten\n",
29 | "from autograd.builtins import tuple\n",
30 | "from autograd.misc.optimizers import adam\n",
31 | "\n",
32 | "odeint = primitive(scipy.integrate.odeint)"
33 | ]
34 | },
35 | {
36 | "cell_type": "markdown",
37 | "metadata": {},
38 | "source": [
39 | "# Training the latent ODE model\n",
40 | "From appendix D\n",
41 | "\n",
42 | "To obtain the latent representation $z_{t_{0}}$, we traverse using RNN and obtain parameters of distribution $ q(\\textbf{z}_{t_{0}} | \\{ \\textbf{x}_{t_{i}}, t_{i} \\}_{i}, \\theta_{enc})$. The algorithm is the following:\n",
43 | "\n",
44 | "\n",
45 | "## Step 1\n",
46 | "Run an RNN encoder through the time series and infer the parameters for the a posterior over $ \\textbf{z}_{t_{0}}$:\n",
47 | "$$ q(\\textbf{z}_{t_{0}} | \\{ \\textbf{x}_{t_{i}}, t_{i} \\}_{i}, \\phi) = \\mathcal{N}(\\textbf{z}_{t_{0}} | \\mu_{\\textbf{z}_{t_{0}}}, \\sigma_{\\textbf{z}_{0}}) $$\n",
48 | "\n",
49 | "where $\\mu_{z_{0}}, \\sigma_{z_{0}}$ comes from hidden state of $ RNN(\\{ \\textbf{x}_{t_{i}} , t_{i} \\}_{i}, \\phi) $\n",
50 | "\n",
51 | "## Step 2\n",
52 | "Sample $ \\textbf{z}_{t_{0}} \\sim q(\\textbf{z}_{t_{0}} | \\{ \\textbf{x}_{t_{i}}, t_{i} \\}_{i}) $"
53 | ]
54 | },
55 | {
56 | "cell_type": "code",
57 | "execution_count": 45,
58 | "metadata": {
59 | "collapsed": true
60 | },
61 | "outputs": [],
62 | "source": [
63 | "# Process Data\n",
64 | "\n",
65 | "# obtain simple time series with sine function\n",
66 | "df = pd.read_csv('./data.csv')\n",
67 | "\n",
68 | "x, y = df[\"x\"], df[\"y\"]\n",
69 | "\n",
70 | "# split y into timesteps for training (-1, 100, 1) we use a sliding window\n",
71 | "timesteps = 5\n",
72 | "\n",
73 | "newY = []\n",
74 | "for i in range(0, len(y)-timesteps):\n",
75 | " temp = y[i:i+timesteps]\n",
76 | " \n",
77 | " temp_ls = []\n",
78 | " for j in temp:\n",
79 | " temp_ls.append([j])\n",
80 | " newY.append(temp_ls)\n",
81 | " \n",
82 | "y = np.array(newY)"
83 | ]
84 | },
85 | {
86 | "cell_type": "markdown",
87 | "metadata": {},
88 | "source": [
89 | "Define and run the autoencoder model"
90 | ]
91 | },
92 | {
93 | "cell_type": "code",
94 | "execution_count": 46,
95 | "metadata": {},
96 | "outputs": [
97 | {
98 | "name": "stdout",
99 | "output_type": "stream",
100 | "text": [
101 | "Epoch 1/20\n",
102 | "1995/1995 [==============================] - 6s 3ms/step - loss: 0.5040\n",
103 | "Epoch 2/20\n",
104 | "1995/1995 [==============================] - 2s 1ms/step - loss: 0.4752\n",
105 | "Epoch 3/20\n",
106 | "1995/1995 [==============================] - 2s 999us/step - loss: 0.4647\n",
107 | "Epoch 4/20\n",
108 | "1995/1995 [==============================] - 2s 983us/step - loss: 0.4599\n",
109 | "Epoch 5/20\n",
110 | "1995/1995 [==============================] - 2s 926us/step - loss: 0.4488\n",
111 | "Epoch 6/20\n",
112 | "1995/1995 [==============================] - 2s 1ms/step - loss: 0.4069\n",
113 | "Epoch 7/20\n",
114 | "1995/1995 [==============================] - 2s 942us/step - loss: 0.3175\n",
115 | "Epoch 8/20\n",
116 | "1995/1995 [==============================] - 2s 995us/step - loss: 0.2431\n",
117 | "Epoch 9/20\n",
118 | "1995/1995 [==============================] - 2s 1ms/step - loss: 0.2179\n",
119 | "Epoch 10/20\n",
120 | "1995/1995 [==============================] - 2s 950us/step - loss: 0.2021\n",
121 | "Epoch 11/20\n",
122 | "1995/1995 [==============================] - 2s 1ms/step - loss: 0.1881\n",
123 | "Epoch 12/20\n",
124 | "1995/1995 [==============================] - 2s 1ms/step - loss: 0.1802\n",
125 | "Epoch 13/20\n",
126 | "1995/1995 [==============================] - 2s 1ms/step - loss: 0.1734\n",
127 | "Epoch 14/20\n",
128 | "1995/1995 [==============================] - 2s 953us/step - loss: 0.1629\n",
129 | "Epoch 15/20\n",
130 | "1995/1995 [==============================] - 2s 939us/step - loss: 0.1601\n",
131 | "Epoch 16/20\n",
132 | "1995/1995 [==============================] - 2s 1ms/step - loss: 0.1570\n",
133 | "Epoch 17/20\n",
134 | "1995/1995 [==============================] - 2s 1ms/step - loss: 0.1520\n",
135 | "Epoch 18/20\n",
136 | "1995/1995 [==============================] - 2s 1ms/step - loss: 0.1479\n",
137 | "Epoch 19/20\n",
138 | "1995/1995 [==============================] - 2s 963us/step - loss: 0.1423\n",
139 | "Epoch 20/20\n",
140 | "1995/1995 [==============================] - 2s 934us/step - loss: 0.1407\n"
141 | ]
142 | },
143 | {
144 | "data": {
145 | "text/plain": [
146 | ""
147 | ]
148 | },
149 | "execution_count": 46,
150 | "metadata": {},
151 | "output_type": "execute_result"
152 | }
153 | ],
154 | "source": [
155 | "# Run an RNN encoder on the time series\n",
156 | "\n",
157 | "# Params\n",
158 | "timesteps = 5\n",
159 | "input_dim = 1\n",
160 | "lstm_dim = 32\n",
161 | "latent_dim = 100\n",
162 | "batch_size = 1\n",
163 | "\n",
164 | "# Encoder model\n",
165 | "def sample_z(args):\n",
166 | " \"\"\"Reparameterization trick by sampling fr an isotropic unit Gaussian.\n",
167 | " # Arguments:\n",
168 | " args (tensor): mean and log of variance of Q(z|X)\n",
169 | " # Returns:\n",
170 | " z (tensor): sampled latent vector\n",
171 | " \"\"\"\n",
172 | "\n",
173 | " z_mean, z_log_var = args\n",
174 | " batch = K.shape(z_mean)[0]\n",
175 | " dim = K.int_shape(z_mean)[1]\n",
176 | " # by default, random_normal has mean=0 and std=1.0\n",
177 | " epsilon = K.random_normal(shape=(batch, dim))\n",
178 | " return z_mean + K.exp(0.5 * z_log_var) * epsilon\n",
179 | "\n",
180 | "\n",
181 | "# Input\n",
182 | "inputs = Input(shape=(timesteps, input_dim,), name='encoder_input')\n",
183 | "\n",
184 | "# LSTM encoding\n",
185 | "h = LSTM(lstm_dim)(inputs)\n",
186 | "\n",
187 | "# VAE Z layer\n",
188 | "z_mean = Dense(latent_dim)(h)\n",
189 | "z_log_sigma = Dense(latent_dim)(h)\n",
190 | "\n",
191 | "# Obtain z\n",
192 | "z = Lambda(sample_z, output_shape=(latent_dim,))([z_mean, z_log_sigma])\n",
193 | "\n",
194 | "# Encoder for sanity checking\n",
195 | "encoder = Model(inputs, z_mean, name=\"encoder\")\n",
196 | "\n",
197 | "# Encoder to extract z values\n",
198 | "encoder_z = Model(inputs, z, name=\"encoder_z\")\n",
199 | "\n",
200 | "# Decoder model\n",
201 | "decoder_h = LSTM(lstm_dim, return_sequences=True)\n",
202 | "decoder_mean = LSTM(input_dim, return_sequences=True)\n",
203 | "\n",
204 | "h_decoded = RepeatVector(timesteps)(z)\n",
205 | "h_decoded = decoder_h(h_decoded)\n",
206 | "\n",
207 | "# decoded layer\n",
208 | "outputs = decoder_mean(h_decoded)\n",
209 | "\n",
210 | "# decoder, from latent space to reconstructed inputs\n",
211 | "decoder_inputs = Input(shape=(latent_dim,))\n",
212 | "\n",
213 | "_h_decoded = RepeatVector(timesteps)(decoder_inputs)\n",
214 | "_h_decoded = decoder_h(_h_decoded)\n",
215 | "\n",
216 | "decoder_outputs = decoder_mean(_h_decoded)\n",
217 | "\n",
218 | "decoder = Model(decoder_inputs, decoder_outputs)\n",
219 | "\n",
220 | "# Build vae\n",
221 | "vae = Model(inputs, outputs, name='vae_lstm')\n",
222 | "def vae_loss(x, x_decoded_mean):\n",
223 | " xent_loss = objectives.mse(x, x_decoded_mean)\n",
224 | " kl_loss = - 0.5 * K.mean(1 + z_log_sigma - K.square(z_mean) - K.exp(z_log_sigma))\n",
225 | " loss = xent_loss + kl_loss\n",
226 | " return loss\n",
227 | "\n",
228 | "vae.compile(optimizer='adam', loss=vae_loss)\n",
229 | "\n",
230 | "# Uncomment to print a summary\n",
231 | "# encoder.summary()\n",
232 | "# decoder.summary()\n",
233 | "# vae.summary()\n",
234 | "\n",
235 | "# Train the VAE to obtain z\n",
236 | "vae.fit(y, y, epochs=20)"
237 | ]
238 | },
239 | {
240 | "cell_type": "code",
241 | "execution_count": 47,
242 | "metadata": {},
243 | "outputs": [
244 | {
245 | "name": "stdout",
246 | "output_type": "stream",
247 | "text": [
248 | "x: (1995, 5, 1), preds: (1995, 5, 1)\n"
249 | ]
250 | },
251 | {
252 | "data": {
253 | "image/png": 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\n",
254 | "text/plain": [
255 | ""
256 | ]
257 | },
258 | "metadata": {
259 | "needs_background": "light"
260 | },
261 | "output_type": "display_data"
262 | }
263 | ],
264 | "source": [
265 | "# Sanity check, we should get a sine graph\n",
266 | "prediction = vae.predict(y, batch_size=batch_size)\n",
267 | "\n",
268 | "# pick a column to plot.\n",
269 | "print(\"x: %s, preds: %s\" % (y.shape, prediction.shape))\n",
270 | "plt.plot(y[:100,0,0], label='data')\n",
271 | "plt.plot(prediction[:100,0,0], label='predict')\n",
272 | "plt.legend()\n",
273 | "plt.show()"
274 | ]
275 | },
276 | {
277 | "cell_type": "markdown",
278 | "metadata": {},
279 | "source": [
280 | "## Step 3\n",
281 | "Obtain $\\textbf{z}_{t_{1}}, \\textbf{z}_{t_{2}}, ..., \\textbf{z}_{t_{M}} $ by solving ODE $ ODESolve(\\textbf{z}_{t_{0}}, f, \\theta_{f}, t_{0},...,t_{M})$ where $f$ is the function defining the gradient $d\\textbf{z}/{dt}$ as a function of $\\textbf{z}$"
282 | ]
283 | },
284 | {
285 | "cell_type": "code",
286 | "execution_count": 48,
287 | "metadata": {},
288 | "outputs": [
289 | {
290 | "name": "stdout",
291 | "output_type": "stream",
292 | "text": [
293 | "(1995, 5, 1)\n",
294 | "[[-0.96730685 -0.30260754 -1.2165959 ... -0.1712243 0.16253346\n",
295 | " 0.1311233 ]\n",
296 | " [ 0.8523834 1.3523002 -0.5332169 ... 0.5856302 0.80972576\n",
297 | " -0.4475613 ]\n",
298 | " [ 1.7198956 1.1818202 -0.38006347 ... -0.61021274 -0.8827091\n",
299 | " -1.177722 ]\n",
300 | " ...\n",
301 | " [ 1.5871499 0.38149977 -1.2908301 ... 1.5604678 -1.1208996\n",
302 | " -0.05023703]\n",
303 | " [ 0.60470605 2.166283 0.07132202 ... -0.35144055 -1.2759343\n",
304 | " -1.1601465 ]\n",
305 | " [-0.84649354 -0.5831001 -0.44895828 ... 1.4420025 0.8956648\n",
306 | " -2.1960166 ]]\n"
307 | ]
308 | }
309 | ],
310 | "source": [
311 | "# We obtain z values from the prior sample by using the predict function\n",
312 | "# As the dataset here is small we just use all y values\n",
313 | "z_val = encoder_z.predict(y)\n",
314 | "print(prediction.shape)\n",
315 | "print(z_val)"
316 | ]
317 | },
318 | {
319 | "cell_type": "code",
320 | "execution_count": 49,
321 | "metadata": {},
322 | "outputs": [],
323 | "source": [
324 | "# From Appendix B\n",
325 | "# For clarity: vjp stands for Vector Jacobian Product\n",
326 | "\n",
327 | "def grad_odeint_all(yt, func, y0, t, func_args, **kwargs):\n",
328 | " \"\"\"\n",
329 | " Extended from \"Scalable Inference of Ordinary Differential\"\n",
330 | " Equation Models of Biochemical Processes\". Sec. 2.4.2\n",
331 | " Fabian Froehlich, Carolin Loos, Jan Hasenauer, 2017\n",
332 | " https://arxiv.org/pdf/1711.08079.pdf\n",
333 | " \"\"\"\n",
334 | " T, D = np.shape(yt)\n",
335 | " flat_args, unflatten = flatten(func_args)\n",
336 | " \n",
337 | " def flat_func(y, t, flat_args):\n",
338 | " return func(y, t, *unflatten(flat_args))\n",
339 | "\n",
340 | " def unpack(x):\n",
341 | " # y, vjp_y, vjp_t, vjp_args\n",
342 | " return x[0:D], x[D:2 * D], x[2 * D], x[2 * D + 1:]\n",
343 | "\n",
344 | " def augmented_dynamics(augmented_state, t, flat_args):\n",
345 | " \"\"\"\n",
346 | " Original system augemented with vjp_y, vjp_t and vjp_args \n",
347 | " \"\"\"\n",
348 | " y, vjp_y, _, _ = unpack(augmented_state)\n",
349 | " vjp_all, dy_dt = make_vjp(flat_func, argnum=(0, 1, 2))(y, t, flat_args)\n",
350 | " vjp_y, vjp_t, vjp_args = vjp_all(-vjp_y)\n",
351 | " return np.hstack((dy_dt, vjp_y, vjp_t, vjp_args))\n",
352 | "\n",
353 | " def vjp_all(g):\n",
354 | " vjp_y = g[-1, :]\n",
355 | " vjp_t0 = 0\n",
356 | " time_vjp_list = []\n",
357 | " vjp_args = np.zeros(np.size(flat_args))\n",
358 | " \n",
359 | " for i in range(T - 1, 0, -1):\n",
360 | "\n",
361 | " # Compute effect of moving measurement time.\n",
362 | " vjp_cur_t = np.dot(func(yt[i, :], t[i], *func_args), g[i, :])\n",
363 | " time_vjp_list.append(vjp_cur_t)\n",
364 | " vjp_t0 = vjp_t0 - vjp_cur_t\n",
365 | "\n",
366 | " # Run augmented system backwards to the previous observation.\n",
367 | " aug_y0 = np.hstack((yt[i, :], vjp_y, vjp_t0, vjp_args))\n",
368 | " aug_ans = odeint(augmented_dynamics, aug_y0,\n",
369 | " np.array([t[i], t[i - 1]]), tuple((flat_args,)), **kwargs)\n",
370 | " _, vjp_y, vjp_t0, vjp_args = unpack(aug_ans[1])\n",
371 | "\n",
372 | " # Add gradient from current output.\n",
373 | " vjp_y = vjp_y + g[i - 1, :]\n",
374 | "\n",
375 | " time_vjp_list.append(vjp_t0)\n",
376 | " vjp_times = np.hstack(time_vjp_list)[::-1]\n",
377 | "\n",
378 | " return None, vjp_y, vjp_times, unflatten(vjp_args)\n",
379 | " return vjp_all\n",
380 | "\n",
381 | "\n",
382 | "def argnums_unpack(all_vjp_builder):\n",
383 | " \"\"\"\n",
384 | " A generic autograd helper function. Takes a function that\n",
385 | " builds vjps for all arguments, and wraps it to return only required vjps.\n",
386 | " \"\"\"\n",
387 | "\n",
388 | " def build_selected_vjps(argnums, ans, combined_args, kwargs):\n",
389 | " vjp_func = all_vjp_builder(ans, *combined_args, **kwargs)\n",
390 | "\n",
391 | " def chosen_vjps(g): # Returns whichever vjps were asked for.\n",
392 | " all_vjps = vjp_func(g)\n",
393 | " return [all_vjps[argnum] for argnum in argnums]\n",
394 | " return chosen_vjps\n",
395 | " return build_selected_vjps\n",
396 | "\n",
397 | "\n",
398 | "# After performing defvjp_argnums, we can use odeint() as a function anywhere now\n",
399 | "# Details of implementation found in autograd library\n",
400 | "# https://github.com/HIPS/autograd/blob/master/autograd/core.py\n",
401 | "\n",
402 | "defvjp_argnums(odeint, argnums_unpack(grad_odeint_all))"
403 | ]
404 | },
405 | {
406 | "cell_type": "code",
407 | "execution_count": 55,
408 | "metadata": {},
409 | "outputs": [],
410 | "source": [
411 | "# define f as sin function\n",
412 | "f = lambda y, t0, z: np.dot(np.sin(y), z)\n",
413 | "\n",
414 | "t = np.linspace(0., max_T, N)\n",
415 | "# odeint(yt, func, y0, t)\n",
416 | "\n",
417 | "# TODO"
418 | ]
419 | },
420 | {
421 | "cell_type": "markdown",
422 | "metadata": {},
423 | "source": [
424 | "## Step 4\n",
425 | "Maximize ELBO (Evidence Lower Bound) \n",
426 | "$$ ELBO = \\sum^{M}_{i=1}\n",
427 | " {\n",
428 | " \\log p(\\textbf{x}_{t_{i}}) | \\textbf{z}_{t_{i}}, \\theta_{\\textbf{x}} ) \n",
429 | " + \\log p(\\textbf{z}_{t_{0}})\n",
430 | " - \\log q(\\textbf{z}_{t_{0}} | \\{ \\textbf{x}_{t_{i}}, t_{i} \\}_{i}, \\phi)\n",
431 | " } \n",
432 | "$$\n",
433 | "\n",
434 | "Where $p(\\textbf{z}_{t_{0}}) = \\mathcal{N}(0,1)$"
435 | ]
436 | },
437 | {
438 | "cell_type": "code",
439 | "execution_count": 54,
440 | "metadata": {},
441 | "outputs": [],
442 | "source": [
443 | "# TODO"
444 | ]
445 | },
446 | {
447 | "cell_type": "code",
448 | "execution_count": null,
449 | "metadata": {
450 | "collapsed": true
451 | },
452 | "outputs": [],
453 | "source": []
454 | }
455 | ],
456 | "metadata": {
457 | "kernelspec": {
458 | "display_name": "Python [conda env:catalyst]",
459 | "language": "python",
460 | "name": "conda-env-catalyst-py"
461 | },
462 | "language_info": {
463 | "codemirror_mode": {
464 | "name": "ipython",
465 | "version": 3
466 | },
467 | "file_extension": ".py",
468 | "mimetype": "text/x-python",
469 | "name": "python",
470 | "nbconvert_exporter": "python",
471 | "pygments_lexer": "ipython3",
472 | "version": "3.6.4"
473 | }
474 | },
475 | "nbformat": 4,
476 | "nbformat_minor": 2
477 | }
478 |
--------------------------------------------------------------------------------
/autograd_extended.py:
--------------------------------------------------------------------------------
1 | """
2 | From Appendix B in the paper
3 | Implementation of autograd
4 | """
5 |
6 | import scipy.integrate
7 |
8 | import autograd.numpy as np
9 | from autograd.extend import primitive, defvjp_argnums
10 | from autograd import make_vjp
11 | from autograd.misc import flatten
12 | from autograd.builtins import tuple
13 |
14 | odeint = primitive(scipy.integrate.odeint)
15 |
16 |
17 | def grad_odeint_all(yt, func, y0, t, func_args, **kwargs):
18 | """
19 | Extended from "Scalable Inference of Ordinary Differential"
20 | Equation Models of Biochemical Processes". Sec. 2.4.2
21 | Fabian Froehlich, Carolin Loos, Jan Hasenauer, 2017
22 | https://arxiv.org/pdf/1711.08079.pdf
23 | """
24 |
25 | T, D = np.shape(yt)
26 | flat_args, unflatten = flatten(func_args)
27 |
28 | def flat_func(y, t, flat_args):
29 | return func(y, t, *unflatten(flat_args))
30 |
31 |
32 | def unpack(x):
33 | # y, vjp_y, vjp_t, vjp_args
34 | return x[0:D], x[D:2 * D], x[2 * D], x[2 * D + 1:]
35 |
36 |
37 | def augmented_dynamics(augmented_state, t, flat_args):
38 | # Original system augemented with vjp_y, vjp_t and vjp_args
39 | y, vjp_y, _, _ = unpack(augmented_state)
40 | vjp_all, dy_dt = make_vjp(flat_func, argnum=(0, 1, 2))(y, t, flat_args)
41 | vjp_y, vjp_t, vjp_args = vjp_all(-vjp_y)
42 | return np.hstack((dy_dt, vjp_y, vjp_t, vjp_args))
43 |
44 |
45 | def vjp_all(g, **kwargs):
46 | vjp_y = g[-1, :]
47 | vjp_t0 = 0
48 | time_vjp_list = []
49 | vjp_args = np.zeros(np.size(flat_args))
50 |
51 | for i in range(T - 1, 0, -1):
52 | # Compute effect of moving current time.
53 | vjp_cur_t = np.dot(func(yt[i, :], t[i], *func_args), g[i, :])
54 | time_vjp_list.append(vjp_cur_t)
55 | vjp_t0 = vjp_t0 - vjp_cur_t
56 |
57 | # Run augmented system backwards to the previous observation
58 | aug_y0 = np.hstack((yt[i, :], vjp_y, vjp_t0, vjp_args))
59 | aug_ans = odeint(augmented_dynamics, aug_y0,
60 | np.array(t[i], t[i - 1]), tuple((flat_args,)), **kwargs)
61 | _, vjp_y, vjp_t0, vjp_args = unpack(aug_ans[1])
62 |
63 | # Add gradient from current output
64 | vjp_y = vjp_y + g[i - 1, :]
65 |
66 | time_vjp_list.append(vjp_t0)
67 | vjp_times = np.hstack(time_vjp_list)[::-1]
68 |
69 | return None, vjp_y, vjp_times, unflatten(vjp_args)
70 |
71 | return vjp_all
72 |
73 |
74 | def grad_argnums_wrapper(all_vjp_builder):
75 | """
76 | A generic autograd helper funciton. Takes a function that
77 | builds vjps for all arguments, and wraps it to return only required vjps.
78 | """
79 | def build_selected_vjps(argnums, ans, combined_args, kwargs):
80 | vjp_func = all_vjp_builder(ans, *combined_args, **kwargs)
81 |
82 | def chosen_vjps(g):
83 | # Return whichever vjps were asked for
84 | all_vjps = vjp_func(g)
85 | return [all_vjps[argnum] for argnum in argnums]
86 |
87 | return chosen_vjps
88 |
89 | return build_selected_vjps
90 |
91 |
92 | if __name__ == '__main__':
93 | print(defvjp_argnums(odeint, grad_argnums_wrapper(grad_odeint_all)))
--------------------------------------------------------------------------------
/data.csv:
--------------------------------------------------------------------------------
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1997 | 1995,-0.0885488432
1998 | 1996,-0.8860086929
1999 | 1997,-0.8688762364
2000 | 1998,-0.0529029752
2001 | 1999,0.8117090374
2002 |
--------------------------------------------------------------------------------
/requirements.txt:
--------------------------------------------------------------------------------
1 | autograd==1.2
2 | certifi==2018.4.16
3 | future==0.16.0
4 | numpy==1.14.5
5 | scipy==1.1.0
6 | wincertstore==0.2
7 |
--------------------------------------------------------------------------------