'
13 |
14 | hr_faded: '
'
15 | hr_shaded: '
'
--------------------------------------------------------------------------------
/torchlife/models/error_dist.py:
--------------------------------------------------------------------------------
1 | # AUTOGENERATED! DO NOT EDIT! File to edit: 65_AFT_error_distributions.ipynb (unless otherwise specified).
2 |
3 | __all__ = ['get_distribution']
4 |
5 | # Cell
6 | from functools import partial
7 |
8 | import torch
9 | import torch.nn as nn
10 | import torch.nn.functional as F
11 |
12 | # Cell
13 | def get_distribution(dist:str):
14 | """
15 | Get the logpdf and logcdf of a given torch distribution
16 | """
17 | dist = getattr(torch.distributions, dist.title())
18 | if not isinstance(dist.support, torch.distributions.constraints._Real):
19 | raise Exception("Distribution needs support over ALL real values.")
20 |
21 | dist = partial(dist, loc=0.0)
22 |
23 | def dist_logpdf(ξ, σ):
24 | return dist(scale=σ).log_prob(ξ)
25 |
26 | def dist_logicdf(ξ, σ):
27 | """
28 | log of inverse cumulative distribution function
29 | """
30 | return torch.log(1 - dist(scale=σ).cdf(ξ))
31 |
32 | return dist_logpdf, dist_logicdf
--------------------------------------------------------------------------------
/docs/hazard.html:
--------------------------------------------------------------------------------
1 | ---
2 |
3 | title: Hazard Models
4 |
5 |
6 | keywords: fastai
7 | sidebar: home_sidebar
8 |
9 | summary: "Hazard based models."
10 | description: "Hazard based models."
11 | nb_path: "50_hazard.ipynb"
12 | ---
13 |
22 |
23 |
24 |
25 | {% raw %}
26 |
27 |
28 |
29 |
30 | {% endraw %}
31 |
32 |
33 |
34 |
We can choose to model the instantaneous hazard directly. There are two methods:
35 |
39 |
40 |
41 |
42 |
43 |
44 |
45 |
46 |
--------------------------------------------------------------------------------
/docs/licenses/LICENSE:
--------------------------------------------------------------------------------
1 | /* This license pertains to the docs template, except for the Navgoco jQuery component. */
2 |
3 | The MIT License (MIT)
4 |
5 | Original theme: Copyright (c) 2016 Tom Johnson
6 | Modifications: Copyright (c) 2017 onwards fast.ai, Inc
7 |
8 | Permission is hereby granted, free of charge, to any person obtaining a copy
9 | of this software and associated documentation files (the "Software"), to deal
10 | in the Software without restriction, including without limitation the rights
11 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
12 | copies of the Software, and to permit persons to whom the Software is
13 | furnished to do so, subject to the following conditions:
14 |
15 | The above copyright notice and this permission notice shall be included in all
16 | copies or substantial portions of the Software.
17 |
18 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
19 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
20 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
21 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
22 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
23 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
24 | SOFTWARE.
25 |
--------------------------------------------------------------------------------
/.github/workflows/main.yml:
--------------------------------------------------------------------------------
1 | name: CI
2 | on: [push]
3 | jobs:
4 | build:
5 | runs-on: ubuntu-latest
6 | steps:
7 | - uses: actions/checkout@v1
8 | - uses: actions/setup-python@v1
9 | with:
10 | python-version: '3.6'
11 | architecture: 'x64'
12 | - name: Install the library
13 | run: |
14 | pip install nbdev jupyter
15 | pip install -e .
16 | - name: Read all notebooks
17 | run: |
18 | nbdev_read_nbs
19 | - name: Check if all notebooks are cleaned
20 | run: |
21 | echo "Check we are starting with clean git checkout"
22 | if [ -n "$(git status -uno -s)" ]; then echo "git status is not clean"; false; fi
23 | echo "Trying to strip out notebooks"
24 | nbdev_clean_nbs
25 | echo "Check that strip out was unnecessary"
26 | git status -s # display the status to see which nbs need cleaning up
27 | if [ -n "$(git status -uno -s)" ]; then echo -e "!!! Detected unstripped out notebooks\n!!!Remember to run nbdev_install_git_hooks"; false; fi
28 | - name: Check if there is no diff library/notebooks
29 | run: |
30 | if [ -n "$(nbdev_diff_nbs)" ]; then echo -e "!!! Detected difference between the notebooks and the library"; false; fi
31 | - name: Run tests
32 | run: |
33 | nbdev_test_nbs
34 |
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/docs/_config.yml:
--------------------------------------------------------------------------------
1 | repository: sachinruk/torchlife
2 | output: web
3 | topnav_title: torchlife
4 | site_title: torchlife
5 | company_name: Sachinthaka Abeywardana
6 | description: Survival Analysis with fastai and pytorch
7 | # Set to false to disable KaTeX math
8 | use_math: true
9 | # Add Google analytics id if you have one and want to use it here
10 | google_analytics:
11 | # See http://nbdev.fast.ai/search for help with adding Search
12 | google_search:
13 |
14 | host: 127.0.0.1
15 | # the preview server used. Leave as is.
16 | port: 4000
17 | # the port where the preview is rendered.
18 |
19 | exclude:
20 | - .idea/
21 | - .gitignore
22 | - vendor
23 |
24 | exclude: [vendor]
25 |
26 | highlighter: rouge
27 | markdown: kramdown
28 | kramdown:
29 | input: GFM
30 | auto_ids: true
31 | hard_wrap: false
32 | syntax_highlighter: rouge
33 |
34 | collections:
35 | tooltips:
36 | output: false
37 |
38 | defaults:
39 | -
40 | scope:
41 | path: ""
42 | type: "pages"
43 | values:
44 | layout: "page"
45 | comments: true
46 | search: true
47 | sidebar: home_sidebar
48 | topnav: topnav
49 | -
50 | scope:
51 | path: ""
52 | type: "tooltips"
53 | values:
54 | layout: "page"
55 | comments: true
56 | search: true
57 | tooltip: true
58 |
59 | sidebars:
60 | - home_sidebar
61 |
62 | theme: jekyll-theme-cayman
63 | baseurl: /torchlife/
--------------------------------------------------------------------------------
/docs/feed.xml:
--------------------------------------------------------------------------------
1 | ---
2 | search: exclude
3 | layout: none
4 | ---
5 |
6 |
7 |
8 |
9 | {{ site.title | xml_escape }}
10 | {{ site.description | xml_escape }}
11 | {{ site.time | date_to_rfc822 }}
14 | {{ site.time | date_to_rfc822 }}
15 | Jekyll v{{ jekyll.version }}
16 | {% for post in site.posts limit:10 %}
17 | -
18 |
{{ post.title | xml_escape }}
19 | {{ post.content | xml_escape }}
20 | {{ post.date | date_to_rfc822 }}
21 | {{ post.url | prepend: site.url }}
23 | {% for tag in post.tags %}
24 | {{ tag | xml_escape }}
25 | {% endfor %}
26 | {% for tag in page.tags %}
27 | {{ cat | xml_escape }}
28 | {% endfor %}
29 |
30 | {% endfor %}
31 |
32 |
33 |
--------------------------------------------------------------------------------
/torchlife/models/km.py:
--------------------------------------------------------------------------------
1 | # AUTOGENERATED! DO NOT EDIT! File to edit: 20_KaplanMeier.ipynb (unless otherwise specified).
2 |
3 | __all__ = ['KaplanMeier']
4 |
5 | # Cell
6 | import pandas as pd
7 | import matplotlib.pyplot as plt
8 | from scipy.interpolate import interp1d
9 |
10 | # Cell
11 | class KaplanMeier:
12 | def fit(self, df):
13 | """
14 | Estimages the Kaplan-Meier survival function
15 | parameters:
16 | - t: time steps
17 | - e: whether death occured at time step (1) or not (0)
18 | """
19 | d = df.groupby("t")["e"].sum()
20 | n = df.groupby("t")["e"].count()
21 | n = n[::-1].cumsum()[::-1]
22 | self.survival_function = (1 - d / n).cumprod()
23 |
24 | if 0 not in self.survival_function:
25 | self.survival_function[0] = 1
26 | self.survival_function.sort_index(inplace=True)
27 |
28 | t = self.survival_function.index
29 | p = self.survival_function.values
30 | self.interpolate = interp1d(t, p, bounds_error=False, fill_value="extrapolate")
31 |
32 | def predict(self, t):
33 | if any(t < 0):
34 | raise Exception("Time cannot be less than 0.")
35 | p = self.interpolate(t)
36 | p[p<0] = 0
37 | return p
38 |
39 | def plot_survival_function(self):
40 | fig, ax = plt.subplots()
41 | ax.plot(self.survival_function)
42 | ax.set_xlabel("Duration")
43 | ax.set_ylabel("Survival Probability")
44 |
45 | ax.set_title("Survival Function")
46 | return ax
--------------------------------------------------------------------------------
/docs/_includes/links.html:
--------------------------------------------------------------------------------
1 | {% comment %}Get links from each sidebar, as listed in the _config.yml file under sidebars{% endcomment %}
2 |
3 | {% for sidebar in site.sidebars %}
4 | {% for entry in site.data.sidebars[sidebar].entries %}
5 | {% for folder in entry.folders %}
6 | {% for folderitem in folder.folderitems %}
7 | {% if folderitem.url contains "html#" %}
8 | [{{folderitem.url | remove: "/" }}]: {{folderitem.url | remove: "/"}}
9 | {% else %}
10 | [{{folderitem.url | remove: "/" | remove: ".html"}}]: {{folderitem.url | remove: "/"}}
11 | {% endif %}
12 | {% for subfolders in folderitem.subfolders %}
13 | {% for subfolderitem in subfolders.subfolderitems %}
14 | [{{subfolderitem.url | remove: "/" | remove: ".html"}}]: {{subfolderitem.url | remove: "/"}}
15 | {% endfor %}
16 | {% endfor %}
17 | {% endfor %}
18 | {% endfor %}
19 | {% endfor %}
20 | {% endfor %}
21 |
22 |
23 | {% comment %} Get links from topnav {% endcomment %}
24 |
25 | {% for entry in site.data.topnav.topnav %}
26 | {% for item in entry.items %}
27 | {% if item.external_url == null %}
28 | [{{item.url | remove: "/" | remove: ".html"}}]: {{item.url | remove: "/"}}
29 | {% endif %}
30 | {% endfor %}
31 | {% endfor %}
32 |
33 | {% comment %}Get links from topnav dropdowns {% endcomment %}
34 |
35 | {% for entry in site.data.topnav.topnav_dropdowns %}
36 | {% for folder in entry.folders %}
37 | {% for folderitem in folder.folderitems %}
38 | {% if folderitem.external_url == null %}
39 | [{{folderitem.url | remove: "/" | remove: ".html"}}]: {{folderitem.url | remove: "/"}}
40 | {% endif %}
41 | {% endfor %}
42 | {% endfor %}
43 | {% endfor %}
44 |
45 |
--------------------------------------------------------------------------------
/docs/_data/sidebars/home_sidebar.yml:
--------------------------------------------------------------------------------
1 |
2 | #################################################
3 | ### THIS FILE WAS AUTOGENERATED! DO NOT EDIT! ###
4 | #################################################
5 | # Instead edit ../../sidebar.json
6 | entries:
7 | - folders:
8 | - folderitems:
9 | - output: web,pdf
10 | title: Overview
11 | url: /
12 | - output: web,pdf
13 | title: Survival Analysis Theory
14 | url: /SAT
15 | - output: web,pdf
16 | title: Kaplan Meier Model
17 | url: /KaplanMeier
18 | subfolders:
19 | - output: web
20 | subfolderitems:
21 | - output: web,pdf
22 | title: Overview
23 | url: /hazard
24 | - output: web,pdf
25 | title: Piecewise Hazard
26 | url: /hazard.PiecewiseHazard
27 | - output: web,pdf
28 | title: Cox Proportional Hazard
29 | url: /hazard.Cox
30 | title: Hazard Models
31 | - output: web
32 | subfolderitems:
33 | - output: web,pdf
34 | title: Error Distributions
35 | url: /AFT_error_distributions
36 | - output: web,pdf
37 | title: Accelerated Failure Time Models
38 | url: /AFT_models
39 | title: AFT
40 | - output: web
41 | subfolderitems:
42 | - output: web,pdf
43 | title: Data
44 | url: /data
45 | - output: web,pdf
46 | title: Base Model
47 | url: /model
48 | - output: web,pdf
49 | title: Losses
50 | url: /Losses
51 | title: Model
52 | output: web
53 | title: torchlife
54 | output: web
55 | title: Sidebar
56 |
--------------------------------------------------------------------------------
/docs/css/modern-business.css:
--------------------------------------------------------------------------------
1 | /*!
2 | * Start Bootstrap - Modern Business HTML Template (http://startbootstrap.com)
3 | * Code licensed under the Apache License v2.0.
4 | * For details, see http://www.apache.org/licenses/LICENSE-2.0.
5 | */
6 |
7 | /* Global Styles */
8 |
9 | html,
10 | body {
11 | height: 100%;
12 | }
13 |
14 | .img-portfolio {
15 | margin-bottom: 30px;
16 | }
17 |
18 | .img-hover:hover {
19 | opacity: 0.8;
20 | }
21 |
22 | /* Home Page Carousel */
23 |
24 | header.carousel {
25 | height: 50%;
26 | }
27 |
28 | header.carousel .item,
29 | header.carousel .item.active,
30 | header.carousel .carousel-inner {
31 | height: 100%;
32 | }
33 |
34 | header.carousel .fill {
35 | width: 100%;
36 | height: 100%;
37 | background-position: center;
38 | background-size: cover;
39 | }
40 |
41 | /* 404 Page Styles */
42 |
43 | .error-404 {
44 | font-size: 100px;
45 | }
46 |
47 | /* Pricing Page Styles */
48 |
49 | .price {
50 | display: block;
51 | font-size: 50px;
52 | line-height: 50px;
53 | }
54 |
55 | .price sup {
56 | top: -20px;
57 | left: 2px;
58 | font-size: 20px;
59 | }
60 |
61 | .period {
62 | display: block;
63 | font-style: italic;
64 | }
65 |
66 | /* Footer Styles */
67 |
68 | footer {
69 | margin: 50px 0;
70 | }
71 |
72 | /* Responsive Styles */
73 |
74 | @media(max-width:991px) {
75 | .client-img,
76 | .img-related {
77 | margin-bottom: 30px;
78 | }
79 | }
80 |
81 | @media(max-width:767px) {
82 | .img-portfolio {
83 | margin-bottom: 15px;
84 | }
85 |
86 | header.carousel .carousel {
87 | height: 70%;
88 | }
89 | }
90 |
--------------------------------------------------------------------------------
/torchlife/_nbdev.py:
--------------------------------------------------------------------------------
1 | # AUTOGENERATED BY NBDEV! DO NOT EDIT!
2 |
3 | __all__ = ["index", "modules", "custom_doc_links", "git_url"]
4 |
5 | index = {"KaplanMeier": "20_KaplanMeier.ipynb",
6 | "torch.Tensor.ndim": "55_hazard.PiecewiseHazard.ipynb",
7 | "PieceWiseHazard": "55_hazard.PiecewiseHazard.ipynb",
8 | "ProportionalHazard": "59_hazard.Cox.ipynb",
9 | "AFTModel": "60_AFT_models.ipynb",
10 | "get_distribution": "65_AFT_error_distributions.ipynb",
11 | "TestData": "80_data.ipynb",
12 | "Data": "80_data.ipynb",
13 | "TestDataFrame": "80_data.ipynb",
14 | "DataFrame": "80_data.ipynb",
15 | "create_dl": "80_data.ipynb",
16 | "create_test_dl": "80_data.ipynb",
17 | "get_breakpoints": "80_data.ipynb",
18 | "GeneralModel": "90_model.ipynb",
19 | "train_model": "90_model.ipynb",
20 | "ModelHazard": "90_model.ipynb",
21 | "ModelAFT": "90_model.ipynb",
22 | "Loss": "95_Losses.ipynb",
23 | "LossType": "95_Losses.ipynb",
24 | "AFTLoss": "95_Losses.ipynb",
25 | "aft_loss": "95_Losses.ipynb",
26 | "HazardLoss": "95_Losses.ipynb",
27 | "hazard_loss": "95_Losses.ipynb"}
28 |
29 | modules = ["models/km.py",
30 | "models/ph.py",
31 | "models/cox.py",
32 | "models/aft.py",
33 | "models/error_dist.py",
34 | "data.py",
35 | "model.py",
36 | "losses.py"]
37 |
38 | doc_url = "https://sachinruk.github.io/torchlife/"
39 |
40 | git_url = "https://github.com/sachinruk/torchlife/tree/master/"
41 |
42 | def custom_doc_links(name): return None
43 |
--------------------------------------------------------------------------------
/docs/_includes/head_print.html:
--------------------------------------------------------------------------------
1 |
2 |
3 |
4 |
5 |
6 |
{% if page.homepage == true %} {{site.homepage_title}} {% elsif page.title %}{{ page.title }}{% endif %} | {{ site.site_title }}
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
23 |
24 |
29 |
--------------------------------------------------------------------------------
/docs/licenses/LICENSE-BSD-NAVGOCO.txt:
--------------------------------------------------------------------------------
1 | /* This license pertains to the Navgoco jQuery component used for the sidebar. */
2 |
3 | Copyright (c) 2013, Christodoulos Tsoulloftas, http://www.komposta.net
4 | All rights reserved.
5 |
6 | Redistribution and use in source and binary forms, with or without modification,
7 | are permitted provided that the following conditions are met:
8 |
9 | * Redistributions of source code must retain the above copyright notice,
10 | this list of conditions and the following disclaimer.
11 | * Redistributions in binary form must reproduce the above copyright notice,
12 | this list of conditions and the following disclaimer in the documentation
13 | and/or other materials provided with the distribution.
14 | * Neither the name of the
nor the names of its
15 | contributors may be used to endorse or promote products derived from this
16 | software without specific prior written permission.
17 |
18 | THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
19 | ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
20 | WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
21 | IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
22 | INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
23 | BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
24 | DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
25 | LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE
26 | OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
27 | OF THE POSSIBILITY OF SUCH DAMAGE.
--------------------------------------------------------------------------------
/docs/_layouts/page.html:
--------------------------------------------------------------------------------
1 | ---
2 | layout: default
3 | ---
4 |
5 |
9 |
10 | {% if page.simple_map == true %}
11 |
12 |
17 |
18 | {% include custom/{{page.map_name}}.html %}
19 |
20 | {% elsif page.complex_map == true %}
21 |
22 |
27 |
28 | {% include custom/{{page.map_name}}.html %}
29 |
30 | {% endif %}
31 |
32 |
33 |
34 | {% if page.summary %}
35 |
{{page.summary}}
36 | {% endif %}
37 |
38 | {% unless page.toc == false %}
39 | {% include toc.html %}
40 | {% endunless %}
41 |
42 |
43 | {% if site.github_editme_path %}
44 |
45 |
46 |
47 | {% endif %}
48 |
49 | {{content}}
50 |
51 |
62 |
63 |
3 |
4 |
13 |
14 |
15 |
16 | {{item.title}} {{item.title}} {{item.title}}
38 | {{ folder.title }}
39 |
50 |
51 | {% endfor %}
52 | {% endfor %}
53 | {% if site.google_search %}
54 |
55 | {% include search_google_custom.html %}
56 |
57 | {% endif %}
58 |
59 |
60 |
63 |
--------------------------------------------------------------------------------
/docs/js/jquery.navgoco.min.js:
--------------------------------------------------------------------------------
1 | /*
2 | * jQuery Navgoco Menus Plugin v0.2.1 (2014-04-11)
3 | * https://github.com/tefra/navgoco
4 | *
5 | * Copyright (c) 2014 Chris T (@tefra)
6 | * BSD - https://github.com/tefra/navgoco/blob/master/LICENSE-BSD
7 | */
8 | !function(a){"use strict";var b=function(b,c,d){return this.el=b,this.$el=a(b),this.options=c,this.uuid=this.$el.attr("id")?this.$el.attr("id"):d,this.state={},this.init(),this};b.prototype={init:function(){var b=this;b._load(),b.$el.find("ul").each(function(c){var d=a(this);d.attr("data-index",c),b.options.save&&b.state.hasOwnProperty(c)?(d.parent().addClass(b.options.openClass),d.show()):d.parent().hasClass(b.options.openClass)?(d.show(),b.state[c]=1):d.hide()});var c=a("{{ page.title }} | {{ site.site_title }}
7 |
22 |
23 | {% raw %}
24 |
25 |
26 |
27 |
28 | {% endraw %}
29 |
30 |
31 |
32 |
Delegated Inheretance The following functions help tab completion and squashing class structure. See the blog post by fastai for details.
33 |
34 |
35 |
36 |
37 | {% raw %}
38 |
39 |
40 |
41 |
42 | {% endraw %}
43 |
44 | {% raw %}
45 |
46 |
47 |
48 |
49 |
50 |
51 |
52 |
53 |
54 |
55 |
delegates(toNonekeepFalse
56 |
57 |
Decorator: replace **kwargs in signature with params from to
58 |
59 |
60 |
61 |
62 |
63 |
64 |
65 |
66 |
67 | {% endraw %}
68 |
69 | {% raw %}
70 |
71 |
72 |
73 |
74 | {% endraw %}
75 |
76 | {% raw %}
77 |
78 |
79 |
80 |
81 |
82 |
83 |
84 |
85 |
86 |
87 |
custom_dir(cadd
88 |
89 |
90 |
91 |
92 |
93 |
94 |
95 |
96 |
97 |
98 | {% endraw %}
99 |
100 | {% raw %}
101 |
102 |
103 |
104 |
105 |
106 |
107 |
108 |
109 |
110 |
111 |
GetAttr()
112 |
113 |
Base class for attr accesses in self._xtra passed down to self.default
114 |
115 |
116 |
117 |
118 |
119 |
120 |
121 |
122 |
123 | {% endraw %}
124 |
125 |
" + txt + " ";
66 | else if (this_level <= level){ // higher level than before; end parent ol
67 | for(i = this_level; i < level; i++) {
68 | html += "" + txt + " ";
71 | }
72 | else if (this_level > level) { // lower level than before; expand the previous to contain a ol
73 | for(i = this_level; i > level; i--) {
74 | html += "<"+settings.listType+">"+((i-level == 2) ? "" : " ")
75 | }
76 | html += "" + txt + " ";
77 | }
78 | level = this_level; // update for the next one
79 | });
80 | html += "";
81 | if (!settings.noBackToTopLinks) {
82 | $(document).on('click', '.back-to-top', function() {
83 | $(window).scrollTop(0);
84 | window.location.hash = '';
85 | });
86 | }
87 |
88 | render[settings.showEffect]();
89 | };
90 | })(jQuery);
91 |
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/docs/_layouts/default.html:
--------------------------------------------------------------------------------
1 |
2 |
3 |
4 | {% include head.html %}
5 |
41 |
46 |
57 | {% if page.datatable == true %}
58 |
59 |
83 |
84 |
85 |
86 | {% assign content_col_size = "col-md-12" %}
87 | {% unless page.hide_sidebar %}
88 |
89 |
92 | {% assign content_col_size = "col-md-9" %}
93 | {% endunless %}
94 |
95 |
96 |
97 | {{content}}
98 |
99 |
100 |
101 |
102 |
103 |
104 |
t)}{dt}\\\\\n",
37 | "$$\n",
38 | "\n",
39 | "The above can be simplified down by using Bayes Rule, and the definition of $S(t)$ above:\n",
40 | "$$\n",
41 | "\\begin{aligned}\n",
42 | "\\lambda(t) =& \\lim\\limits_{dt\\to0} \\frac{P(t t)}{P(T > t)\\quad dt}\\\\\n",
43 | "=& \\lim\\limits_{dt\\to0} \\frac{P(t t$. Therefore the likelihood $L$ can be defined as:\n",
66 | "$$\n",
67 | "L_i = \\begin{cases}\n",
68 | "f(t_i) = S(t_i)\\lambda(t_i) &\\text{ when }d_i = 1 \\\\\n",
69 | "\\int^{\\infty}_t f(x) dx = S(t_i) &\\text{ when }d_i = 0\n",
70 | "\\end{cases}\n",
71 | "$$\n",
72 | "\n",
73 | "The above can be simplified as:\n",
74 | "$$\n",
75 | "\\begin{aligned}\n",
76 | "L =& \\prod_{i=1}^N L_i = \\prod_{i=1}^N \\lambda(t_i)^{d_i} S(t_i) \\\\\n",
77 | "\\log L =& \\sum_{i=1}^N d_i \\log \\lambda(t_i) - \\Lambda(t_i) \\\\\n",
78 | "-\\log L =& \\sum_{i=1}^N \\Lambda(t_i) - d_i \\log \\lambda(t_i)\n",
79 | "\\end{aligned}\n",
80 | "$$\n",
81 | "where $\\Lambda(t)\\equiv -\\log S(t)$ is cumulative hazard function.\n",
82 | "\n",
83 | "Similarly if we wish to avoid taking into account the hazard function, we can define the likelihood function to be:\n",
84 | "$$\n",
85 | "\\begin{aligned}\n",
86 | "L =& \\prod_{i=1}^N L_i = \\prod_{i=1}^N f(t_i)^{d_i} S(t_i)^{1-d_i} \\\\\n",
87 | "-log L =& -\\sum_{i=1}^N d_i \\log f(t_i) + (1 - d_i) \\log S(t_i)\n",
88 | "\\end{aligned}\n",
89 | "$$\n",
90 | "\n",
91 | "These two formats of the likelihood will be used when modelling the behaviours of censored data (in different modelling settings). We use the negative log likelihood as this is more accommodating for modern deep learning libraries that do gradient descent."
92 | ]
93 | },
94 | {
95 | "cell_type": "code",
96 | "execution_count": null,
97 | "metadata": {},
98 | "outputs": [],
99 | "source": [
100 | " "
101 | ]
102 | }
103 | ],
104 | "metadata": {
105 | "kernelspec": {
106 | "display_name": "Python 3",
107 | "language": "python",
108 | "name": "python3"
109 | }
110 | },
111 | "nbformat": 4,
112 | "nbformat_minor": 2
113 | }
114 |
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/docs/SAT.html:
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1 | ---
2 |
3 | title: Survival Analysis Theory
4 |
5 |
6 | keywords: fastai
7 | sidebar: home_sidebar
8 |
9 | summary: "The maths behind survival analysis."
10 | description: "The maths behind survival analysis."
11 | nb_path: "10_SAT.ipynb"
12 | ---
13 |
22 |
23 |
24 |
25 | {% raw %}
26 |
27 |
28 |
29 |
30 | {% endraw %}
31 |
32 |
39 |
40 |
41 |
The Survival Function Let us define $S(t)$ to be the probability that an object will survive beyond time $t$. If $f(t)$ is the instantaneous probability that a death would be observed at time $t$, the survival function is defined as:
42 | $$
43 | S(t) = P(T > t) = 1 - \int_{-\infty}^t f(x) dx
44 | $$
45 |
46 |
47 |
48 |
49 |
50 |
51 |
The Hazard Function Another important concept is the hazard function, $\lambda(t)$, which is the instantaneous rate of occurence, given that the object has survived until time $t$.
52 | $$
53 | \lambda(t) = \lim\limits_{dt\to0} \frac{P(t<T<t+dt | T > t)}{dt}\\
54 | $$
55 |
The above can be simplified down by using Bayes Rule, and the definition of $S(t)$ above:
56 | $$
57 | \begin{aligned}
58 | \lambda(t) =& \lim\limits_{dt\to0} \frac{P(t<T<t+dt, T > t)}{P(T > t)\quad dt}\\
59 | =& \lim\limits_{dt\to0} \frac{P(t<T<t+dt)}{dt} \frac{1}{S(t)}\\
60 | =& \frac{f(t)}{S(t)}
61 | \end{aligned}
62 | $$
63 |
Since $S'(t) = -f(t)$ from the first equation, we can also state:
64 | $$
65 | \lambda(t) = - \frac{d}{dt}\log S(t)
66 | $$
67 |
Therefore, the survival function will can be stated as:
68 | $$
69 | S(t) = \exp\left(-\int_{-\infty}^t \lambda(x) dx\right)
70 | $$
71 | and this will come in handy when we are coding up the survival function.
72 |
73 |
74 |
75 |
76 |
77 |
78 |
Likelihood Function In any probabilistic framework we wish to maxmise the likelihood of observed data given the probability functions. However, unlike classification/ regression situations we need to modify the likelihood $f(t)$. Let us define the case where death, $d_i$ hasn't been observed as censored observations. In those case we know that death will occur at a point $T > t$. Therefore the likelihood $L$ can be defined as:
79 | $$
80 | L_i = \begin{cases}
81 | f(t_i) = S(t_i)\lambda(t_i) &\text{ when }d_i = 1 \\
82 | \int^{\infty}_t f(x) dx = S(t_i) &\text{ when }d_i = 0
83 | \end{cases}
84 | $$
85 |
The above can be simplified as:
86 | $$
87 | \begin{aligned}
88 | L =& \prod_{i=1}^N L_i = \prod_{i=1}^N \lambda(t_i)^{d_i} S(t_i) \\
89 | \log L =& \sum_{i=1}^N d_i \log \lambda(t_i) - \Lambda(t_i) \\
90 | -\log L =& \sum_{i=1}^N \Lambda(t_i) - d_i \log \lambda(t_i)
91 | \end{aligned}
92 | $$
93 | where $\Lambda(t)\equiv -\log S(t)$ is cumulative hazard function.
94 |
Similarly if we wish to avoid taking into account the hazard function, we can define the likelihood function to be:
95 | $$
96 | \begin{aligned}
97 | L =& \prod_{i=1}^N L_i = \prod_{i=1}^N f(t_i)^{d_i} S(t_i)^{1-d_i} \\
98 | -log L =& -\sum_{i=1}^N d_i \log f(t_i) + (1 - d_i) \log S(t_i)
99 | \end{aligned}
100 | $$
101 |
These two formats of the likelihood will be used when modelling the behaviours of censored data (in different modelling settings). We use the negative log likelihood as this is more accommodating for modern deep learning libraries that do gradient descent.
102 |
103 |
104 |
105 |
106 | {% raw %}
107 |
108 |
121 | {% endraw %}
122 |
123 |
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2 |
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/docs/AFT_models.html:
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1 | ---
2 |
3 | title: Accelerated Failure Time Models
4 |
5 |
6 | keywords: fastai
7 | sidebar: home_sidebar
8 |
9 | summary: "AFT Model theory."
10 | description: "AFT Model theory."
11 | nb_path: "60_AFT_models.ipynb"
12 | ---
13 |
22 |
23 |
24 |
25 | {% raw %}
26 |
27 |
28 |
29 |
30 | {% endraw %}
31 |
32 |
33 |
34 |
We can model the time to failure as:
35 | $$
36 | \log T_i = \mu + \xi_i
37 | $$
38 | where $\xi_i\sim p(\xi|\theta)$ and $\mu$ is the most likely log time of death (the mode of the distribution of $T_i$). We model log death as that way we do not need to restrict $\mu + \xi_i$ to be positive.
39 |
In the censored case, where $t_i$ is the time where an instance was censored, and $T_i$ is the unobserved time of death, we have:
40 | $$
41 | \begin{aligned}
42 | \log T_i &= \mu(x_i) + \xi_i > \log t_i\\
43 | \therefore \xi_i &> \log t_i - \mu(x_i)
44 | \end{aligned}
45 | $$
46 | Note that $\mu$ is a function of the features $x$. The log likelihood of the data ($\mathcal{D}$) can then shown to be:
47 | $$
48 | \begin{aligned}
49 | \log p(\mathcal{D}) = \sum_{i=1}^N \mathcal{1}(y_i=1)\log p(\xi_i = \log t_i - \mu(x_i)) + \mathcal{1}(y_i=0)\log p(\xi_i &> \log t_i - \mu(x_i))
50 | \end{aligned}
51 | $$
52 |
53 |
54 |
55 |
56 | {% raw %}
57 |
58 |
59 |
60 |
61 | {% endraw %}
62 |
63 | {% raw %}
64 |
65 |
66 |
67 |
68 |
69 |
70 |
71 |
72 |
73 |
74 |
AFTModel(distributionstr, input_dimint, htuple=()Module
75 |
76 |
Accelerated Failure Time model
77 | parameters:
78 |
79 | Distribution of which the error is assumed to be
80 | dim (optional): input dimensionality of variables
81 | h (optional): number of hidden nodes
82 |
83 |
84 |
85 |
86 |
87 |
88 |
89 |
90 |
91 |
92 | {% endraw %}
93 |
94 | {% raw %}
95 |
96 |
97 |
98 |
99 | {% endraw %}
100 |
101 |
102 |
103 |
Modelling based on only time and (death) event variables:
104 |
105 |
106 |
107 |
108 | {% raw %}
109 |
110 |
135 | {% endraw %}
136 |
137 | {% raw %}
138 |
139 |
159 | {% endraw %}
160 |
161 | {% raw %}
162 |
163 |
176 | {% endraw %}
177 |
178 | {% raw %}
179 |
180 |
193 | {% endraw %}
194 |
195 |
83 |
96 |
97 |
98 |
99 | t
101 | e
102 | fin
103 | age
104 | race
105 | wexp
106 | mar
107 | paro
108 | prio
109 |
110 |
111 |
112 |
113 | 0
114 | 20
115 | 1
116 | 0
117 | 27
118 | 1
119 | 0
120 | 0
121 | 1
122 | 3
123 |
124 |
125 | 1
126 | 17
127 | 1
128 | 0
129 | 18
130 | 1
131 | 0
132 | 0
133 | 1
134 | 8
135 |
136 |
137 | 2
138 | 25
139 | 1
140 | 0
141 | 19
142 | 0
143 | 1
144 | 0
145 | 1
146 | 13
147 |
148 |
149 | 3
150 | 52
151 | 0
152 | 1
153 | 23
154 | 1
155 | 1
156 | 1
157 | 1
158 | 1
159 |
160 |
161 | 4
162 | 52
163 | 0
164 | 0
165 | 19
166 | 0
167 | 1
168 | 0
169 | 1
170 | 3
171 |
172 |
173 |
174 |
24 |
25 | {% raw %}
26 |
27 |
28 |
29 |
30 | {% endraw %}
31 |
32 | {% raw %}
33 |
34 |
35 |
36 |
37 | {% endraw %}
38 |
39 |
40 |
41 |
Suppose that we have:
42 | $$
43 | t_i = \mu + \xi_i
44 | $$
45 | and $\xi_i\sim p(\xi_i|\theta)$. Then $\xi_i|\mu\sim p_\mu(\xi_i|\theta)$ where $p_\mu(\xi_i|\theta)$ is simply the distribution $p(\xi_i|\theta)$ shifted to the left by $\mu$.
46 |
In the event that the event is censored ($e_i=0$), we know that $t_i < \mu + \xi_i$ since the 'death' offset of $\xi_i$ is not observed.
47 |
Therefore we may write the likelihood of
48 | $$
49 | \begin{aligned}
50 | p(t_i, e_i|\mu) =& \left(p(t_i-\mu)\right)^{e_i} \left(\int_{t_i}^\infty p(t-\mu) dt\right)^{1-e_i}\\
51 | \log p(t_i, e_i|\mu) =& e_i \log p(t-\mu) + (1 - e_i) \log \left(1 - \int_{-\infty}^{t_i} p(t-\mu) dt \right)
52 | \end{aligned}
53 | $$
54 |
55 |
56 |
57 |
58 | {% raw %}
59 |
60 |
61 |
62 |
63 |
64 |
65 |
66 |
67 |
68 |
69 |
Loss() :: ABC
70 |
71 |
Helper class that provides a standard way to create an ABC using
72 | inheritance.
73 |
74 |
75 |
76 |
77 |
78 |
79 |
80 |
81 |
82 | {% endraw %}
83 |
84 | {% raw %}
85 |
86 |
87 |
88 |
89 | {% endraw %}
90 |
91 | {% raw %}
92 |
93 |
94 |
95 |
96 | {% endraw %}
97 |
98 | {% raw %}
99 |
100 |
101 |
102 |
103 |
104 |
105 |
106 |
107 |
108 |
109 |
AFTLoss() :: Loss
110 |
111 |
Helper class that provides a standard way to create an ABC using
112 | inheritance.
113 |
114 |
115 |
116 |
117 |
118 |
119 |
120 |
121 |
122 | {% endraw %}
123 |
124 | {% raw %}
125 |
126 |
127 |
128 |
129 | {% endraw %}
130 |
131 | {% raw %}
132 |
133 |
134 |
150 |
151 |
152 |
153 |
154 |
155 |
156 |
157 |
158 |
159 |
tensor(-0.0400)
160 |
161 |
162 |
163 |
164 |
165 |
166 |
167 |
168 | {% endraw %}
169 |
170 | {% raw %}
171 |
172 |
173 |
174 |
175 |
176 |
177 |
178 |
179 |
180 |
181 |
aft_loss(log_probe
182 |
183 |
184 |
185 |
186 |
187 |
188 |
189 |
190 |
191 |
192 | {% endraw %}
193 |
194 | {% raw %}
195 |
196 |
197 |
198 |
199 | {% endraw %}
200 |
201 |
202 |
203 |
We use the following loss function to infer our model. See here for theory.
204 | $$
205 | -\log L = \sum_{i=1}^N \Lambda(t_i) - d_i \log \lambda(t_i)
206 | $$
207 |
208 |
209 |
210 |
211 | {% raw %}
212 |
213 |
214 |
215 |
216 |
217 |
218 |
219 |
220 |
221 |
222 |
HazardLoss() :: Loss
223 |
224 |
Helper class that provides a standard way to create an ABC using
225 | inheritance.
226 |
227 |
228 |
229 |
230 |
231 |
232 |
233 |
234 |
235 | {% endraw %}
236 |
237 | {% raw %}
238 |
239 |
240 |
241 |
242 | {% endraw %}
243 |
244 | {% raw %}
245 |
246 |
247 |
248 |
249 |
250 |
251 |
252 |
253 |
254 |
255 |
hazard_loss(hazardTuple[Tensor, Tensor], eTensor)
256 |
257 |
parameters:
258 |
259 | hazard: log hazard and Cumulative hazard
260 | e: torch.Tensor of 1 if death event occured and 0 otherwise
261 |
262 |
263 |
264 |
265 |
266 |
267 |
268 |
269 |
270 |
271 | {% endraw %}
272 |
273 | {% raw %}
274 |
275 |
276 |
277 |
278 | {% endraw %}
279 |
280 |
24 |
25 | {% raw %}
26 |
27 |
28 |
29 |
30 | {% endraw %}
31 |
32 | {% raw %}
33 |
34 |
35 |
36 |
37 | {% endraw %}
38 |
39 | {% raw %}
40 |
41 |
42 |
43 |
44 |
45 |
46 |
47 |
48 |
49 |
50 |
TestData(tarray, bOptional[array]=NonexOptional[array]=Nonet_scalerMaxAbsScaler=Nonex_scalerStandardScaler=NoneDataset
51 |
52 |
Create pyTorch Dataset
53 | parameters:
54 |
55 | t: time elapsed
56 | b: (optional) breakpoints where the hazard is different to previous segment of time.
57 | Must include 0 as first element and the maximum time as last element
58 | x: (optional) features
59 |
60 |
61 |
62 |
63 |
64 |
65 |
66 |
67 |
68 |
69 | {% endraw %}
70 |
71 | {% raw %}
72 |
73 |
74 |
75 |
76 | {% endraw %}
77 |
78 | {% raw %}
79 |
80 |
81 |
82 |
83 |
84 |
85 |
86 |
87 |
88 |
89 |
Data(tarray, earray, bOptional[array]=NonexOptional[array]=Nonet_scalerMaxAbsScaler=Nonex_scalerStandardScaler=NoneTestData
90 |
91 |
Create pyTorch Dataset
92 | parameters:
93 |
94 | t: time elapsed
95 | e: (death) event observed. 1 if observed, 0 otherwise.
96 | b: (optional) breakpoints where the hazard is different to previous segment of time.
97 | x: (optional) features
98 |
99 |
100 |
101 |
102 |
103 |
104 |
105 |
106 |
107 |
108 | {% endraw %}
109 |
110 | {% raw %}
111 |
112 |
113 |
114 |
115 | {% endraw %}
116 |
117 | {% raw %}
118 |
119 |
120 |
121 |
122 |
123 |
124 |
125 |
126 |
127 |
128 |
TestDataFrame(dfDataFramebOptional[array]=Nonet_scalerMaxAbsScaler=Nonex_scalerStandardScaler=NoneTestData
129 |
130 |
Wrapper around Data Class that takes in a dataframe instead
131 | parameters:
132 |
133 | df: dataframe. **Must have t (time) and e (event) columns, other cols optional.
134 | b: breakpoints of time (optional)
135 |
136 |
137 |
138 |
139 |
140 |
141 |
142 |
143 |
144 |
145 | {% endraw %}
146 |
147 | {% raw %}
148 |
149 |
150 |
151 |
152 | {% endraw %}
153 |
154 | {% raw %}
155 |
156 |
157 |
158 |
159 |
160 |
161 |
162 |
163 |
164 |
165 |
DataFrame(dataNoneindexOptional[Collection[T_co]]=NonecolumnsOptional[Collection[T_co]]=NonedtypeUnion[ForwardRef('ExtensionDtype'), str, dtype, Type[Union[str, float, int, complex, bool]], NoneType]=Nonecopybool=FalseNDFrame
166 |
167 |
Two-dimensional, size-mutable, potentially heterogeneous tabular data.
168 |
Data structure also contains labeled axes (rows and columns).
169 | Arithmetic operations align on both row and column labels. Can be
170 | thought of as a dict-like container for Series objects. The primary
171 | pandas data structure.
172 |
Parameters data : ndarray (structured or homogeneous), Iterable, dict, or DataFrame
173 | Dict can contain Series, arrays, constants, or list-like objects.
174 |
175 |
.. versionchanged:: 0.23.0
176 | If data is a dict, column order follows insertion-order for
177 | Python 3.6 and later.
178 |
179 | .. versionchanged:: 0.25.0
180 | If data is a list of dicts, column order follows insertion-order
181 | for Python 3.6 and later.
182 |
183 |
184 |
index : Index or array-like
185 | Index to use for resulting frame. Will default to RangeIndex if
186 | no indexing information part of input data and no index provided.
187 | columns : Index or array-like
188 | Column labels to use for resulting frame. Will default to
189 | RangeIndex (0, 1, 2, ..., n) if no column labels are provided.
190 | dtype : dtype, default None
191 | Data type to force. Only a single dtype is allowed. If None, infer.
192 | copy : bool, default False
193 | Copy data from inputs. Only affects DataFrame / 2d ndarray input.
194 |
See Also DataFrame.from_records : Constructor from tuples, also record arrays.
195 | DataFrame.from_dict : From dicts of Series, arrays, or dicts.
196 | read_csv : Read a comma-separated values (csv) file into DataFrame.
197 | read_table : Read general delimited file into DataFrame.
198 | read_clipboard : Read text from clipboard into DataFrame.
199 |
Examples Constructing DataFrame from a dictionary.
200 |
d = {'col1': [1, 2], 'col2': [3, 4]}
201 | df = pd.DataFrame(data=d)
202 | df
203 | col1 col2
204 | 0 1 3
205 | 1 2 4
206 |
209 |
Notice that the inferred dtype is int64.
210 |
df.dtypes
211 | col1 int64
212 | col2 int64
213 | dtype: object
214 |
217 |
To enforce a single dtype:
218 |
df = pd.DataFrame(data=d, dtype=np.int8)
219 | df.dtypes
220 | col1 int8
221 | col2 int8
222 | dtype: object
223 |
226 |
Constructing DataFrame from numpy ndarray:
227 |
df2 = pd.DataFrame(np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]),
228 | ... columns=['a', 'b', 'c'])
229 | df2
230 | a b c
231 | 0 1 2 3
232 | 1 4 5 6
233 | 2 7 8 9
234 |
237 |
238 |
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240 |
241 |
242 |
243 |
244 |
245 |
246 | {% endraw %}
247 |
248 | {% raw %}
249 |
250 |
251 |
252 |
253 | {% endraw %}
254 |
255 |
256 |
257 |
Create iterable data loaders/ fastai databunch using above:
258 |
259 |
260 |
261 |
262 | {% raw %}
263 |
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265 |
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267 |
268 |
269 |
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273 |
create_dl(dfDataFramebOptional[array]=Nonetrain_sizefloat=0.8random_stateNonebsint=128
274 |
275 |
Take dataframe and split into train, test, val (optional)
276 | and convert to Fastai databunch
277 |
parameters:
278 |
279 | df: pandas dataframe
280 | b(optional): breakpoints of time. Must include 0 as first element and the maximum time as last element
281 | train_p: training percentage
282 | bs: batch size
283 |
284 |
285 |
286 |
287 |
288 |
289 |
290 |
291 |
292 |
293 | {% endraw %}
294 |
295 | {% raw %}
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301 |
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305 |
306 |
create_test_dl(dfDataFramebOptional[array]=Nonet_scalerMaxAbsScaler=Nonex_scalerStandardScaler=Nonebsint=128only_xbool=False
307 |
308 |
Take dataframe and return a pytorch dataloader.
309 | parameters:
310 |
311 | df: pandas dataframe
312 | b: breakpoints of time (optional)
313 | bs: batch size
314 |
315 |
316 |
317 |
318 |
319 |
320 |
321 |
322 |
323 |
324 | {% endraw %}
325 |
326 | {% raw %}
327 |
328 |
329 |
330 |
331 | {% endraw %}
332 |
333 | {% raw %}
334 |
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336 |
337 |
338 |
339 |
340 |
341 |
342 |
343 |
344 |
get_breakpoints(dfDataFramepercentileslist=[20, 40, 60, 80]
345 |
346 |
Gives the times at which death events occur at given percentile
347 | parameters:
348 | df - must contain columns 't' (time) and 'e' (death event)
349 | percentiles - list of percentages at which breakpoints occur (do not include 0 and 100)
350 |
351 |
352 |
353 |
354 |
355 |
356 |
357 |
358 |
359 | {% endraw %}
360 |
361 | {% raw %}
362 |
363 |
364 |
365 |
366 | {% endraw %}
367 |
368 |