dimitri/blog
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

Cosmetic improvements

Browse source
This commit is contained in:
Dimitri Lozeve 2020-08-30 23:10:39 +02:00
parent 921dda9a72
commit 55b9e2523c
32 changed files with 88 additions and 358 deletions
Download patch file Download diff file Expand all files Collapse all files

18
_site/archive.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="./rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="./rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>
@ -50,7 +40,7 @@
</article> </article>
Here you can find all my previous posts: <p>Here you can find all my previous posts:</p>
<ul> <ul>
<li> <li>

2
_site/atom.xml
View file

@ -637,7 +637,7 @@
x_n)\)</span>, and <span class="math inline">\(y = (y_1, y_2, \ldots, y_n)\)</span>, along with probability distributions <span class="math inline">\(p \in \Delta^n\)</span>, <span class="math inline">\(q \in \Delta^m\)</span> over <span class="math inline">\(x\)</span> and <span class="math inline">\(y\)</span> (<span class="math inline">\(\Delta^n\)</span> is the probability simplex of dimension <span class="math inline">\(n\)</span>, i.e. the set of vectors of size <span class="math inline">\(n\)</span> summing to 1). We can then define the Wasserstein distance as <span class="math display">\[ x_n)\)</span>, and <span class="math inline">\(y = (y_1, y_2, \ldots, y_n)\)</span>, along with probability distributions <span class="math inline">\(p \in \Delta^n\)</span>, <span class="math inline">\(q \in \Delta^m\)</span> over <span class="math inline">\(x\)</span> and <span class="math inline">\(y\)</span> (<span class="math inline">\(\Delta^n\)</span> is the probability simplex of dimension <span class="math inline">\(n\)</span>, i.e. the set of vectors of size <span class="math inline">\(n\)</span> summing to 1). We can then define the Wasserstein distance as <span class="math display">\[
W_1(p, q) = \min_{P \in \mathbb{R}_+^{n\times m}} \sum_{i,j} C_{i,j} P_{i,j} W_1(p, q) = \min_{P \in \mathbb{R}_+^{n\times m}} \sum_{i,j} C_{i,j} P_{i,j}
\]</span> <span class="math display">\[ \]</span> <span class="math display">\[
\text{\small subject to } \sum_j P_{i,j} = p_i \text{ \small and } \sum_i P_{i,j} = q_j, \text{subject to } \sum_j P_{i,j} = p_i \text{ and } \sum_i P_{i,j} = q_j,
\]</span> where <span class="math inline">\(C_{i,j} = d(x_i, x_j)\)</span> are the costs computed from the original distance between points, and <span class="math inline">\(P_{i,j}\)</span> represent the amount we are moving from pile <span class="math inline">\(i\)</span> to pile <span class="math inline">\(j\)</span>.</p> \]</span> where <span class="math inline">\(C_{i,j} = d(x_i, x_j)\)</span> are the costs computed from the original distance between points, and <span class="math inline">\(P_{i,j}\)</span> represent the amount we are moving from pile <span class="math inline">\(i\)</span> to pile <span class="math inline">\(j\)</span>.</p>
<p>Now, how can this be applied to a natural language setting? Once we have word embeddings, we can consider that the vocabulary forms a metric space (we can compute a distance, for instance the euclidean or the <a href="https://en.wikipedia.org/wiki/Cosine_similarity">cosine distance</a>, between two word embeddings). The key is to define documents as <em>distributions</em> over words.</p> <p>Now, how can this be applied to a natural language setting? Once we have word embeddings, we can consider that the vocabulary forms a metric space (we can compute a distance, for instance the euclidean or the <a href="https://en.wikipedia.org/wiki/Cosine_similarity">cosine distance</a>, between two word embeddings). The key is to define documents as <em>distributions</em> over words.</p>
<p>Given a vocabulary <span class="math inline">\(V \subset \mathbb{R}^n\)</span> and a corpus <span class="math inline">\(D = (d^1, d^2, \ldots, d^{\lvert D \rvert})\)</span>, we represent a document as <span class="math inline">\(d^i \in \Delta^{l_i}\)</span> where <span class="math inline">\(l_i\)</span> is the number of unique words in <span class="math inline">\(d^i\)</span>, and <span class="math inline">\(d^i_j\)</span> is the proportion of word <span class="math inline">\(v_j\)</span> in the document <span class="math inline">\(d^i\)</span>. The word mover’s distance (WMD) is then defined simply as <span class="math display">\[ \operatorname{WMD}(d^1, d^2) = W_1(d^1, d^2). \]</span></p> <p>Given a vocabulary <span class="math inline">\(V \subset \mathbb{R}^n\)</span> and a corpus <span class="math inline">\(D = (d^1, d^2, \ldots, d^{\lvert D \rvert})\)</span>, we represent a document as <span class="math inline">\(d^i \in \Delta^{l_i}\)</span> where <span class="math inline">\(l_i\)</span> is the number of unique words in <span class="math inline">\(d^i\)</span>, and <span class="math inline">\(d^i_j\)</span> is the proportion of word <span class="math inline">\(v_j\)</span> in the document <span class="math inline">\(d^i\)</span>. The word mover’s distance (WMD) is then defined simply as <span class="math display">\[ \operatorname{WMD}(d^1, d^2) = W_1(d^1, d^2). \]</span></p>

16
_site/contact.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="./rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="./rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

2
_site/css/default.css
View file

@ -1 +1 @@
body{background:#fafafa;counter-reset:theorem;counter-reset:definition;counter-reset:sidenote-counter}header{margin:1em 0 2em 0}header nav{width:87.5%}header nav a{display:inline-block;font-size:1.4rem;font-weight:bold;text-decoration:none!important;margin:0 0.5rem;padding:0 0}header nav a:first-child{margin-left:0}header nav a:last-child{margin-right:0}footer{margin-top:3rem;padding:.5rem 0;border-top:0.1rem solid #000;color:#555}article .header{font-style:italic;color:#555}blockquote{display:block;border-left:2px solid #808080;padding-left:1rem;margin-top:1rem;margin-bottom:1rem;color:#333;background:#eeeeee}.definition,.proposition,.theorem{display:block;border-left:2px solid #808080;padding-left:1rem;margin-top:1rem;margin-bottom:1rem}.proposition,.theorem{counter-increment:theorem;font-style:italic}.definition p:first-child,.proposition p:first-child,.theorem p:first-child,.proof p:first-child{display:inline}.definition p,.proposition p,.theorem p,.proof p{margin-top:0.4rem;margin-bottom:0.4rem;padding-left:1rem}.theorem:before{content:"Theorem " counter(theorem) ".";font-weight:bold;font-style:normal}.proposition:before{content:"Proposition " counter(theorem) ".";font-weight:bold;font-style:normal}.definition:before{counter-increment:definition;content:"Definition " counter(definition) ".";font-weight:bold;font-style:normal}.proof:before{content:"Proof.";font-style:italic}.proof:after{content:"\220E";float:right} body{background:#fafafa}header{margin:1em 0 2em 0}header nav{width:87.5%}header nav a{display:inline-block;font-size:1.4rem;font-weight:bold;text-decoration:none!important;margin:0 0.5rem;padding:0 0}header nav a:first-child{margin-left:0}header nav a:last-child{margin-right:0}footer{margin-top:3rem;padding:.5rem 0;border-top:0.1rem solid #000;color:#555}article .header{font-style:italic;color:#555}blockquote{display:block;border-left:2px solid #808080;padding-left:1rem;margin-top:1rem;margin-bottom:1rem;color:#333;background:#eeeeee}.definition,.proposition,.theorem{display:block;border-left:2px solid #808080;padding-left:1rem;margin-top:1rem;margin-bottom:1rem}.proposition,.theorem{font-style:italic}.definition p:first-child,.proposition p:first-child,.theorem p:first-child,.proof p:first-child{display:inline}.definition p,.proposition p,.theorem p,.proof p{margin-top:0.4rem;margin-bottom:0.4rem;padding-left:1rem}.theorem:before{content:"Theorem.";font-weight:bold;font-style:normal}.proposition:before{content:"Proposition.";font-weight:bold;font-style:normal}.definition:before{content:"Definition.";font-weight:bold;font-style:normal}.proof:before{content:"Proof.";font-style:italic}.proof:after{content:"\220E";float:right}

16
_site/cv.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="./rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="./rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/index.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="./rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="./rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/posts/dyalog-apl-competition-2020-phase-1.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/posts/dyalog-apl-competition-2020-phase-2.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/posts/ginibre-ensemble.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

18
_site/posts/hierarchical-optimal-transport-for-document-classification.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>
@ -81,7 +71,7 @@
x_n)\)</span>, and <span class="math inline">\(y = (y_1, y_2, \ldots, y_n)\)</span>, along with probability distributions <span class="math inline">\(p \in \Delta^n\)</span>, <span class="math inline">\(q \in \Delta^m\)</span> over <span class="math inline">\(x\)</span> and <span class="math inline">\(y\)</span> (<span class="math inline">\(\Delta^n\)</span> is the probability simplex of dimension <span class="math inline">\(n\)</span>, i.e. the set of vectors of size <span class="math inline">\(n\)</span> summing to 1). We can then define the Wasserstein distance as <span class="math display">\[ x_n)\)</span>, and <span class="math inline">\(y = (y_1, y_2, \ldots, y_n)\)</span>, along with probability distributions <span class="math inline">\(p \in \Delta^n\)</span>, <span class="math inline">\(q \in \Delta^m\)</span> over <span class="math inline">\(x\)</span> and <span class="math inline">\(y\)</span> (<span class="math inline">\(\Delta^n\)</span> is the probability simplex of dimension <span class="math inline">\(n\)</span>, i.e. the set of vectors of size <span class="math inline">\(n\)</span> summing to 1). We can then define the Wasserstein distance as <span class="math display">\[
W_1(p, q) = \min_{P \in \mathbb{R}_+^{n\times m}} \sum_{i,j} C_{i,j} P_{i,j} W_1(p, q) = \min_{P \in \mathbb{R}_+^{n\times m}} \sum_{i,j} C_{i,j} P_{i,j}
\]</span> <span class="math display">\[ \]</span> <span class="math display">\[
\text{\small subject to } \sum_j P_{i,j} = p_i \text{ \small and } \sum_i P_{i,j} = q_j, \text{subject to } \sum_j P_{i,j} = p_i \text{ and } \sum_i P_{i,j} = q_j,
\]</span> where <span class="math inline">\(C_{i,j} = d(x_i, x_j)\)</span> are the costs computed from the original distance between points, and <span class="math inline">\(P_{i,j}\)</span> represent the amount we are moving from pile <span class="math inline">\(i\)</span> to pile <span class="math inline">\(j\)</span>.</p> \]</span> where <span class="math inline">\(C_{i,j} = d(x_i, x_j)\)</span> are the costs computed from the original distance between points, and <span class="math inline">\(P_{i,j}\)</span> represent the amount we are moving from pile <span class="math inline">\(i\)</span> to pile <span class="math inline">\(j\)</span>.</p>
<p>Now, how can this be applied to a natural language setting? Once we have word embeddings, we can consider that the vocabulary forms a metric space (we can compute a distance, for instance the euclidean or the <a href="https://en.wikipedia.org/wiki/Cosine_similarity">cosine distance</a>, between two word embeddings). The key is to define documents as <em>distributions</em> over words.</p> <p>Now, how can this be applied to a natural language setting? Once we have word embeddings, we can consider that the vocabulary forms a metric space (we can compute a distance, for instance the euclidean or the <a href="https://en.wikipedia.org/wiki/Cosine_similarity">cosine distance</a>, between two word embeddings). The key is to define documents as <em>distributions</em> over words.</p>
<p>Given a vocabulary <span class="math inline">\(V \subset \mathbb{R}^n\)</span> and a corpus <span class="math inline">\(D = (d^1, d^2, \ldots, d^{\lvert D \rvert})\)</span>, we represent a document as <span class="math inline">\(d^i \in \Delta^{l_i}\)</span> where <span class="math inline">\(l_i\)</span> is the number of unique words in <span class="math inline">\(d^i\)</span>, and <span class="math inline">\(d^i_j\)</span> is the proportion of word <span class="math inline">\(v_j\)</span> in the document <span class="math inline">\(d^i\)</span>. The word mover’s distance (WMD) is then defined simply as <span class="math display">\[ \operatorname{WMD}(d^1, d^2) = W_1(d^1, d^2). \]</span></p> <p>Given a vocabulary <span class="math inline">\(V \subset \mathbb{R}^n\)</span> and a corpus <span class="math inline">\(D = (d^1, d^2, \ldots, d^{\lvert D \rvert})\)</span>, we represent a document as <span class="math inline">\(d^i \in \Delta^{l_i}\)</span> where <span class="math inline">\(l_i\)</span> is the number of unique words in <span class="math inline">\(d^i\)</span>, and <span class="math inline">\(d^i_j\)</span> is the proportion of word <span class="math inline">\(v_j\)</span> in the document <span class="math inline">\(d^i\)</span>. The word mover’s distance (WMD) is then defined simply as <span class="math display">\[ \operatorname{WMD}(d^1, d^2) = W_1(d^1, d^2). \]</span></p>

16
_site/posts/iclr-2020-notes.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/posts/ising-apl.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/posts/ising-model.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/posts/lsystems.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/posts/operations-research-references.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/posts/peano.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/posts/reinforcement-learning-1.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/posts/self-learning-chatbots-destygo.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/projects.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="./rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="./rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/projects/adsb.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/projects/civilisation.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/projects/community-detection.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/projects/ising-model.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/projects/lsystems.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/projects/orbit.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/projects/satrap.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/projects/tda.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

16
_site/projects/ww2-bombings.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="../rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

2
_site/rss.xml
View file

@ -633,7 +633,7 @@
x_n)\)</span>, and <span class="math inline">\(y = (y_1, y_2, \ldots, y_n)\)</span>, along with probability distributions <span class="math inline">\(p \in \Delta^n\)</span>, <span class="math inline">\(q \in \Delta^m\)</span> over <span class="math inline">\(x\)</span> and <span class="math inline">\(y\)</span> (<span class="math inline">\(\Delta^n\)</span> is the probability simplex of dimension <span class="math inline">\(n\)</span>, i.e. the set of vectors of size <span class="math inline">\(n\)</span> summing to 1). We can then define the Wasserstein distance as <span class="math display">\[ x_n)\)</span>, and <span class="math inline">\(y = (y_1, y_2, \ldots, y_n)\)</span>, along with probability distributions <span class="math inline">\(p \in \Delta^n\)</span>, <span class="math inline">\(q \in \Delta^m\)</span> over <span class="math inline">\(x\)</span> and <span class="math inline">\(y\)</span> (<span class="math inline">\(\Delta^n\)</span> is the probability simplex of dimension <span class="math inline">\(n\)</span>, i.e. the set of vectors of size <span class="math inline">\(n\)</span> summing to 1). We can then define the Wasserstein distance as <span class="math display">\[
W_1(p, q) = \min_{P \in \mathbb{R}_+^{n\times m}} \sum_{i,j} C_{i,j} P_{i,j} W_1(p, q) = \min_{P \in \mathbb{R}_+^{n\times m}} \sum_{i,j} C_{i,j} P_{i,j}
\]</span> <span class="math display">\[ \]</span> <span class="math display">\[
\text{\small subject to } \sum_j P_{i,j} = p_i \text{ \small and } \sum_i P_{i,j} = q_j, \text{subject to } \sum_j P_{i,j} = p_i \text{ and } \sum_i P_{i,j} = q_j,
\]</span> where <span class="math inline">\(C_{i,j} = d(x_i, x_j)\)</span> are the costs computed from the original distance between points, and <span class="math inline">\(P_{i,j}\)</span> represent the amount we are moving from pile <span class="math inline">\(i\)</span> to pile <span class="math inline">\(j\)</span>.</p> \]</span> where <span class="math inline">\(C_{i,j} = d(x_i, x_j)\)</span> are the costs computed from the original distance between points, and <span class="math inline">\(P_{i,j}\)</span> represent the amount we are moving from pile <span class="math inline">\(i\)</span> to pile <span class="math inline">\(j\)</span>.</p>
<p>Now, how can this be applied to a natural language setting? Once we have word embeddings, we can consider that the vocabulary forms a metric space (we can compute a distance, for instance the euclidean or the <a href="https://en.wikipedia.org/wiki/Cosine_similarity">cosine distance</a>, between two word embeddings). The key is to define documents as <em>distributions</em> over words.</p> <p>Now, how can this be applied to a natural language setting? Once we have word embeddings, we can consider that the vocabulary forms a metric space (we can compute a distance, for instance the euclidean or the <a href="https://en.wikipedia.org/wiki/Cosine_similarity">cosine distance</a>, between two word embeddings). The key is to define documents as <em>distributions</em> over words.</p>
<p>Given a vocabulary <span class="math inline">\(V \subset \mathbb{R}^n\)</span> and a corpus <span class="math inline">\(D = (d^1, d^2, \ldots, d^{\lvert D \rvert})\)</span>, we represent a document as <span class="math inline">\(d^i \in \Delta^{l_i}\)</span> where <span class="math inline">\(l_i\)</span> is the number of unique words in <span class="math inline">\(d^i\)</span>, and <span class="math inline">\(d^i_j\)</span> is the proportion of word <span class="math inline">\(v_j\)</span> in the document <span class="math inline">\(d^i\)</span>. The word mover’s distance (WMD) is then defined simply as <span class="math display">\[ \operatorname{WMD}(d^1, d^2) = W_1(d^1, d^2). \]</span></p> <p>Given a vocabulary <span class="math inline">\(V \subset \mathbb{R}^n\)</span> and a corpus <span class="math inline">\(D = (d^1, d^2, \ldots, d^{\lvert D \rvert})\)</span>, we represent a document as <span class="math inline">\(d^i \in \Delta^{l_i}\)</span> where <span class="math inline">\(l_i\)</span> is the number of unique words in <span class="math inline">\(d^i\)</span>, and <span class="math inline">\(d^i_j\)</span> is the proportion of word <span class="math inline">\(v_j\)</span> in the document <span class="math inline">\(d^i\)</span>. The word mover’s distance (WMD) is then defined simply as <span class="math display">\[ \operatorname{WMD}(d^1, d^2) = W_1(d^1, d^2). \]</span></p>

16
_site/skills.html
View file

@ -15,19 +15,9 @@
<!-- RSS feed --> <!-- RSS feed -->
<link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="./rss.xml" /> <link rel="alternate" type="application/rss+xml" title="Dimitri Lozeve's blog" href="./rss.xml" />
<!-- KaTeX CSS styles --> <!-- MathJax -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous"> <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<!-- <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> -->
<!-- <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> -->
</head> </head>
<body> <body>
<article> <article>

2
site.hs
View file

@ -164,7 +164,7 @@ myReadPandocBiblio ropt csl biblio item = do
return $ fmap (const pandoc') item return $ fmap (const pandoc') item
-- Pandoc compiler with KaTeX and bibliography support -------------------- -- Pandoc compiler with maths, TOC, sidenots, and bibliography support --------------------
customPandocCompiler :: Bool -> Compiler (Item String) customPandocCompiler :: Bool -> Compiler (Item String)
customPandocCompiler withTOC = customPandocCompiler withTOC =
let customExtensions = extensionsFromList [Ext_latex_macros] let customExtensions = extensionsFromList [Ext_latex_macros]

2
templates/archive.html
View file

@ -1,2 +1,2 @@
Here you can find all my previous posts: <p>Here you can find all my previous posts:</p>
$partial("templates/post-list.html")$ $partial("templates/post-list.html")$