build based on 5cc6f44

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-11T20:44:19","documenter_version":"1.2.1"}}
+{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-12T10:00:14","documenter_version":"1.2.1"}}

dev/examples/autodiff/index.html

@@ -41,4 +41,4 @@
     Enzyme.Duplicated(params, params_shadow),
 )
 
-grad_e = params_shadow</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">ComponentVector{Float64}(init = [2.461586483904971, 0.15365406438011528], trans = [13.541230697414639 16.653550286760073; 13.64721549300123 13.472726825544802], means = [-1.5783255775403202, -2.098528923154286])</code></pre><pre><code class="language-julia hljs">grad_e ≈ grad_f</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">true</code></pre><h2 id="Gradient-methods"><a class="docs-heading-anchor" href="#Gradient-methods">Gradient methods</a><a id="Gradient-methods-1"></a><a class="docs-heading-anchor-permalink" href="#Gradient-methods" title="Permalink"></a></h2><p>Once we have gradients of the loglikelihood, it is a natural idea to perform gradient descent in order to fit the parameters of a custom HMM. However, there are two caveats we must keep in mind.</p><p>First, computing a gradient essentially requires running the forward-backward algorithm, which means it is expensive. Given the output of forward-backward, if there is a way to perform a more accurate parameter update (like going straight to the maximum likelihood value), it is probably worth it. That is what we show in the other tutorials with the reimplementation of the <code>fit!</code> method.</p><p>Second, HMM parameters live in a constrained space, which calls for a projected gradient descent. Most notably, the transition matrix must be stochastic, and the orthogonal projection onto this set (the Birkhoff polytope) is not easy to obtain.</p><p>Still, first order optimization can be relevant when we lack explicit formulas for maximum likelihood.</p><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../interfaces/">« Interfaces</a><a class="docs-footer-nextpage" href="../temporal/">Time dependency »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Monday 11 December 2023 20:44">Monday 11 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+grad_e = params_shadow</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">ComponentVector{Float64}(init = [2.461586483904971, 0.15365406438011528], trans = [13.541230697414639 16.653550286760073; 13.64721549300123 13.472726825544802], means = [-1.5783255775403202, -2.098528923154286])</code></pre><pre><code class="language-julia hljs">grad_e ≈ grad_f</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">true</code></pre><h2 id="Gradient-methods"><a class="docs-heading-anchor" href="#Gradient-methods">Gradient methods</a><a id="Gradient-methods-1"></a><a class="docs-heading-anchor-permalink" href="#Gradient-methods" title="Permalink"></a></h2><p>Once we have gradients of the loglikelihood, it is a natural idea to perform gradient descent in order to fit the parameters of a custom HMM. However, there are two caveats we must keep in mind.</p><p>First, computing a gradient essentially requires running the forward-backward algorithm, which means it is expensive. Given the output of forward-backward, if there is a way to perform a more accurate parameter update (like going straight to the maximum likelihood value), it is probably worth it. That is what we show in the other tutorials with the reimplementation of the <code>fit!</code> method.</p><p>Second, HMM parameters live in a constrained space, which calls for a projected gradient descent. Most notably, the transition matrix must be stochastic, and the orthogonal projection onto this set (the Birkhoff polytope) is not easy to obtain.</p><p>Still, first order optimization can be relevant when we lack explicit formulas for maximum likelihood.</p><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../interfaces/">« Interfaces</a><a class="docs-footer-nextpage" href="../temporal/">Time dependency »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Tuesday 12 December 2023 10:00">Tuesday 12 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/examples/basics/index.html

@@ -44,4 +44,4 @@
  0.7  0.3
  0.3  0.7</code></pre><pre><code class="language-julia hljs">map(dist -&gt; dist.μ, hcat(obs_distributions(hmm_est_concat), obs_distributions(hmm)))</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">2×2 Matrix{Vector{Float64}}:
  [-0.924126, -1.03495, -1.03126]  [-1.0, -1.0, -1.0]
- [0.989244, 1.00748, 0.933342]    [1.0, 1.0, 1.0]</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../api/">« API reference</a><a class="docs-footer-nextpage" href="../types/">Types »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Monday 11 December 2023 20:44">Monday 11 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ [0.989244, 1.00748, 0.933342]    [1.0, 1.0, 1.0]</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../api/">« API reference</a><a class="docs-footer-nextpage" href="../types/">Types »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Tuesday 12 December 2023 10:00">Tuesday 12 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/examples/controlled/index.html

@@ -74,4 +74,4 @@
  -0.994459  -1.0</code></pre><pre><code class="language-julia hljs">hcat(hmm_est.dist_coeffs[2], hmm.dist_coeffs[2])</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">3×2 Matrix{Float64}:
  0.994041  1.0
  0.994866  1.0
- 1.02258   1.0</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../temporal/">« Time dependency</a><a class="docs-footer-nextpage" href="../../alternatives/">Alternatives »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Monday 11 December 2023 20:44">Monday 11 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ 1.02258   1.0</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../temporal/">« Time dependency</a><a class="docs-footer-nextpage" href="../../alternatives/">Alternatives »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Tuesday 12 December 2023 10:00">Tuesday 12 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/examples/interfaces/index.html

@@ -88,4 +88,4 @@
 
 [:, :, 2] =
  0.591969  0.408031
- 0.42277   0.57723</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../types/">« Types</a><a class="docs-footer-nextpage" href="../autodiff/">Autodiff »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Monday 11 December 2023 20:44">Monday 11 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ 0.42277   0.57723</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../types/">« Types</a><a class="docs-footer-nextpage" href="../autodiff/">Autodiff »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Tuesday 12 December 2023 10:00">Tuesday 12 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/examples/temporal/index.html

@@ -99,4 +99,4 @@
  Distributions.Normal{Float64}(μ=-0.953169, σ=0.999476)  …  Distributions.Normal{Float64}(μ=-1.0, σ=1.0)
  Distributions.Normal{Float64}(μ=-1.96275, σ=1.00499)       Distributions.Normal{Float64}(μ=-2.0, σ=1.0)</code></pre><pre><code class="language-julia hljs">hcat(obs_distributions(hmm_est, 2), obs_distributions(hmm, 2))</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">2×2 Matrix{Distributions.Normal{Float64}}:
  Distributions.Normal{Float64}(μ=0.948362, σ=0.976429)  …  Distributions.Normal{Float64}(μ=1.0, σ=1.0)
- Distributions.Normal{Float64}(μ=1.99179, σ=0.994492)      Distributions.Normal{Float64}(μ=2.0, σ=1.0)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../autodiff/">« Autodiff</a><a class="docs-footer-nextpage" href="../controlled/">Control dependency »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Monday 11 December 2023 20:44">Monday 11 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ Distributions.Normal{Float64}(μ=1.99179, σ=0.994492)      Distributions.Normal{Float64}(μ=2.0, σ=1.0)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../autodiff/">« Autodiff</a><a class="docs-footer-nextpage" href="../controlled/">Control dependency »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Tuesday 12 December 2023 10:00">Tuesday 12 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>