build based on 8939ff8

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.11.0","generation_timestamp":"2024-10-11T05:33:36","documenter_version":"1.7.0"}}
+{"documenter":{"julia_version":"1.11.0","generation_timestamp":"2024-10-11T05:49:33","documenter_version":"1.7.0"}}

dev/index.html

@@ -13,4 +13,4 @@
 Y_compressed = compress(poisson_epca, Y; maxiter=200, verbose=true)
 
 X_reconstructed = decompress(poisson_epca, X_compressed)
-Y_reconstructed = decompress(poisson_epca, Y_compressed)</code></pre><h2 id="Supported-Distributions"><a class="docs-heading-anchor" href="#Supported-Distributions">Supported Distributions</a><a id="Supported-Distributions-1"></a><a class="docs-heading-anchor-permalink" href="#Supported-Distributions" title="Permalink"></a></h2><table><tr><th style="text-align: right">Distribution</th><th style="text-align: right"><code>ExpFamilyPCA.jl</code></th><th style="text-align: right">Objective</th><th style="text-align: right">Link Function <span>$g(\theta)$</span></th></tr><tr><td style="text-align: right">Bernoulli</td><td style="text-align: right"><code>BernoulliEPCA</code></td><td style="text-align: right"><span>$\log(1 + e^{\theta - 2x\theta})$</span></td><td style="text-align: right"><span>$\frac{e^\theta}{1 + e^\theta}$</span></td></tr><tr><td style="text-align: right">Binomial</td><td style="text-align: right"><code>BinomialEPCA</code></td><td style="text-align: right"><span>$n \log(1 + e^\theta) - x\theta$</span></td><td style="text-align: right"><span>$\frac{ne^\theta}{1 + e^\theta}$</span></td></tr><tr><td style="text-align: right">Continuous Bernoulli</td><td style="text-align: right"><code>ContinuousBernoulliEPCA</code></td><td style="text-align: right"><span>$\log\left(\frac{e^\theta - 1}{\theta}\right) - x\theta$</span></td><td style="text-align: right"><span>$\frac{\theta - 1}{\theta} + \frac{1}{e^\theta - 1}$</span></td></tr><tr><td style="text-align: right">Gamma¹</td><td style="text-align: right"><code>GammaEPCA</code> or <code>ItakuraSaitoEPCA</code></td><td style="text-align: right"><span>$-\log(-\theta) - x\theta$</span></td><td style="text-align: right"><span>$-\frac{1}{\theta}$</span></td></tr><tr><td style="text-align: right">Gaussian²</td><td style="text-align: right"><code>GaussianEPCA</code> or <code>NormalEPCA</code></td><td style="text-align: right"><span>$\frac{1}{2}(x - \theta)^2$</span></td><td style="text-align: right"><span>$\theta$</span></td></tr><tr><td style="text-align: right">Negative Binomial</td><td style="text-align: right"><code>NegativeBinomialEPCA</code></td><td style="text-align: right"><span>$-r \log(1 - e^\theta) - x\theta$</span></td><td style="text-align: right"><span>$\frac{-re^\theta}{e^\theta - 1}$</span></td></tr><tr><td style="text-align: right">Pareto</td><td style="text-align: right"><code>ParetoEPCA</code></td><td style="text-align: right"><span>$-\log(-1 - \theta) + \theta \log m - x\theta$</span></td><td style="text-align: right"><span>$\log m - \frac{1}{\theta + 1}$</span></td></tr><tr><td style="text-align: right">Poisson³</td><td style="text-align: right"><code>PoissonEPCA</code></td><td style="text-align: right"><span>$e^\theta - x\theta$</span></td><td style="text-align: right"><span>$e^\theta$</span></td></tr><tr><td style="text-align: right">Weibull</td><td style="text-align: right"><code>WeibullEPCA</code></td><td style="text-align: right"><span>$-\log(-\theta) - x\theta$</span></td><td style="text-align: right"><span>$-\frac{1}{\theta}$</span></td></tr></table><p>¹: For the Gamma distribution, the link function is typically based on the inverse relationship.  </p><p>²: For Gaussian, also known as Normal distribution, the link function is the identity. </p><p>³: The Poisson distribution link function is exponential.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="math/intro/">Introduction »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 11 October 2024 05:33">Friday 11 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+Y_reconstructed = decompress(poisson_epca, Y_compressed)</code></pre><h2 id="Supported-Distributions"><a class="docs-heading-anchor" href="#Supported-Distributions">Supported Distributions</a><a id="Supported-Distributions-1"></a><a class="docs-heading-anchor-permalink" href="#Supported-Distributions" title="Permalink"></a></h2><table><tr><th style="text-align: right">Distribution</th><th style="text-align: right"><code>ExpFamilyPCA.jl</code></th><th style="text-align: right">Objective</th><th style="text-align: right">Link Function <span>$g(\theta)$</span></th></tr><tr><td style="text-align: right">Bernoulli</td><td style="text-align: right"><code>BernoulliEPCA</code></td><td style="text-align: right"><span>$\log(1 + e^{\theta - 2x\theta})$</span></td><td style="text-align: right"><span>$\frac{e^\theta}{1 + e^\theta}$</span></td></tr><tr><td style="text-align: right">Binomial</td><td style="text-align: right"><code>BinomialEPCA</code></td><td style="text-align: right"><span>$n \log(1 + e^\theta) - x\theta$</span></td><td style="text-align: right"><span>$\frac{ne^\theta}{1 + e^\theta}$</span></td></tr><tr><td style="text-align: right">Continuous Bernoulli</td><td style="text-align: right"><code>ContinuousBernoulliEPCA</code></td><td style="text-align: right"><span>$\log\left(\frac{e^\theta - 1}{\theta}\right) - x\theta$</span></td><td style="text-align: right"><span>$\frac{\theta - 1}{\theta} + \frac{1}{e^\theta - 1}$</span></td></tr><tr><td style="text-align: right">Gamma¹</td><td style="text-align: right"><code>GammaEPCA</code> or <code>ItakuraSaitoEPCA</code></td><td style="text-align: right"><span>$-\log(-\theta) - x\theta$</span></td><td style="text-align: right"><span>$-\frac{1}{\theta}$</span></td></tr><tr><td style="text-align: right">Gaussian²</td><td style="text-align: right"><code>GaussianEPCA</code> or <code>NormalEPCA</code></td><td style="text-align: right"><span>$\frac{1}{2}(x - \theta)^2$</span></td><td style="text-align: right"><span>$\theta$</span></td></tr><tr><td style="text-align: right">Negative Binomial</td><td style="text-align: right"><code>NegativeBinomialEPCA</code></td><td style="text-align: right"><span>$-r \log(1 - e^\theta) - x\theta$</span></td><td style="text-align: right"><span>$\frac{-re^\theta}{e^\theta - 1}$</span></td></tr><tr><td style="text-align: right">Pareto</td><td style="text-align: right"><code>ParetoEPCA</code></td><td style="text-align: right"><span>$-\log(-1 - \theta) + \theta \log m - x\theta$</span></td><td style="text-align: right"><span>$\log m - \frac{1}{\theta + 1}$</span></td></tr><tr><td style="text-align: right">Poisson³</td><td style="text-align: right"><code>PoissonEPCA</code></td><td style="text-align: right"><span>$e^\theta - x\theta$</span></td><td style="text-align: right"><span>$e^\theta$</span></td></tr><tr><td style="text-align: right">Weibull</td><td style="text-align: right"><code>WeibullEPCA</code></td><td style="text-align: right"><span>$-\log(-\theta) - x\theta$</span></td><td style="text-align: right"><span>$-\frac{1}{\theta}$</span></td></tr></table><p>¹: For the Gamma distribution, the link function is typically based on the inverse relationship.  </p><p>²: For Gaussian, also known as Normal distribution, the link function is the identity. </p><p>³: The Poisson distribution link function is exponential.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="math/intro/">Introduction »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 11 October 2024 05:49">Friday 11 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/math/appendix/expectation/index.html

@@ -7,4 +7,4 @@
 &= \int x \exp(x \theta - G(\theta)) h(x) \, dx \\
 &= \int x p_\theta(x) \, dx \\
 &= \mathbb{E}_\theta[X].
-\end{aligned}\]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../inverses/">« Inverse Link Functions</a><a class="docs-footer-nextpage" href="../../references/">References »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 11 October 2024 05:33">Friday 11 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+\end{aligned}\]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../inverses/">« Inverse Link Functions</a><a class="docs-footer-nextpage" href="../../references/">References »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 11 October 2024 05:49">Friday 11 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/math/appendix/gamma/index.html

@@ -11,4 +11,4 @@
 &= \frac{p}{q} - \log \frac{p}{q} - 1,
 \end{aligned}\]</p><p>so <span>$B_F$</span> is the Itakura-Saito (<a href="../../references/#ItakuraSaito">Itakura and Saito, 1968</a>) distance as desired. Further, the EPCA objective is</p><p class="math-container">\[\begin{aligned}
 B_F(x \| g(\theta)) = \frac{p}{g(\theta)} - \log \frac{p}{g(\theta)} - 1 = -p\theta - \log(-p\theta) - 1.
-\end{aligned}\]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../objectives/">« EPCA Objectives</a><a class="docs-footer-nextpage" href="../poisson/">Poisson EPCA and Generalized KL-Divergence »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 11 October 2024 05:33">Friday 11 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+\end{aligned}\]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../objectives/">« EPCA Objectives</a><a class="docs-footer-nextpage" href="../poisson/">Poisson EPCA and Generalized KL-Divergence »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 11 October 2024 05:49">Friday 11 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/math/appendix/gaussian/index.html

@@ -6,4 +6,4 @@
 &= \frac{1}{2} \big[ \langle A, A \rangle - 2\langle B, A \rangle + \langle B, B \rangle \big] \\
 &= \frac{1}{2} \langle A - B, A - B \rangle \\
 &= \frac{1}{2} \| A - B \|_F^2.
-\end{aligned}\]</p><p>Similarly, the Bregman divergence induced from the log-partition of the Gaussian <span>$G(\theta) = \theta^2/2$</span> is the squared Euclidean distance.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../poisson/">« Poisson EPCA and Generalized KL-Divergence</a><a class="docs-footer-nextpage" href="../inverses/">Inverse Link Functions »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 11 October 2024 05:33">Friday 11 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+\end{aligned}\]</p><p>Similarly, the Bregman divergence induced from the log-partition of the Gaussian <span>$G(\theta) = \theta^2/2$</span> is the squared Euclidean distance.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../poisson/">« Poisson EPCA and Generalized KL-Divergence</a><a class="docs-footer-nextpage" href="../inverses/">Inverse Link Functions »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 11 October 2024 05:49">Friday 11 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>