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update week 13
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doc/pub/week13/html/week13-bs.html

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'boltzmann-machines-and-energy-based-models-and-contrastive-optimization'),
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('Energy models', 2, None, 'energy-models'),
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('Probability model', 2, None, 'probability-model'),
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('Marginal and conditional probabilities',
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<!-- navigation toc: --> <li><a href="#plans-for-the-week-april-21-25-2025" style="font-size: 80%;">Plans for the week April 21-25, 2025</a></li>
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<!-- navigation toc: --> <li><a href="#summary-of-variational-autoencoders-vaes" style="font-size: 80%;">Summary of Variational Autoencoders (VAEs)</a></li>
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<!-- navigation toc: --> <li><a href="#boltzmann-machines-and-energy-based-models-and-contrastive-optimization" style="font-size: 80%;">Boltzmann machines and energy-based models and contrastive optimization</a></li>
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<!-- navigation toc: --> <li><a href="#energy-models" style="font-size: 80%;">Energy models</a></li>
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<!-- navigation toc: --> <li><a href="#probability-model" style="font-size: 80%;">Probability model</a></li>
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<!-- navigation toc: --> <li><a href="#marginal-and-conditional-probabilities" style="font-size: 80%;">Marginal and conditional probabilities</a></li>
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<!-- navigation toc: --> <li><a href="#partition-function" style="font-size: 80%;">Partition function</a></li>
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<!-- todo: add about Langevin sampling, see <a href="https://www.lyndonduong.com/sgmcmc/" target="_self"><tt>https://www.lyndonduong.com/sgmcmc/</tt></a> -->
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<!-- code for VAEs applied to MNIST -->
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<!-- !split -->
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<h2 id="summary-of-variational-autoencoders-vaes" class="anchor">Summary of Variational Autoencoders (VAEs) </h2>
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<p>In our short summary of VAes, we will also remind you about the
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<p>In our summary of VAes from last time, we will also remind you about the
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mathematics of Boltzmann machines and the Kullback-Leibler divergence,
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leading to various ways to optimize the probability
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distributions, namely what is called
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<h2 id="boltzmann-machines-and-energy-based-models-and-contrastive-optimization" class="anchor">Boltzmann machines and energy-based models and contrastive optimization </h2>
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<!-- !split -->
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<h2 id="energy-models" class="anchor">Energy models </h2>
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<p>For Boltzmann machines we defined a domain \( \boldsymbol{X} \) of stochastic variables \( \boldsymbol{X}= \{x_0,x_1, \dots , x_{n-1}\} \) with a pertinent probability distribution</p>
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$$
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p(\boldsymbol{X})=\prod_{x_i\in \boldsymbol{X}}p(x_i),

doc/pub/week13/html/week13-reveal.html

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<!-- todo: add about Langevin sampling, see <a href="https://www.lyndonduong.com/sgmcmc/" target="_blank"><tt>https://www.lyndonduong.com/sgmcmc/</tt></a> -->
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<!-- code for VAEs applied to MNIST -->
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</section>
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<section>
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<h2 id="summary-of-variational-autoencoders-vaes">Summary of Variational Autoencoders (VAEs) </h2>
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<p>In our short summary of VAes, we will also remind you about the
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<p>In our summary of VAes from last time, we will also remind you about the
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mathematics of Boltzmann machines and the Kullback-Leibler divergence,
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leading to various ways to optimize the probability
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distributions, namely what is called
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<section>
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<h2 id="boltzmann-machines-and-energy-based-models-and-contrastive-optimization">Boltzmann machines and energy-based models and contrastive optimization </h2>
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</section>
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<section>
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<h2 id="energy-models">Energy models </h2>
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<p>For Boltzmann machines we defined a domain \( \boldsymbol{X} \) of stochastic variables \( \boldsymbol{X}= \{x_0,x_1, \dots , x_{n-1}\} \) with a pertinent probability distribution</p>
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<p>&nbsp;<br>

doc/pub/week13/html/week13-solarized.html

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'boltzmann-machines-and-energy-based-models-and-contrastive-optimization'),
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('Energy models', 2, None, 'energy-models'),
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('Marginal and conditional probabilities',
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<!-- todo: add about Langevin sampling, see <a href="https://www.lyndonduong.com/sgmcmc/" target="_blank"><tt>https://www.lyndonduong.com/sgmcmc/</tt></a> -->
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<!-- code for VAEs applied to MNIST and CIFAR perhaps -->
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<!-- code for VAEs applied to MNIST -->
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="summary-of-variational-autoencoders-vaes">Summary of Variational Autoencoders (VAEs) </h2>
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<p>In our short summary of VAes, we will also remind you about the
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<p>In our summary of VAes from last time, we will also remind you about the
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mathematics of Boltzmann machines and the Kullback-Leibler divergence,
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leading to various ways to optimize the probability
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distributions, namely what is called
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="boltzmann-machines-and-energy-based-models-and-contrastive-optimization">Boltzmann machines and energy-based models and contrastive optimization </h2>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="energy-models">Energy models </h2>
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<p>For Boltzmann machines we defined a domain \( \boldsymbol{X} \) of stochastic variables \( \boldsymbol{X}= \{x_0,x_1, \dots , x_{n-1}\} \) with a pertinent probability distribution</p>
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doc/pub/week13/html/week13.html

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('Marginal and conditional probabilities',
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<!-- todo: add about Langevin sampling, see <a href="https://www.lyndonduong.com/sgmcmc/" target="_blank"><tt>https://www.lyndonduong.com/sgmcmc/</tt></a> -->
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<!-- code for VAEs applied to MNIST and CIFAR perhaps -->
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<!-- code for VAEs applied to MNIST -->
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="summary-of-variational-autoencoders-vaes">Summary of Variational Autoencoders (VAEs) </h2>
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<p>In our short summary of VAes, we will also remind you about the
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<p>In our summary of VAes from last time, we will also remind you about the
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mathematics of Boltzmann machines and the Kullback-Leibler divergence,
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leading to various ways to optimize the probability
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distributions, namely what is called
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<h2 id="boltzmann-machines-and-energy-based-models-and-contrastive-optimization">Boltzmann machines and energy-based models and contrastive optimization </h2>
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<h2 id="energy-models">Energy models </h2>
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<p>For Boltzmann machines we defined a domain \( \boldsymbol{X} \) of stochastic variables \( \boldsymbol{X}= \{x_0,x_1, \dots , x_{n-1}\} \) with a pertinent probability distribution</p>
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$$
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p(\boldsymbol{X})=\prod_{x_i\in \boldsymbol{X}}p(x_i),
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