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2020-11-25 10:38:50 +01:00
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doc/pub/week48/html/._week48-bs000.html
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@@ -260,7 +260,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>Nov 23, 2020</h4></center> <!-- date -->
<center><h4>Nov 25, 2020</h4></center> <!-- date -->
<br>
<p>
doc/pub/week48/html/._week48-bs001.html
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@@ -244,7 +244,7 @@ MathJax.Hub.Config({
<h2 id="___sec0" class="anchor">Overview of week 48 </h2>
<ul>
<li> <b>Thursday</b>: Support Vector Machines, Kernels, Classification and Regression</li>
<li> <b>Thursday</b>: Support Vector Machines: Kernels, Classification and Regression</li>
<li> <b>Friday</b>: Summary of course with perspectives for future studies</li>
</ul>
doc/pub/week48/html/._week48-bs031.html
+1 -1
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@@ -263,7 +263,7 @@ Some of the most common tasks are:
<li> Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning.</li>
<li> Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values.</li>
<li> Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning.</li>
<li> Other unsupervised learning algortihms like Boltzmann machines</li>
<li> Other unsupervised learning algortihms like <b>Boltzmann machines</b></li>
</ul>
</div>
</div>
doc/pub/week48/html/._week48-bs032.html
+1 -1
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@@ -251,7 +251,7 @@ One of the major reasons is that they can be stacked layer-wise to build deep ne
The original RBMs had just one visible layer and a hidden layer, but recently so-called Gaussian-binary RBMs have gained quite some popularity in imaging since they are capable of modeling continuous data that are common to natural images.
<p>
Furthermore, they have been used to solve complicated quantum mechanical many-particle problems or classical statistical physics problems like the Ising and Potts classes of models.
Furthermore, they have been used to solve complicated <a href="https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.91.045002" target="_self">quantum mechanical many-particle problems or classical statistical physics problems like the Ising and Potts classes of models</a>.
<p>
<p>
doc/pub/week48/html/._week48-bs033.html
+2 -2
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@@ -252,8 +252,8 @@ Why use a generative model rather than the more well known discriminative deep n
<ol type="a"></li>
<li> A model for images could learn to draw new examples of cats and dogs, given a training dataset of images of cats and dogs.</li>
<li> Generate a sample of an ordered or disordered Ising model phase, having been given samples of such phases.</li>
<li> Model the trial function for Monte Carlo calculations</li>
<li> Generate a sample of an ordered or disordered phase, having been given samples of such phases.</li>
<li> Model the trial function for <a href="https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.91.045002" target="_self">Monte Carlo calculations</a>.</li>
</ol>
</ul>
doc/pub/week48/html/._week48-bs034.html
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@@ -249,7 +249,7 @@ MathJax.Hub.Config({
<li> DNNs often have several hidden layers. A restricted Boltzmann machine has only one hidden layer, however several RBMs can be stacked to make up Deep Belief Networks, of which they constitute the building blocks.</li>
</ol>
History: The RBM was developed by amongst others Geoffrey Hinton, called by some the "Godfather of Deep Learning", working with the University of Toronto and Google.
History: The RBM was developed by amongst others <a href="https://en.wikipedia.org/wiki/Geoffrey_Hinton" target="_self">Geoffrey Hinton</a>, called by some the "Godfather of Deep Learning", working with the University of Toronto and Google.
<p>
<p>
doc/pub/week48/html/._week48-bs038.html
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@@ -247,7 +247,7 @@ MathJax.Hub.Config({
<b>The network layers</b>:
<ol>
<li> A function \( \mathbf{x} \) that represents the visible layer, a vector of \( M \) elements (nodes). This layer represents both what the RBM might be given as training input, and what we want it to be able to reconstruct. This might for example be the pixels of an image, the spin values of the Ising model, or coefficients representing speech.</li>
<li> A function \( \mathbf{x} \) that represents the visible layer, a vector of \( M \) elements (nodes). This layer represents both what the RBM might be given as training input, and what we want it to be able to reconstruct. This might for example be given by the pixels of an image or coefficients representing speech, or the coordinates of a quantum mechanical state function.</li>
<li> The function \( \mathbf{h} \) represents the hidden, or latent, layer. A vector of \( N \) elements (nodes). Also called "feature detectors".</li>
</ol>
doc/pub/week48/html/._week48-bs039.html
+6 -9
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@@ -244,17 +244,14 @@ MathJax.Hub.Config({
<h2 id="___sec38" class="anchor">Goals </h2>
<p>
The goal of the hidden layer is to increase the model's expressive power. We encode complex interactions between visible variables by introducing additional, hidden variables that interact with visible degrees of freedom in a simple manner, yet still reproduce the complex correlations between visible degrees in the data once marginalized over (integrated out).
The goal of the hidden layer is to increase the model's expressive
power. We encode complex interactions between visible variables by
introducing additional, hidden variables that interact with visible
degrees of freedom in a simple manner, yet still reproduce the complex
correlations between visible degrees in the data once marginalized
over (integrated out).
<p>
Examples of this trick being employed in for example physics:
<ol>
<li> The Hubbard-Stratonovich transformation</li>
<li> The introduction of ghost fields in gauge theory</li>
<li> Shadow wave functions in Quantum Monte Carlo simulations</li>
</ol>
<b>The network parameters, to be optimized/learned</b>:
<ol>
doc/pub/week48/html/._week48-bs040.html
+2
View File
@@ -242,6 +242,8 @@ MathJax.Hub.Config({
<!-- !split -->
<h2 id="___sec39" class="anchor">Joint distribution </h2>
<p>
The restricted Boltzmann machine is described by a Bolztmann distribution
$$
\begin{align}
doc/pub/week48/html/._week48-bs044.html
+3
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@@ -273,6 +273,9 @@ learn the identity function under some constraints.
<p>
<a href="https://www.coursera.org/lecture/building-deep-learning-models-with-tensorflow/autoencoders-1U4L3" target="_self">Video on autoencoders</a>
<p>
See also A. Geron's textbook, chapter 15.
<p>
<p>
<!-- navigation buttons at the bottom of the page -->
doc/pub/week48/html/._week48-bs046.html
+8 -1
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@@ -244,7 +244,13 @@ MathJax.Hub.Config({
<h2 id="___sec45" class="anchor">Reinforcement Learning </h2>
<p>
Reinforcement learning is a sub-area of machine learning. It studies
Reinforcement Learning (RL) is one of the most exciting fields of
Machine Learning today, and also one of the oldest. It has been around
since the 1950s, producing many interesting applications over the
years.
<p>
It studies
how agents take actions based on trial and error, so as to maximize
some notion of cumulative reward in a dynamic system or
environment. Due to its generality, the problem has also been studied
@@ -266,6 +272,7 @@ learning.
<a href="https://www.youtube.com/watch?v=FgzM3zpZ55o&ab_channel=stanfordonline" target="_self">Lecture on Reinforcement Learning</a>.
<p>
See also A. Geron's textbook, chapter 16.
<p>
<!-- navigation buttons at the bottom of the page -->
<ul class="pagination">
doc/pub/week48/html/._week48-bs047.html
+1 -2
View File
@@ -251,8 +251,7 @@ rationality of doing so lies in that usually the source and target
tasks have inter-correlations, and therefore either the features,
samples, or models in the source task might provide useful information
for us to better solve the target task. Transfer learning is a hot
research topic in recent years, with many problems still waiting to be
solved in this space.
research topic in recent years, with many problems still waiting to be studied.
<p>
<a href="https://www.ias.edu/video/machinelearning/2020/0331-SamoryKpotufe" target="_self">Lecture on transfer learning</a>.
doc/pub/week48/html/._week48-bs053.html
+6 -3
View File
@@ -251,14 +251,17 @@ stage in terms of explaining why those effective models work and how
they work.
<p>
What is missing: the gap between correlation and causation Most
<b>What is missing: the gap between correlation and causation</b>. Standard Machine Learning is based on what e have called a frequentist approach.
<p>
Most
machine learning techniques, especially the statistical ones, depend
highly on data correlation to make predictions and analyses. In
highly on correlations in data sets to make predictions and analyses. In
contrast, rational humans tend to reply on clear and trustworthy
causality relations obtained via logical reasoning on real and clear
facts. It is one of the core goals of explainable machine learning to
transition from solving problems by data correlation to solving
problems by logical reasoning.
problems by logical reasoning. Bayesian Machine Learning is one of the exciting research directions in this field.
<p>
<p>
doc/pub/week48/html/._week48-bs054.html
+4 -1
View File
@@ -264,7 +264,10 @@ algorithms (on classic computers) to analyze and improve quantum
computing systems.
<p>
<a href="https://www.youtube.com/watch?v=Lbndu5EIWvI&ab_channel=%E6%85%B6%E6%87%89%E7%BE%A9%E5%A1%BEKeioUniversity" target="_self">Lecture on Quantum ML</a>.
<a href="https://www.youtube.com/watch?v=Xh9pUu3-WxM&ab_channel=InstituteforPure%26AppliedMathematics%28IPAM%29" target="_self">Lecture on Quantum ML</a>.
<p>
<a href="https://physics.aps.org/articles/v13/179?utm_campaign=weekly&utm_medium=email&utm_source=emailalert" target="_self">Read interview with Maria Schuld on her work on Quantum Machine Learning</a>. See also <a href="https://www.springer.com/gp/book/9783319964232" target="_self">her recent textbook</a>.
<p>
<p>
doc/pub/week48/html/week48-bs.html
+1 -1
View File
@@ -260,7 +260,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>Nov 23, 2020</h4></center> <!-- date -->
<center><h4>Nov 25, 2020</h4></center> <!-- date -->
<br>
<p>
doc/pub/week48/html/week48-reveal.html
+40 -25
View File
@@ -148,7 +148,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>&nbsp;<br>
<center><h4>Nov 23, 2020</h4></center> <!-- date -->
<center><h4>Nov 25, 2020</h4></center> <!-- date -->
<br>
<p>
@@ -162,7 +162,7 @@ MathJax.Hub.Config({
<h2 id="___sec0">Overview of week 48 </h2>
<ul>
<p><li> <b>Thursday</b>: Support Vector Machines, Kernels, Classification and Regression</li>
<p><li> <b>Thursday</b>: Support Vector Machines: Kernels, Classification and Regression</li>
<p><li> <b>Friday</b>: Summary of course with perspectives for future studies</li>
</ul>
<p>
@@ -1122,7 +1122,7 @@ Some of the most common tasks are:
<p><li> Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning.</li>
<p><li> Other unsupervised learning algortihms like Boltzmann machines</li>
<p><li> Other unsupervised learning algortihms like <b>Boltzmann machines</b></li>
</ul>
</div>
</section>
@@ -1139,7 +1139,7 @@ One of the major reasons is that they can be stacked layer-wise to build deep ne
The original RBMs had just one visible layer and a hidden layer, but recently so-called Gaussian-binary RBMs have gained quite some popularity in imaging since they are capable of modeling continuous data that are common to natural images.
<p>
Furthermore, they have been used to solve complicated quantum mechanical many-particle problems or classical statistical physics problems like the Ising and Potts classes of models.
Furthermore, they have been used to solve complicated <a href="https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.91.045002" target="_blank">quantum mechanical many-particle problems or classical statistical physics problems like the Ising and Potts classes of models</a>.
</section>
@@ -1155,8 +1155,8 @@ Why use a generative model rather than the more well known discriminative deep n
<ol type="a"></li>
<p><li> A model for images could learn to draw new examples of cats and dogs, given a training dataset of images of cats and dogs.</li>
<p><li> Generate a sample of an ordered or disordered Ising model phase, having been given samples of such phases.</li>
<p><li> Model the trial function for Monte Carlo calculations</li>
<p><li> Generate a sample of an ordered or disordered phase, having been given samples of such phases.</li>
<p><li> Model the trial function for <a href="https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.91.045002" target="_blank">Monte Carlo calculations</a>.</li>
</ol>
<p>
</ul>
@@ -1173,7 +1173,7 @@ Why use a generative model rather than the more well known discriminative deep n
</ol>
<p>
History: The RBM was developed by amongst others Geoffrey Hinton, called by some the "Godfather of Deep Learning", working with the University of Toronto and Google.
History: The RBM was developed by amongst others <a href="https://en.wikipedia.org/wiki/Geoffrey_Hinton" target="_blank">Geoffrey Hinton</a>, called by some the "Godfather of Deep Learning", working with the University of Toronto and Google.
</section>
@@ -1253,7 +1253,7 @@ Here we take away all lateral connections between nodes in the visible layer as
<b>The network layers</b>:
<ol>
<p><li> A function \( \mathbf{x} \) that represents the visible layer, a vector of \( M \) elements (nodes). This layer represents both what the RBM might be given as training input, and what we want it to be able to reconstruct. This might for example be the pixels of an image, the spin values of the Ising model, or coefficients representing speech.</li>
<p><li> A function \( \mathbf{x} \) that represents the visible layer, a vector of \( M \) elements (nodes). This layer represents both what the RBM might be given as training input, and what we want it to be able to reconstruct. This might for example be given by the pixels of an image or coefficients representing speech, or the coordinates of a quantum mechanical state function.</li>
<p><li> The function \( \mathbf{h} \) represents the hidden, or latent, layer. A vector of \( N \) elements (nodes). Also called "feature detectors".</li>
</ol>
</section>
@@ -1263,18 +1263,14 @@ Here we take away all lateral connections between nodes in the visible layer as
<h2 id="___sec38">Goals </h2>
<p>
The goal of the hidden layer is to increase the model's expressive power. We encode complex interactions between visible variables by introducing additional, hidden variables that interact with visible degrees of freedom in a simple manner, yet still reproduce the complex correlations between visible degrees in the data once marginalized over (integrated out).
The goal of the hidden layer is to increase the model's expressive
power. We encode complex interactions between visible variables by
introducing additional, hidden variables that interact with visible
degrees of freedom in a simple manner, yet still reproduce the complex
correlations between visible degrees in the data once marginalized
over (integrated out).
<p>
Examples of this trick being employed in for example physics:
<ol>
<p><li> The Hubbard-Stratonovich transformation</li>
<p><li> The introduction of ghost fields in gauge theory</li>
<p><li> Shadow wave functions in Quantum Monte Carlo simulations</li>
</ol>
<p>
<b>The network parameters, to be optimized/learned</b>:
<ol>
@@ -1287,6 +1283,8 @@ Examples of this trick being employed in for example physics:
<section>
<h2 id="___sec39">Joint distribution </h2>
<p>
The restricted Boltzmann machine is described by a Bolztmann distribution
<p>&nbsp;<br>
$$
@@ -1430,6 +1428,9 @@ learn the identity function under some constraints.
<p>
<a href="https://www.coursera.org/lecture/building-deep-learning-models-with-tensorflow/autoencoders-1U4L3" target="_blank">Video on autoencoders</a>
<p>
See also A. Geron's textbook, chapter 15.
</section>
@@ -1459,7 +1460,13 @@ See also the <a href="https://github.com/CompPhysics/MachineLearning/blob/master
<h2 id="___sec45">Reinforcement Learning </h2>
<p>
Reinforcement learning is a sub-area of machine learning. It studies
Reinforcement Learning (RL) is one of the most exciting fields of
Machine Learning today, and also one of the oldest. It has been around
since the 1950s, producing many interesting applications over the
years.
<p>
It studies
how agents take actions based on trial and error, so as to maximize
some notion of cumulative reward in a dynamic system or
environment. Due to its generality, the problem has also been studied
@@ -1479,6 +1486,9 @@ learning.
<p>
<a href="https://www.youtube.com/watch?v=FgzM3zpZ55o&ab_channel=stanfordonline" target="_blank">Lecture on Reinforcement Learning</a>.
<p>
See also A. Geron's textbook, chapter 16.
</section>
@@ -1493,8 +1503,7 @@ rationality of doing so lies in that usually the source and target
tasks have inter-correlations, and therefore either the features,
samples, or models in the source task might provide useful information
for us to better solve the target task. Transfer learning is a hot
research topic in recent years, with many problems still waiting to be
solved in this space.
research topic in recent years, with many problems still waiting to be studied.
<p>
<a href="https://www.ias.edu/video/machinelearning/2020/0331-SamoryKpotufe" target="_blank">Lecture on transfer learning</a>.
@@ -1597,14 +1606,17 @@ stage in terms of explaining why those effective models work and how
they work.
<p>
What is missing: the gap between correlation and causation Most
<b>What is missing: the gap between correlation and causation</b>. Standard Machine Learning is based on what e have called a frequentist approach.
<p>
Most
machine learning techniques, especially the statistical ones, depend
highly on data correlation to make predictions and analyses. In
highly on correlations in data sets to make predictions and analyses. In
contrast, rational humans tend to reply on clear and trustworthy
causality relations obtained via logical reasoning on real and clear
facts. It is one of the core goals of explainable machine learning to
transition from solving problems by data correlation to solving
problems by logical reasoning.
problems by logical reasoning. Bayesian Machine Learning is one of the exciting research directions in this field.
</section>
@@ -1632,7 +1644,10 @@ algorithms (on classic computers) to analyze and improve quantum
computing systems.
<p>
<a href="https://www.youtube.com/watch?v=Lbndu5EIWvI&ab_channel=%E6%85%B6%E6%87%89%E7%BE%A9%E5%A1%BEKeioUniversity" target="_blank">Lecture on Quantum ML</a>.
<a href="https://www.youtube.com/watch?v=Xh9pUu3-WxM&ab_channel=InstituteforPure%26AppliedMathematics%28IPAM%29" target="_blank">Lecture on Quantum ML</a>.
<p>
<a href="https://physics.aps.org/articles/v13/179?utm_campaign=weekly&utm_medium=email&utm_source=emailalert" target="_blank">Read interview with Maria Schuld on her work on Quantum Machine Learning</a>. See also <a href="https://www.springer.com/gp/book/9783319964232" target="_blank">her recent textbook</a>.
</section>
doc/pub/week48/html/week48-solarized.html
+38 -24
View File
@@ -190,7 +190,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>Nov 23, 2020</h4></center> <!-- date -->
<center><h4>Nov 25, 2020</h4></center> <!-- date -->
<br>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -198,7 +198,7 @@ MathJax.Hub.Config({
<h2 id="___sec0">Overview of week 48 </h2>
<ul>
<li> <b>Thursday</b>: Support Vector Machines, Kernels, Classification and Regression</li>
<li> <b>Thursday</b>: Support Vector Machines: Kernels, Classification and Regression</li>
<li> <b>Friday</b>: Summary of course with perspectives for future studies</li>
</ul>
@@ -1100,7 +1100,7 @@ Some of the most common tasks are:
<li> Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning.</li>
<li> Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values.</li>
<li> Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning.</li>
<li> Other unsupervised learning algortihms like Boltzmann machines</li>
<li> Other unsupervised learning algortihms like <b>Boltzmann machines</b></li>
</ul>
</div>
@@ -1118,7 +1118,7 @@ One of the major reasons is that they can be stacked layer-wise to build deep ne
The original RBMs had just one visible layer and a hidden layer, but recently so-called Gaussian-binary RBMs have gained quite some popularity in imaging since they are capable of modeling continuous data that are common to natural images.
<p>
Furthermore, they have been used to solve complicated quantum mechanical many-particle problems or classical statistical physics problems like the Ising and Potts classes of models.
Furthermore, they have been used to solve complicated <a href="https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.91.045002" target="_blank">quantum mechanical many-particle problems or classical statistical physics problems like the Ising and Potts classes of models</a>.
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -1134,8 +1134,8 @@ Why use a generative model rather than the more well known discriminative deep n
<ol type="a"></li>
<li> A model for images could learn to draw new examples of cats and dogs, given a training dataset of images of cats and dogs.</li>
<li> Generate a sample of an ordered or disordered Ising model phase, having been given samples of such phases.</li>
<li> Model the trial function for Monte Carlo calculations</li>
<li> Generate a sample of an ordered or disordered phase, having been given samples of such phases.</li>
<li> Model the trial function for <a href="https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.91.045002" target="_blank">Monte Carlo calculations</a>.</li>
</ol>
</ul>
@@ -1150,7 +1150,7 @@ Why use a generative model rather than the more well known discriminative deep n
<li> DNNs often have several hidden layers. A restricted Boltzmann machine has only one hidden layer, however several RBMs can be stacked to make up Deep Belief Networks, of which they constitute the building blocks.</li>
</ol>
History: The RBM was developed by amongst others Geoffrey Hinton, called by some the "Godfather of Deep Learning", working with the University of Toronto and Google.
History: The RBM was developed by amongst others <a href="https://en.wikipedia.org/wiki/Geoffrey_Hinton" target="_blank">Geoffrey Hinton</a>, called by some the "Godfather of Deep Learning", working with the University of Toronto and Google.
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -1234,7 +1234,7 @@ Here we take away all lateral connections between nodes in the visible layer as
<b>The network layers</b>:
<ol>
<li> A function \( \mathbf{x} \) that represents the visible layer, a vector of \( M \) elements (nodes). This layer represents both what the RBM might be given as training input, and what we want it to be able to reconstruct. This might for example be the pixels of an image, the spin values of the Ising model, or coefficients representing speech.</li>
<li> A function \( \mathbf{x} \) that represents the visible layer, a vector of \( M \) elements (nodes). This layer represents both what the RBM might be given as training input, and what we want it to be able to reconstruct. This might for example be given by the pixels of an image or coefficients representing speech, or the coordinates of a quantum mechanical state function.</li>
<li> The function \( \mathbf{h} \) represents the hidden, or latent, layer. A vector of \( N \) elements (nodes). Also called "feature detectors".</li>
</ol>
@@ -1243,17 +1243,14 @@ Here we take away all lateral connections between nodes in the visible layer as
<h2 id="___sec38">Goals </h2>
<p>
The goal of the hidden layer is to increase the model's expressive power. We encode complex interactions between visible variables by introducing additional, hidden variables that interact with visible degrees of freedom in a simple manner, yet still reproduce the complex correlations between visible degrees in the data once marginalized over (integrated out).
The goal of the hidden layer is to increase the model's expressive
power. We encode complex interactions between visible variables by
introducing additional, hidden variables that interact with visible
degrees of freedom in a simple manner, yet still reproduce the complex
correlations between visible degrees in the data once marginalized
over (integrated out).
<p>
Examples of this trick being employed in for example physics:
<ol>
<li> The Hubbard-Stratonovich transformation</li>
<li> The introduction of ghost fields in gauge theory</li>
<li> Shadow wave functions in Quantum Monte Carlo simulations</li>
</ol>
<b>The network parameters, to be optimized/learned</b>:
<ol>
@@ -1265,6 +1262,8 @@ Examples of this trick being employed in for example physics:
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec39">Joint distribution </h2>
<p>
The restricted Boltzmann machine is described by a Bolztmann distribution
$$
\begin{align}
@@ -1402,6 +1401,9 @@ learn the identity function under some constraints.
<p>
<a href="https://www.coursera.org/lecture/building-deep-learning-models-with-tensorflow/autoencoders-1U4L3" target="_blank">Video on autoencoders</a>
<p>
See also A. Geron's textbook, chapter 15.
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -1430,7 +1432,13 @@ See also the <a href="https://github.com/CompPhysics/MachineLearning/blob/master
<h2 id="___sec45">Reinforcement Learning </h2>
<p>
Reinforcement learning is a sub-area of machine learning. It studies
Reinforcement Learning (RL) is one of the most exciting fields of
Machine Learning today, and also one of the oldest. It has been around
since the 1950s, producing many interesting applications over the
years.
<p>
It studies
how agents take actions based on trial and error, so as to maximize
some notion of cumulative reward in a dynamic system or
environment. Due to its generality, the problem has also been studied
@@ -1452,6 +1460,7 @@ learning.
<a href="https://www.youtube.com/watch?v=FgzM3zpZ55o&ab_channel=stanfordonline" target="_blank">Lecture on Reinforcement Learning</a>.
<p>
See also A. Geron's textbook, chapter 16.
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec46">Transfer learning </h2>
@@ -1464,8 +1473,7 @@ rationality of doing so lies in that usually the source and target
tasks have inter-correlations, and therefore either the features,
samples, or models in the source task might provide useful information
for us to better solve the target task. Transfer learning is a hot
research topic in recent years, with many problems still waiting to be
solved in this space.
research topic in recent years, with many problems still waiting to be studied.
<p>
<a href="https://www.ias.edu/video/machinelearning/2020/0331-SamoryKpotufe" target="_blank">Lecture on transfer learning</a>.
@@ -1568,14 +1576,17 @@ stage in terms of explaining why those effective models work and how
they work.
<p>
What is missing: the gap between correlation and causation Most
<b>What is missing: the gap between correlation and causation</b>. Standard Machine Learning is based on what e have called a frequentist approach.
<p>
Most
machine learning techniques, especially the statistical ones, depend
highly on data correlation to make predictions and analyses. In
highly on correlations in data sets to make predictions and analyses. In
contrast, rational humans tend to reply on clear and trustworthy
causality relations obtained via logical reasoning on real and clear
facts. It is one of the core goals of explainable machine learning to
transition from solving problems by data correlation to solving
problems by logical reasoning.
problems by logical reasoning. Bayesian Machine Learning is one of the exciting research directions in this field.
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -1603,7 +1614,10 @@ algorithms (on classic computers) to analyze and improve quantum
computing systems.
<p>
<a href="https://www.youtube.com/watch?v=Lbndu5EIWvI&ab_channel=%E6%85%B6%E6%87%89%E7%BE%A9%E5%A1%BEKeioUniversity" target="_blank">Lecture on Quantum ML</a>.
<a href="https://www.youtube.com/watch?v=Xh9pUu3-WxM&ab_channel=InstituteforPure%26AppliedMathematics%28IPAM%29" target="_blank">Lecture on Quantum ML</a>.
<p>
<a href="https://physics.aps.org/articles/v13/179?utm_campaign=weekly&utm_medium=email&utm_source=emailalert" target="_blank">Read interview with Maria Schuld on her work on Quantum Machine Learning</a>. See also <a href="https://www.springer.com/gp/book/9783319964232" target="_blank">her recent textbook</a>.
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
doc/pub/week48/html/week48.html
+38 -24
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@@ -195,7 +195,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>Nov 23, 2020</h4></center> <!-- date -->
<center><h4>Nov 25, 2020</h4></center> <!-- date -->
<br>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -203,7 +203,7 @@ MathJax.Hub.Config({
<h2 id="___sec0">Overview of week 48 </h2>
<ul>
<li> <b>Thursday</b>: Support Vector Machines, Kernels, Classification and Regression</li>
<li> <b>Thursday</b>: Support Vector Machines: Kernels, Classification and Regression</li>
<li> <b>Friday</b>: Summary of course with perspectives for future studies</li>
</ul>
@@ -1105,7 +1105,7 @@ Some of the most common tasks are:
<li> Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning.</li>
<li> Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values.</li>
<li> Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning.</li>
<li> Other unsupervised learning algortihms like Boltzmann machines</li>
<li> Other unsupervised learning algortihms like <b>Boltzmann machines</b></li>
</ul>
</div>
@@ -1123,7 +1123,7 @@ One of the major reasons is that they can be stacked layer-wise to build deep ne
The original RBMs had just one visible layer and a hidden layer, but recently so-called Gaussian-binary RBMs have gained quite some popularity in imaging since they are capable of modeling continuous data that are common to natural images.
<p>
Furthermore, they have been used to solve complicated quantum mechanical many-particle problems or classical statistical physics problems like the Ising and Potts classes of models.
Furthermore, they have been used to solve complicated <a href="https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.91.045002" target="_blank">quantum mechanical many-particle problems or classical statistical physics problems like the Ising and Potts classes of models</a>.
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -1139,8 +1139,8 @@ Why use a generative model rather than the more well known discriminative deep n
<ol type="a"></li>
<li> A model for images could learn to draw new examples of cats and dogs, given a training dataset of images of cats and dogs.</li>
<li> Generate a sample of an ordered or disordered Ising model phase, having been given samples of such phases.</li>
<li> Model the trial function for Monte Carlo calculations</li>
<li> Generate a sample of an ordered or disordered phase, having been given samples of such phases.</li>
<li> Model the trial function for <a href="https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.91.045002" target="_blank">Monte Carlo calculations</a>.</li>
</ol>
</ul>
@@ -1155,7 +1155,7 @@ Why use a generative model rather than the more well known discriminative deep n
<li> DNNs often have several hidden layers. A restricted Boltzmann machine has only one hidden layer, however several RBMs can be stacked to make up Deep Belief Networks, of which they constitute the building blocks.</li>
</ol>
History: The RBM was developed by amongst others Geoffrey Hinton, called by some the "Godfather of Deep Learning", working with the University of Toronto and Google.
History: The RBM was developed by amongst others <a href="https://en.wikipedia.org/wiki/Geoffrey_Hinton" target="_blank">Geoffrey Hinton</a>, called by some the "Godfather of Deep Learning", working with the University of Toronto and Google.
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -1239,7 +1239,7 @@ Here we take away all lateral connections between nodes in the visible layer as
<b>The network layers</b>:
<ol>
<li> A function \( \mathbf{x} \) that represents the visible layer, a vector of \( M \) elements (nodes). This layer represents both what the RBM might be given as training input, and what we want it to be able to reconstruct. This might for example be the pixels of an image, the spin values of the Ising model, or coefficients representing speech.</li>
<li> A function \( \mathbf{x} \) that represents the visible layer, a vector of \( M \) elements (nodes). This layer represents both what the RBM might be given as training input, and what we want it to be able to reconstruct. This might for example be given by the pixels of an image or coefficients representing speech, or the coordinates of a quantum mechanical state function.</li>
<li> The function \( \mathbf{h} \) represents the hidden, or latent, layer. A vector of \( N \) elements (nodes). Also called "feature detectors".</li>
</ol>
@@ -1248,17 +1248,14 @@ Here we take away all lateral connections between nodes in the visible layer as
<h2 id="___sec38">Goals </h2>
<p>
The goal of the hidden layer is to increase the model's expressive power. We encode complex interactions between visible variables by introducing additional, hidden variables that interact with visible degrees of freedom in a simple manner, yet still reproduce the complex correlations between visible degrees in the data once marginalized over (integrated out).
The goal of the hidden layer is to increase the model's expressive
power. We encode complex interactions between visible variables by
introducing additional, hidden variables that interact with visible
degrees of freedom in a simple manner, yet still reproduce the complex
correlations between visible degrees in the data once marginalized
over (integrated out).
<p>
Examples of this trick being employed in for example physics:
<ol>
<li> The Hubbard-Stratonovich transformation</li>
<li> The introduction of ghost fields in gauge theory</li>
<li> Shadow wave functions in Quantum Monte Carlo simulations</li>
</ol>
<b>The network parameters, to be optimized/learned</b>:
<ol>
@@ -1270,6 +1267,8 @@ Examples of this trick being employed in for example physics:
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec39">Joint distribution </h2>
<p>
The restricted Boltzmann machine is described by a Bolztmann distribution
$$
\begin{align}
@@ -1407,6 +1406,9 @@ learn the identity function under some constraints.
<p>
<a href="https://www.coursera.org/lecture/building-deep-learning-models-with-tensorflow/autoencoders-1U4L3" target="_blank">Video on autoencoders</a>
<p>
See also A. Geron's textbook, chapter 15.
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -1435,7 +1437,13 @@ See also the <a href="https://github.com/CompPhysics/MachineLearning/blob/master
<h2 id="___sec45">Reinforcement Learning </h2>
<p>
Reinforcement learning is a sub-area of machine learning. It studies
Reinforcement Learning (RL) is one of the most exciting fields of
Machine Learning today, and also one of the oldest. It has been around
since the 1950s, producing many interesting applications over the
years.
<p>
It studies
how agents take actions based on trial and error, so as to maximize
some notion of cumulative reward in a dynamic system or
environment. Due to its generality, the problem has also been studied
@@ -1457,6 +1465,7 @@ learning.
<a href="https://www.youtube.com/watch?v=FgzM3zpZ55o&ab_channel=stanfordonline" target="_blank">Lecture on Reinforcement Learning</a>.
<p>
See also A. Geron's textbook, chapter 16.
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec46">Transfer learning </h2>
@@ -1469,8 +1478,7 @@ rationality of doing so lies in that usually the source and target
tasks have inter-correlations, and therefore either the features,
samples, or models in the source task might provide useful information
for us to better solve the target task. Transfer learning is a hot
research topic in recent years, with many problems still waiting to be
solved in this space.
research topic in recent years, with many problems still waiting to be studied.
<p>
<a href="https://www.ias.edu/video/machinelearning/2020/0331-SamoryKpotufe" target="_blank">Lecture on transfer learning</a>.
@@ -1573,14 +1581,17 @@ stage in terms of explaining why those effective models work and how
they work.
<p>
What is missing: the gap between correlation and causation Most
<b>What is missing: the gap between correlation and causation</b>. Standard Machine Learning is based on what e have called a frequentist approach.
<p>
Most
machine learning techniques, especially the statistical ones, depend
highly on data correlation to make predictions and analyses. In
highly on correlations in data sets to make predictions and analyses. In
contrast, rational humans tend to reply on clear and trustworthy
causality relations obtained via logical reasoning on real and clear
facts. It is one of the core goals of explainable machine learning to
transition from solving problems by data correlation to solving
problems by logical reasoning.
problems by logical reasoning. Bayesian Machine Learning is one of the exciting research directions in this field.
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -1608,7 +1619,10 @@ algorithms (on classic computers) to analyze and improve quantum
computing systems.
<p>
<a href="https://www.youtube.com/watch?v=Lbndu5EIWvI&ab_channel=%E6%85%B6%E6%87%89%E7%BE%A9%E5%A1%BEKeioUniversity" target="_blank">Lecture on Quantum ML</a>.
<a href="https://www.youtube.com/watch?v=Xh9pUu3-WxM&ab_channel=InstituteforPure%26AppliedMathematics%28IPAM%29" target="_blank">Lecture on Quantum ML</a>.
<p>
<a href="https://physics.aps.org/articles/v13/179?utm_campaign=weekly&utm_medium=email&utm_source=emailalert" target="_blank">Read interview with Maria Schuld on her work on Quantum Machine Learning</a>. See also <a href="https://www.springer.com/gp/book/9783319964232" target="_blank">her recent textbook</a>.
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
doc/pub/week48/ipynb/ipynb-week48-src.tar.gz
BIN
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Binary file not shown.
doc/pub/week48/ipynb/week48.ipynb
+35 -24
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@@ -10,7 +10,7 @@
"<!-- Author: --> \n",
"**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
"\n",
"Date: **Nov 23, 2020**\n",
"Date: **Nov 25, 2020**\n",
"\n",
"Copyright 1999-2020, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
"\n",
@@ -18,7 +18,7 @@
"\n",
"## Overview of week 48\n",
"\n",
"* **Thursday**: Support Vector Machines, Kernels, Classification and Regression\n",
"* **Thursday**: Support Vector Machines: Kernels, Classification and Regression\n",
"\n",
"* **Friday**: Summary of course with perspectives for future studies\n",
"\n",
@@ -1064,7 +1064,7 @@
"\n",
" * Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning.\n",
"\n",
" * Other unsupervised learning algortihms like Boltzmann machines\n",
" * Other unsupervised learning algortihms like **Boltzmann machines**\n",
"\n",
"\n",
"\n",
@@ -1076,7 +1076,7 @@
"\n",
"The original RBMs had just one visible layer and a hidden layer, but recently so-called Gaussian-binary RBMs have gained quite some popularity in imaging since they are capable of modeling continuous data that are common to natural images. \n",
"\n",
"Furthermore, they have been used to solve complicated quantum mechanical many-particle problems or classical statistical physics problems like the Ising and Potts classes of models. \n",
"Furthermore, they have been used to solve complicated [quantum mechanical many-particle problems or classical statistical physics problems like the Ising and Potts classes of models](https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.91.045002). \n",
"\n",
"\n",
"## Boltzmann Machines\n",
@@ -1089,9 +1089,9 @@
"\n",
"a. A model for images could learn to draw new examples of cats and dogs, given a training dataset of images of cats and dogs.\n",
"\n",
"b. Generate a sample of an ordered or disordered Ising model phase, having been given samples of such phases.\n",
"b. Generate a sample of an ordered or disordered phase, having been given samples of such phases.\n",
"\n",
"c. Model the trial function for Monte Carlo calculations\n",
"c. Model the trial function for [Monte Carlo calculations](https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.91.045002).\n",
"\n",
"\n",
"## Some similarities and differences from DNNs\n",
@@ -1102,7 +1102,7 @@
"\n",
"3. DNNs often have several hidden layers. A restricted Boltzmann machine has only one hidden layer, however several RBMs can be stacked to make up Deep Belief Networks, of which they constitute the building blocks.\n",
"\n",
"History: The RBM was developed by amongst others Geoffrey Hinton, called by some the \"Godfather of Deep Learning\", working with the University of Toronto and Google.\n",
"History: The RBM was developed by amongst others [Geoffrey Hinton](https://en.wikipedia.org/wiki/Geoffrey_Hinton), called by some the \"Godfather of Deep Learning\", working with the University of Toronto and Google.\n",
"\n",
"\n",
"## Boltzmann machines (BM)\n",
@@ -1159,20 +1159,18 @@
"## The network\n",
"\n",
"**The network layers**:\n",
"1. A function $\\mathbf{x}$ that represents the visible layer, a vector of $M$ elements (nodes). This layer represents both what the RBM might be given as training input, and what we want it to be able to reconstruct. This might for example be the pixels of an image, the spin values of the Ising model, or coefficients representing speech.\n",
"1. A function $\\mathbf{x}$ that represents the visible layer, a vector of $M$ elements (nodes). This layer represents both what the RBM might be given as training input, and what we want it to be able to reconstruct. This might for example be given by the pixels of an image or coefficients representing speech, or the coordinates of a quantum mechanical state function.\n",
"\n",
"2. The function $\\mathbf{h}$ represents the hidden, or latent, layer. A vector of $N$ elements (nodes). Also called \"feature detectors\".\n",
"\n",
"## Goals\n",
"\n",
"The goal of the hidden layer is to increase the model's expressive power. We encode complex interactions between visible variables by introducing additional, hidden variables that interact with visible degrees of freedom in a simple manner, yet still reproduce the complex correlations between visible degrees in the data once marginalized over (integrated out).\n",
"\n",
"Examples of this trick being employed in for example physics: \n",
"1. The Hubbard-Stratonovich transformation\n",
"\n",
"2. The introduction of ghost fields in gauge theory\n",
"\n",
"3. Shadow wave functions in Quantum Monte Carlo simulations\n",
"The goal of the hidden layer is to increase the model's expressive\n",
"power. We encode complex interactions between visible variables by\n",
"introducing additional, hidden variables that interact with visible\n",
"degrees of freedom in a simple manner, yet still reproduce the complex\n",
"correlations between visible degrees in the data once marginalized\n",
"over (integrated out).\n",
"\n",
"**The network parameters, to be optimized/learned**:\n",
"1. $\\mathbf{a}$ represents the visible bias, a vector of same length as $\\mathbf{x}$.\n",
@@ -1182,6 +1180,7 @@
"3. $W$ represents the interaction weights, a matrix of size $M\\times N$.\n",
"\n",
"## Joint distribution\n",
"\n",
"The restricted Boltzmann machine is described by a Bolztmann distribution"
]
},
@@ -1360,7 +1359,7 @@
"\n",
"[Video on autoencoders](https://www.coursera.org/lecture/building-deep-learning-models-with-tensorflow/autoencoders-1U4L3)\n",
"\n",
"\n",
"See also A. Geron's textbook, chapter 15.\n",
"\n",
"## Bayesian Machine Learning\n",
"\n",
@@ -1379,7 +1378,12 @@
"\n",
"## Reinforcement Learning\n",
"\n",
"Reinforcement learning is a sub-area of machine learning. It studies\n",
"Reinforcement Learning (RL) is one of the most exciting fields of\n",
"Machine Learning today, and also one of the oldest. It has been around\n",
"since the 1950s, producing many interesting applications over the\n",
"years.\n",
"\n",
"It studies\n",
"how agents take actions based on trial and error, so as to maximize\n",
"some notion of cumulative reward in a dynamic system or\n",
"environment. Due to its generality, the problem has also been studied\n",
@@ -1398,6 +1402,7 @@
"\n",
"[Lecture on Reinforcement Learning](https://www.youtube.com/watch?v=FgzM3zpZ55o&ab_channel=stanfordonline).\n",
"\n",
"See also A. Geron's textbook, chapter 16.\n",
"## Transfer learning\n",
"\n",
"The goal of transfer learning is to transfer the model or knowledge\n",
@@ -1407,8 +1412,7 @@
"tasks have inter-correlations, and therefore either the features,\n",
"samples, or models in the source task might provide useful information\n",
"for us to better solve the target task. Transfer learning is a hot\n",
"research topic in recent years, with many problems still waiting to be\n",
"solved in this space.\n",
"research topic in recent years, with many problems still waiting to be studied.\n",
"\n",
"[Lecture on transfer learning](https://www.ias.edu/video/machinelearning/2020/0331-SamoryKpotufe).\n",
"\n",
@@ -1485,14 +1489,16 @@
"stage in terms of explaining why those effective models work and how\n",
"they work.\n",
"\n",
"What is missing: the gap between correlation and causation Most\n",
"**What is missing: the gap between correlation and causation**. Standard Machine Learning is based on what e have called a frequentist approach. \n",
"\n",
"Most\n",
"machine learning techniques, especially the statistical ones, depend\n",
"highly on data correlation to make predictions and analyses. In\n",
"highly on correlations in data sets to make predictions and analyses. In\n",
"contrast, rational humans tend to reply on clear and trustworthy\n",
"causality relations obtained via logical reasoning on real and clear\n",
"facts. It is one of the core goals of explainable machine learning to\n",
"transition from solving problems by data correlation to solving\n",
"problems by logical reasoning.\n",
"problems by logical reasoning. Bayesian Machine Learning is one of the exciting research directions in this field.\n",
"\n",
"## Quantum machine learning\n",
"\n",
@@ -1513,7 +1519,10 @@
"algorithms (on classic computers) to analyze and improve quantum\n",
"computing systems.\n",
"\n",
"[Lecture on Quantum ML](https://www.youtube.com/watch?v=Lbndu5EIWvI&ab_channel=%E6%85%B6%E6%87%89%E7%BE%A9%E5%A1%BEKeioUniversity).\n",
"[Lecture on Quantum ML](https://www.youtube.com/watch?v=Xh9pUu3-WxM&ab_channel=InstituteforPure%26AppliedMathematics%28IPAM%29).\n",
"\n",
"[Read interview with Maria Schuld on her work on Quantum Machine Learning](https://physics.aps.org/articles/v13/179?utm_campaign=weekly&utm_medium=email&utm_source=emailalert). See also [her recent textbook](https://www.springer.com/gp/book/9783319964232). \n",
"\n",
"\n",
"## Quantum machine learning algorithms based on linear algebra\n",
"\n",
@@ -1569,6 +1578,8 @@
"\n",
"And much more.\n",
"\n",
"\n",
"\n",
"## The last words?\n",
"\n",
"Early computer scientist Alan Kay said, **The best way to predict the\n",