From ebc57fcb4067d798b3d8969bf7ec702af44c5ba6 Mon Sep 17 00:00:00 2001 From: Morten Hjorth-Jensen Date: Wed, 25 Nov 2020 08:07:12 +0100 Subject: [PATCH] lectures week 48 --- doc/src/week48/week48.do.txt | 54 +++++++++++++++++++++++------------- 1 file changed, 34 insertions(+), 20 deletions(-) diff --git a/doc/src/week48/week48.do.txt b/doc/src/week48/week48.do.txt index 241c53058..dc17c1c00 100644 --- a/doc/src/week48/week48.do.txt +++ b/doc/src/week48/week48.do.txt @@ -5,7 +5,7 @@ DATE: today !split ===== Overview of week 48 ===== -* _Thursday_: Support Vector Machines, Kernels, Classification and Regression +* _Thursday_: Support Vector Machines: Kernels, Classification and Regression * _Friday_: Summary of course with perspectives for future studies @@ -781,7 +781,7 @@ Some of the most common tasks are: * Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning. - * Other unsupervised learning algortihms like Boltzmann machines + * Other unsupervised learning algortihms like _Boltzmann machines_ !eblock @@ -793,7 +793,7 @@ 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. -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 "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". !split @@ -806,8 +806,8 @@ Why use a generative model rather than the more well known discriminative deep n * A generative model can learn to represent and sample from a probability distribution. The core idea is to learn a parametric model of the probability distribution from which the training data was drawn. As an example o A model for images could learn to draw new examples of cats and dogs, given a training dataset of images of cats and dogs. - o Generate a sample of an ordered or disordered Ising model phase, having been given samples of such phases. - o Model the trial function for Monte Carlo calculations + o Generate a sample of an ordered or disordered phase, having been given samples of such phases. + o Model the trial function for "Monte Carlo calculations":"https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.91.045002". !split @@ -817,7 +817,7 @@ Why use a generative model rather than the more well known discriminative deep n o Energy based models don't use backpropagation and automatic differentiation for computing gradients, instead turning to Markov Chain Monte Carlo methods. o 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. -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 "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. !split @@ -871,18 +871,19 @@ FIGURE: [figures/RBM.pdf, width=800 frac=1.0] ===== The network ===== _The network layers_: - o 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. + o 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. o The function $\mathbf{h}$ represents the hidden, or latent, layer. A vector of $N$ elements (nodes). Also called "feature detectors". !split ===== Goals ===== -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). -Examples of this trick being employed in for example physics: - o The Hubbard-Stratonovich transformation - o The introduction of ghost fields in gauge theory - o Shadow wave functions in Quantum Monte Carlo simulations _The network parameters, to be optimized/learned_: o $\mathbf{a}$ represents the visible bias, a vector of same length as $\mathbf{x}$. o $\mathbf{b}$ represents the hidden bias, a vector of same lenght as $\mathbf{h}$. @@ -893,6 +894,7 @@ _The network parameters, to be optimized/learned_: !split ===== Joint distribution ===== + The restricted Boltzmann machine is described by a Bolztmann distribution !bt \begin{align} @@ -999,7 +1001,7 @@ learn the identity function under some constraints. "Video on autoencoders":"https://www.coursera.org/lecture/building-deep-learning-models-with-tensorflow/autoencoders-1U4L3" - +See also A. Geron's textbook, chapter 15. !split ===== Bayesian Machine Learning ===== @@ -1020,7 +1022,12 @@ See also the "slides here":"https://github.com/CompPhysics/MachineLearning/blob/ !split ===== Reinforcement Learning ===== -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. + +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 @@ -1039,6 +1046,7 @@ learning. "Lecture on Reinforcement Learning":"https://www.youtube.com/watch?v=FgzM3zpZ55o&ab_channel=stanfordonline". +See also A. Geron's textbook, chapter 16. !split ===== Transfer learning ===== @@ -1049,8 +1057,7 @@ 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. "Lecture on transfer learning":"https://www.ias.edu/video/machinelearning/2020/0331-SamoryKpotufe". @@ -1133,14 +1140,16 @@ becomes narrower and narrower. However, we are still in the very early stage in terms of explaining why those effective models work and how they work. -What is missing: the gap between correlation and causation Most +_What is missing: the gap between correlation and causation_. Standard Machine Learning is based on what e have called a frequentist approach. + +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. !split ===== Quantum machine learning ===== @@ -1162,7 +1171,10 @@ learning algorithms. In addition, we can also use the machine learning algorithms (on classic computers) to analyze and improve quantum computing systems. -"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". +"Lecture on Quantum ML":"https://www.youtube.com/watch?v=Xh9pUu3-WxM&ab_channel=InstituteforPure%26AppliedMathematics%28IPAM%29". + +"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". + !split ===== Quantum machine learning algorithms based on linear algebra ===== @@ -1222,6 +1234,8 @@ intelligent, interpretable “social machine learning”? And much more. + + !split ===== The last words? =====