Kyle Reing University of Southern California April 18, 2018
|
|
|
- Hillary Sparks
- 5 years ago
- Views:
Transcription
1 Renormalization Group and Information Theory Kyle Reing University of Southern California April 18, 2018
2 Overview Renormalization Group Overview Information Theoretic Preliminaries Real Space Mutual Information Better ways to do this? The ML and Physics Friendship
3 Renormalization Group Example: Block Spin Renormalization Group
4 Renormalization Group Describe system in terms of block variables (ex: average spin of the block) Use the same form for the Hamiltonian, except defined over blocks, with different values for the parameters (ex: coupling strength) Change in parameters after renormalization defines a RG Flow Limit of flow often leads to fixed point characterizations (ex: Ising ferromagnetic/ paramagnetic)
5 Another Perspective Sufficient Statistic: A statistic (function) of the data that contains all of the information with respect to some model (ex: mean/ variance with Gaussians) Can think of RG as a (lossy) compression, for some course graining operation R, data X, and measure of macro scale properties Y, want:
6 Super Quick Info Theory Definitions (Shannon) Entropy Measure of uncertainty in a random variable, how spread out is the distribution? Discrete Continuous Mutual Information Measure of similarity between two random variables, reduction in uncertainty when we know another variable
7 Learning Relevant Degrees of Freedom? For a given model, RG procedure is often explicitly defined ( what are the fast/ slow degrees of freedom, what is the course graining procedure, how many steps to take, what is the relevant macro scale property?) What if we wanted to learn the relevant degrees of freedom and course graining automatically in a data driven way?
8
9 Real Space Mutual Information Algorithm: Estimate data marginals using RBM s and contrastive divergence training Use these data estimates to optimize another RBM between hidden degrees of freedom (a function of some small subset of sites) and the environment (the remaining sites) through gradient descent
10 Restricted Boltzmann Machines Hamiltonian (Energy Function) given by: Boltzmann distribution:
11 Contrastive Divergence Speed up sampling from Restricted Boltzmann Machines Want P(X), run a Markov Chain to convergence using Gibbs Sampling Gibbs Sampling in RBM s: Fix value of hidden, sample marginal probability of a single spin conditioned on all other spins Fix value of observed, sample marginal probability of hidden conditioned on other hidden Repeat many times Contrastive Divergence: Initialize Markov Chain close to target distribution, not randomly Samples of P(X) not gathered after chain convergence, gathered after k steps of Gibbs sampling (often k=1)
12 Real Space Mutual Information Intuition behind I(H:E) as a measure of macro scale information: Hidden variables H should contain information in V that overlaps with E If E contained all the information in V, H would try to copy V By restricting the support/ number of variables in H, can ensure that V can never be fully copied, introducing some potential information loss each renormalization step
13 Possible Issues Each renormalization step is computationally expensive (relies on many Monte Carlo samples to construct data distribution, and maximizes I(H:E) at every step for some partition) Depending on the information present in the subset V, a renormalization step may result in undesirable loss of information about macro scale
14 Possible Alternatives Shameless plug: Multivariate Mutual Information Mutual Information: How much information is shared between two random variables? Multivariate Mutual Information: How much information is shared between a group of random variables? Information among a group of random variables can be shared in different ways! (Redundantly, Synergistically)
15 Redundancy as Macro Scale One interpretation of macro scale properties of a system corresponds to information in a system that is consistently repeated Extracting / preserving redundant information (if present) would have a similar effect as a large number of renormalization course graining steps There are measures of multivariate mutual information that are maximized for redundancy (total correlation)
16 Redundancy as Macro Scale There are efficient algorithms (O(n) time!) for extracting redundancy in a similar fashion as Real Space Mutual Information Next step: run it and see if it works!
17 Final Note Physics helps ML, ML helps Physics?
Restricted Boltzmann Machines for Collaborative Filtering
Restricted Boltzmann Machines for Collaborative Filtering Authors: Ruslan Salakhutdinov Andriy Mnih Geoffrey Hinton Benjamin Schwehn Presentation by: Ioan Stanculescu 1 Overview The Netflix prize problem
Machine Learning Techniques for Computer Vision
Machine Learning Techniques for Computer Vision Part 2: Unsupervised Learning Microsoft Research Cambridge x 3 1 0.5 0.2 0 0.5 0.3 0 0.5 1 ECCV 2004, Prague x 2 x 1 Overview of Part 2 Mixture models EM
Introduction to the Renormalization Group
Introduction to the Renormalization Group Gregory Petropoulos University of Colorado Boulder March 4, 2015 1 / 17 Summary Flavor of Statistical Physics Universality / Critical Exponents Ising Model Renormalization
Deep Learning Srihari. Deep Belief Nets. Sargur N. Srihari
Deep Belief Nets Sargur N. Srihari srihari@cedar.buffalo.edu Topics 1. Boltzmann machines 2. Restricted Boltzmann machines 3. Deep Belief Networks 4. Deep Boltzmann machines 5. Boltzmann machines for continuous
Energy Based Models. Stefano Ermon, Aditya Grover. Stanford University. Lecture 13
Energy Based Models Stefano Ermon, Aditya Grover Stanford University Lecture 13 Stefano Ermon, Aditya Grover (AI Lab) Deep Generative Models Lecture 13 1 / 21 Summary Story so far Representation: Latent
ECE521 lecture 4: 19 January Optimization, MLE, regularization
ECE521 lecture 4: 19 January 2017 Optimization, MLE, regularization First four lectures Lectures 1 and 2: Intro to ML Probability review Types of loss functions and algorithms Lecture 3: KNN Convexity
Information Theory. Coding and Information Theory. Information Theory Textbooks. Entropy
Coding and Information Theory Chris Williams, School of Informatics, University of Edinburgh Overview What is information theory? Entropy Coding Information Theory Shannon (1948): Information theory is
Lecture 1: Introduction, Entropy and ML estimation
0-704: Information Processing and Learning Spring 202 Lecture : Introduction, Entropy and ML estimation Lecturer: Aarti Singh Scribes: Min Xu Disclaimer: These notes have not been subjected to the usual
Restricted Boltzmann Machines
Restricted Boltzmann Machines http://deeplearning4.org/rbm-mnist-tutorial.html Slides from Hugo Larochelle, Geoffrey Hinton, and Yoshua Bengio CSC321: Intro to Machine Learning and Neural Networks, Winter
Pattern Recognition and Machine Learning
Christopher M. Bishop Pattern Recognition and Machine Learning ÖSpri inger Contents Preface Mathematical notation Contents vii xi xiii 1 Introduction 1 1.1 Example: Polynomial Curve Fitting 4 1.2 Probability
Robust Classification using Boltzmann machines by Vasileios Vasilakakis
Robust Classification using Boltzmann machines by Vasileios Vasilakakis The scope of this report is to propose an architecture of Boltzmann machines that could be used in the context of classification,
Deep Boltzmann Machines
Deep Boltzmann Machines Ruslan Salakutdinov and Geoffrey E. Hinton Amish Goel University of Illinois Urbana Champaign agoel10@illinois.edu December 2, 2016 Ruslan Salakutdinov and Geoffrey E. Hinton Amish
COMP9444 Neural Networks and Deep Learning 11. Boltzmann Machines. COMP9444 c Alan Blair, 2017
COMP9444 Neural Networks and Deep Learning 11. Boltzmann Machines COMP9444 17s2 Boltzmann Machines 1 Outline Content Addressable Memory Hopfield Network Generative Models Boltzmann Machine Restricted Boltzmann
Self Supervised Boosting
Self Supervised Boosting Max Welling, Richard S. Zemel, and Geoffrey E. Hinton Department of omputer Science University of Toronto 1 King s ollege Road Toronto, M5S 3G5 anada Abstract Boosting algorithms
STA 4273H: Statistical Machine Learning
STA 4273H: Statistical Machine Learning Russ Salakhutdinov Department of Statistics! rsalakhu@utstat.toronto.edu! http://www.utstat.utoronto.ca/~rsalakhu/ Sidney Smith Hall, Room 6002 Lecture 7 Approximate
CPSC 540: Machine Learning
CPSC 540: Machine Learning MCMC and Non-Parametric Bayes Mark Schmidt University of British Columbia Winter 2016 Admin I went through project proposals: Some of you got a message on Piazza. No news is
Learning MN Parameters with Alternative Objective Functions. Sargur Srihari
Learning MN Parameters with Alternative Objective Functions Sargur srihari@cedar.buffalo.edu 1 Topics Max Likelihood & Contrastive Objectives Contrastive Objective Learning Methods Pseudo-likelihood Gradient
Lecture 16 Deep Neural Generative Models
Lecture 16 Deep Neural Generative Models CMSC 35246: Deep Learning Shubhendu Trivedi & Risi Kondor University of Chicago May 22, 2017 Approach so far: We have considered simple models and then constructed
Pattern Recognition and Machine Learning. Bishop Chapter 11: Sampling Methods
Pattern Recognition and Machine Learning Chapter 11: Sampling Methods Elise Arnaud Jakob Verbeek May 22, 2008 Outline of the chapter 11.1 Basic Sampling Algorithms 11.2 Markov Chain Monte Carlo 11.3 Gibbs
Internal Covariate Shift Batch Normalization Implementation Experiments. Batch Normalization. Devin Willmott. University of Kentucky.
Batch Normalization Devin Willmott University of Kentucky October 23, 2017 Overview 1 Internal Covariate Shift 2 Batch Normalization 3 Implementation 4 Experiments Covariate Shift Suppose we have two distributions,
5 Mutual Information and Channel Capacity
5 Mutual Information and Channel Capacity In Section 2, we have seen the use of a quantity called entropy to measure the amount of randomness in a random variable. In this section, we introduce several
Rapid Introduction to Machine Learning/ Deep Learning
Rapid Introduction to Machine Learning/ Deep Learning Hyeong In Choi Seoul National University 1/24 Lecture 5b Markov random field (MRF) November 13, 2015 2/24 Table of contents 1 1. Objectives of Lecture
Introduction to Restricted Boltzmann Machines
Introduction to Restricted Boltzmann Machines Ilija Bogunovic and Edo Collins EPFL {ilija.bogunovic,edo.collins}@epfl.ch October 13, 2014 Introduction Ingredients: 1. Probabilistic graphical models (undirected,
Algorithms other than SGD. CS6787 Lecture 10 Fall 2017
Algorithms other than SGD CS6787 Lecture 10 Fall 2017 Machine learning is not just SGD Once a model is trained, we need to use it to classify new examples This inference task is not computed with SGD There
Learning MN Parameters with Approximation. Sargur Srihari
Learning MN Parameters with Approximation Sargur srihari@cedar.buffalo.edu 1 Topics Iterative exact learning of MN parameters Difficulty with exact methods Approximate methods Approximate Inference Belief
Stochastic Gradient Estimate Variance in Contrastive Divergence and Persistent Contrastive Divergence
ESANN 0 proceedings, European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning. Bruges (Belgium), 7-9 April 0, idoc.com publ., ISBN 97-7707-. Stochastic Gradient
Connections between score matching, contrastive divergence, and pseudolikelihood for continuous-valued variables. Revised submission to IEEE TNN
Connections between score matching, contrastive divergence, and pseudolikelihood for continuous-valued variables Revised submission to IEEE TNN Aapo Hyvärinen Dept of Computer Science and HIIT University
Basic Principles of Unsupervised and Unsupervised
Basic Principles of Unsupervised and Unsupervised Learning Toward Deep Learning Shun ichi Amari (RIKEN Brain Science Institute) collaborators: R. Karakida, M. Okada (U. Tokyo) Deep Learning Self Organization
Speaker Representation and Verification Part II. by Vasileios Vasilakakis
Speaker Representation and Verification Part II by Vasileios Vasilakakis Outline -Approaches of Neural Networks in Speaker/Speech Recognition -Feed-Forward Neural Networks -Training with Back-propagation
Information Theory Primer:
Information Theory Primer: Entropy, KL Divergence, Mutual Information, Jensen s inequality Seungjin Choi Department of Computer Science and Engineering Pohang University of Science and Technology 77 Cheongam-ro,
Gaussian Mixture Models
Gaussian Mixture Models David Rosenberg, Brett Bernstein New York University April 26, 2017 David Rosenberg, Brett Bernstein (New York University) DS-GA 1003 April 26, 2017 1 / 42 Intro Question Intro
Machine Learning for Data Science (CS4786) Lecture 24
Machine Learning for Data Science (CS4786) Lecture 24 Graphical Models: Approximate Inference Course Webpage : http://www.cs.cornell.edu/courses/cs4786/2016sp/ BELIEF PROPAGATION OR MESSAGE PASSING Each
STA 4273H: Statistical Machine Learning
STA 4273H: Statistical Machine Learning Russ Salakhutdinov Department of Statistics! rsalakhu@utstat.toronto.edu! http://www.utstat.utoronto.ca/~rsalakhu/ Sidney Smith Hall, Room 6002 Lecture 3 Linear
Need for Sampling in Machine Learning. Sargur Srihari
Need for Sampling in Machine Learning Sargur srihari@cedar.buffalo.edu 1 Rationale for Sampling 1. ML methods model data with probability distributions E.g., p(x,y; θ) 2. Models are used to answer queries,
Deep unsupervised learning
Deep unsupervised learning Advanced data-mining Yongdai Kim Department of Statistics, Seoul National University, South Korea Unsupervised learning In machine learning, there are 3 kinds of learning paradigm.
CS 630 Basic Probability and Information Theory. Tim Campbell
CS 630 Basic Probability and Information Theory Tim Campbell 21 January 2003 Probability Theory Probability Theory is the study of how best to predict outcomes of events. An experiment (or trial or event)
Learning Energy-Based Models of High-Dimensional Data
Learning Energy-Based Models of High-Dimensional Data Geoffrey Hinton Max Welling Yee-Whye Teh Simon Osindero www.cs.toronto.edu/~hinton/energybasedmodelsweb.htm Discovering causal structure as a goal
Review: Directed Models (Bayes Nets)
X Review: Directed Models (Bayes Nets) Lecture 3: Undirected Graphical Models Sam Roweis January 2, 24 Semantics: x y z if z d-separates x and y d-separation: z d-separates x from y if along every undirected
Deep learning / Ian Goodfellow, Yoshua Bengio and Aaron Courville. - Cambridge, MA ; London, Spis treści
Deep learning / Ian Goodfellow, Yoshua Bengio and Aaron Courville. - Cambridge, MA ; London, 2017 Spis treści Website Acknowledgments Notation xiii xv xix 1 Introduction 1 1.1 Who Should Read This Book?
A graph contains a set of nodes (vertices) connected by links (edges or arcs)
BOLTZMANN MACHINES Generative Models Graphical Models A graph contains a set of nodes (vertices) connected by links (edges or arcs) In a probabilistic graphical model, each node represents a random variable,
Annealing Between Distributions by Averaging Moments
Annealing Between Distributions by Averaging Moments Chris J. Maddison Dept. of Comp. Sci. University of Toronto Roger Grosse CSAIL MIT Ruslan Salakhutdinov University of Toronto Partition Functions We
Chapter 11. Stochastic Methods Rooted in Statistical Mechanics
Chapter 11. Stochastic Methods Rooted in Statistical Mechanics Neural Networks and Learning Machines (Haykin) Lecture Notes on Self-learning Neural Algorithms Byoung-Tak Zhang School of Computer Science
Variational Autoencoder
Variational Autoencoder Göker Erdo gan August 8, 2017 The variational autoencoder (VA) [1] is a nonlinear latent variable model with an efficient gradient-based training procedure based on variational
Inductive Principles for Restricted Boltzmann Machine Learning
Inductive Principles for Restricted Boltzmann Machine Learning Benjamin Marlin Department of Computer Science University of British Columbia Joint work with Kevin Swersky, Bo Chen and Nando de Freitas
Introduction to Machine Learning
Introduction to Machine Learning Brown University CSCI 1950-F, Spring 2012 Prof. Erik Sudderth Lecture 25: Markov Chain Monte Carlo (MCMC) Course Review and Advanced Topics Many figures courtesy Kevin
Bayesian Machine Learning
Bayesian Machine Learning Andrew Gordon Wilson ORIE 6741 Lecture 2: Bayesian Basics https://people.orie.cornell.edu/andrew/orie6741 Cornell University August 25, 2016 1 / 17 Canonical Machine Learning
Performance Evaluation and Comparison
Outline Hong Chang Institute of Computing Technology, Chinese Academy of Sciences Machine Learning Methods (Fall 2012) Outline Outline I 1 Introduction 2 Cross Validation and Resampling 3 Interval Estimation
Information theoretic perspectives on learning algorithms
Information theoretic perspectives on learning algorithms Varun Jog University of Wisconsin - Madison Departments of ECE and Mathematics Shannon Channel Hangout! May 8, 2018 Jointly with Adrian Tovar-Lopez
Probabilistic Graphical Models
Probabilistic Graphical Models Brown University CSCI 295-P, Spring 213 Prof. Erik Sudderth Lecture 11: Inference & Learning Overview, Gaussian Graphical Models Some figures courtesy Michael Jordan s draft
Expectation Maximization
Expectation Maximization Seungjin Choi Department of Computer Science and Engineering Pohang University of Science and Technology 77 Cheongam-ro, Nam-gu, Pohang 37673, Korea seungjin@postech.ac.kr 1 /
Recent Advances in Bayesian Inference Techniques
Recent Advances in Bayesian Inference Techniques Christopher M. Bishop Microsoft Research, Cambridge, U.K. research.microsoft.com/~cmbishop SIAM Conference on Data Mining, April 2004 Abstract Bayesian
STA414/2104 Statistical Methods for Machine Learning II
STA414/2104 Statistical Methods for Machine Learning II Murat A. Erdogdu & David Duvenaud Department of Computer Science Department of Statistical Sciences Lecture 3 Slide credits: Russ Salakhutdinov Announcements
Undirected Graphical Models: Markov Random Fields
Undirected Graphical Models: Markov Random Fields 40-956 Advanced Topics in AI: Probabilistic Graphical Models Sharif University of Technology Soleymani Spring 2015 Markov Random Field Structure: undirected
Monte Carlo Simulation of the Ising Model. Abstract
Monte Carlo Simulation of the Ising Model Saryu Jindal 1 1 Department of Chemical Engineering and Material Sciences, University of California, Davis, CA 95616 (Dated: June 9, 2007) Abstract This paper
Contrastive Divergence
Contrastive Divergence Training Products of Experts by Minimizing CD Hinton, 2002 Helmut Puhr Institute for Theoretical Computer Science TU Graz June 9, 2010 Contents 1 Theory 2 Argument 3 Contrastive
19 : Slice Sampling and HMC
10-708: Probabilistic Graphical Models 10-708, Spring 2018 19 : Slice Sampling and HMC Lecturer: Kayhan Batmanghelich Scribes: Boxiang Lyu 1 MCMC (Auxiliary Variables Methods) In inference, we are often
Computational Physics (6810): Session 13
Computational Physics (6810): Session 13 Dick Furnstahl Nuclear Theory Group OSU Physics Department April 14, 2017 6810 Endgame Various recaps and followups Random stuff (like RNGs :) Session 13 stuff
Latent Variable Models
Latent Variable Models Stefano Ermon, Aditya Grover Stanford University Lecture 5 Stefano Ermon, Aditya Grover (AI Lab) Deep Generative Models Lecture 5 1 / 31 Recap of last lecture 1 Autoregressive models:
Accelerated Monte Carlo simulations with restricted Boltzmann machines
Accelerated simulations with restricted Boltzmann machines Li Huang 1 Lei Wang 2 1 China Academy of Engineering Physics 2 Institute of Physics, Chinese Academy of Sciences July 6, 2017 Machine Learning
Why is Deep Learning so effective?
Ma191b Winter 2017 Geometry of Neuroscience The unreasonable effectiveness of deep learning This lecture is based entirely on the paper: Reference: Henry W. Lin and Max Tegmark, Why does deep and cheap
Learning Tetris. 1 Tetris. February 3, 2009
Learning Tetris Matt Zucker Andrew Maas February 3, 2009 1 Tetris The Tetris game has been used as a benchmark for Machine Learning tasks because its large state space (over 2 200 cell configurations are
Active learning in sequence labeling
Active learning in sequence labeling Tomáš Šabata 11. 5. 2017 Czech Technical University in Prague Faculty of Information technology Department of Theoretical Computer Science Table of contents 1. Introduction
Lecture : Probabilistic Machine Learning
Lecture : Probabilistic Machine Learning Riashat Islam Reasoning and Learning Lab McGill University September 11, 2018 ML : Many Methods with Many Links Modelling Views of Machine Learning Machine Learning
Distributed Estimation, Information Loss and Exponential Families. Qiang Liu Department of Computer Science Dartmouth College
Distributed Estimation, Information Loss and Exponential Families Qiang Liu Department of Computer Science Dartmouth College Statistical Learning / Estimation Learning generative models from data Topic
The Origin of Deep Learning. Lili Mou Jan, 2015
The Origin of Deep Learning Lili Mou Jan, 2015 Acknowledgment Most of the materials come from G. E. Hinton s online course. Outline Introduction Preliminary Boltzmann Machines and RBMs Deep Belief Nets
Error Functions & Linear Regression (1)
Error Functions & Linear Regression (1) John Kelleher & Brian Mac Namee Machine Learning @ DIT Overview 1 Introduction Overview 2 Univariate Linear Regression Linear Regression Analytical Solution Gradient
ECE521 Lecture 19 HMM cont. Inference in HMM
ECE521 Lecture 19 HMM cont. Inference in HMM Outline Hidden Markov models Model definitions and notations Inference in HMMs Learning in HMMs 2 Formally, a hidden Markov model defines a generative process
13 : Variational Inference: Loopy Belief Propagation and Mean Field
10-708: Probabilistic Graphical Models 10-708, Spring 2012 13 : Variational Inference: Loopy Belief Propagation and Mean Field Lecturer: Eric P. Xing Scribes: Peter Schulam and William Wang 1 Introduction
Graphical Models for Collaborative Filtering
Graphical Models for Collaborative Filtering Le Song Machine Learning II: Advanced Topics CSE 8803ML, Spring 2012 Sequence modeling HMM, Kalman Filter, etc.: Similarity: the same graphical model topology,
arxiv: v2 [cs.ne] 22 Feb 2013
![arxiv: v2 [cs.ne] 22 Feb 2013](/thumbs/76/74046790.jpg "arxiv: v2 [cs.ne] 22 Feb 2013")
Sparse Penalty in Deep Belief Networks: Using the Mixed Norm Constraint arxiv:1301.3533v2 [cs.ne] 22 Feb 2013 Xanadu C. Halkias DYNI, LSIS, Universitè du Sud, Avenue de l Université - BP20132, 83957 LA
Bayesian Mixtures of Bernoulli Distributions
Bayesian Mixtures of Bernoulli Distributions Laurens van der Maaten Department of Computer Science and Engineering University of California, San Diego Introduction The mixture of Bernoulli distributions
Deep Learning. What Is Deep Learning? The Rise of Deep Learning. Long History (in Hind Sight)
CSCE 636 Neural Networks Instructor: Yoonsuck Choe Deep Learning What Is Deep Learning? Learning higher level abstractions/representations from data. Motivation: how the brain represents sensory information
Lecture 7 and 8: Markov Chain Monte Carlo
Lecture 7 and 8: Markov Chain Monte Carlo 4F13: Machine Learning Zoubin Ghahramani and Carl Edward Rasmussen Department of Engineering University of Cambridge http://mlg.eng.cam.ac.uk/teaching/4f13/ Ghahramani
3 Undirected Graphical Models
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.438 Algorithms For Inference Fall 2014 3 Undirected Graphical Models In this lecture, we discuss undirected
Complex Systems Methods 9. Critical Phenomena: The Renormalization Group
Complex Systems Methods 9. Critical Phenomena: The Renormalization Group Eckehard Olbrich e.olbrich@gmx.de http://personal-homepages.mis.mpg.de/olbrich/complex systems.html Potsdam WS 2007/08 Olbrich (Leipzig)
Lecture 2: Linear regression
Lecture 2: Linear regression Roger Grosse 1 Introduction Let s ump right in and look at our first machine learning algorithm, linear regression. In regression, we are interested in predicting a scalar-valued
How to Quantitate a Markov Chain? Stochostic project 1
How to Quantitate a Markov Chain? Stochostic project 1 Chi-Ning,Chou Wei-chang,Lee PROFESSOR RAOUL NORMAND April 18, 2015 Abstract In this project, we want to quantitatively evaluate a Markov chain. In
Learning in Markov Random Fields An Empirical Study
Learning in Markov Random Fields An Empirical Study Sridevi Parise, Max Welling University of California, Irvine sparise,welling@ics.uci.edu Abstract Learning the parameters of an undirected graphical
Lecture 13 : Variational Inference: Mean Field Approximation
10-708: Probabilistic Graphical Models 10-708, Spring 2017 Lecture 13 : Variational Inference: Mean Field Approximation Lecturer: Willie Neiswanger Scribes: Xupeng Tong, Minxing Liu 1 Problem Setup 1.1
Chapter 16. Structured Probabilistic Models for Deep Learning
Peng et al.: Deep Learning and Practice 1 Chapter 16 Structured Probabilistic Models for Deep Learning Peng et al.: Deep Learning and Practice 2 Structured Probabilistic Models way of using graphs to describe
Deep Learning. What Is Deep Learning? The Rise of Deep Learning. Long History (in Hind Sight)
CSCE 636 Neural Networks Instructor: Yoonsuck Choe Deep Learning What Is Deep Learning? Learning higher level abstractions/representations from data. Motivation: how the brain represents sensory information
Outline of Today s Lecture
University of Washington Department of Electrical Engineering Computer Speech Processing EE516 Winter 2005 Jeff A. Bilmes Lecture 12 Slides Feb 23 rd, 2005 Outline of Today s
Lecture 4: Types of errors. Bayesian regression models. Logistic regression
Lecture 4: Types of errors. Bayesian regression models. Logistic regression A Bayesian interpretation of regularization Bayesian vs maximum likelihood fitting more generally COMP-652 and ECSE-68, Lecture
Submodularity in Machine Learning
Saifuddin Syed MLRG Summer 2016 1 / 39 What are submodular functions Outline 1 What are submodular functions Motivation Submodularity and Concavity Examples 2 Properties of submodular functions Submodularity
Based on slides by Richard Zemel
CSC 412/2506 Winter 2018 Probabilistic Learning and Reasoning Lecture 3: Directed Graphical Models and Latent Variables Based on slides by Richard Zemel Learning outcomes What aspects of a model can we
Different Criteria for Active Learning in Neural Networks: A Comparative Study
Different Criteria for Active Learning in Neural Networks: A Comparative Study Jan Poland and Andreas Zell University of Tübingen, WSI - RA Sand 1, 72076 Tübingen, Germany Abstract. The field of active
Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm
Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm Qiang Liu and Dilin Wang NIPS 2016 Discussion by Yunchen Pu March 17, 2017 March 17, 2017 1 / 8 Introduction Let x R d
Undirected Graphical Models
Outline Hong Chang Institute of Computing Technology, Chinese Academy of Sciences Machine Learning Methods (Fall 2012) Outline Outline I 1 Introduction 2 Properties Properties 3 Generative vs. Conditional
Bayesian Networks BY: MOHAMAD ALSABBAGH
Bayesian Networks BY: MOHAMAD ALSABBAGH Outlines Introduction Bayes Rule Bayesian Networks (BN) Representation Size of a Bayesian Network Inference via BN BN Learning Dynamic BN Introduction Conditional
Physics 403. Segev BenZvi. Numerical Methods, Maximum Likelihood, and Least Squares. Department of Physics and Astronomy University of Rochester
Physics 403 Numerical Methods, Maximum Likelihood, and Least Squares Segev BenZvi Department of Physics and Astronomy University of Rochester Table of Contents 1 Review of Last Class Quadratic Approximation
Assignment 6: MCMC Simulation and Review Problems
Massachusetts Institute of Technology MITES 2018 Physics III Assignment 6: MCMC Simulation and Review Problems Due Monday July 30 at 11:59PM in Instructor s Inbox Preface: In this assignment, you will
Bayesian Methods for Machine Learning
Bayesian Methods for Machine Learning CS 584: Big Data Analytics Material adapted from Radford Neal s tutorial (http://ftp.cs.utoronto.ca/pub/radford/bayes-tut.pdf), Zoubin Ghahramni (http://hunch.net/~coms-4771/zoubin_ghahramani_bayesian_learning.pdf),
Learning to Disentangle Factors of Variation with Manifold Learning
Learning to Disentangle Factors of Variation with Manifold Learning Scott Reed Kihyuk Sohn Yuting Zhang Honglak Lee University of Michigan, Department of Electrical Engineering and Computer Science 08
8.3.2 The finite size scaling method
232 Chapter 8: Analysing Monte Carlo data In general we don t know this value, which makes it difficult to perform the fit. It is possible to guess T c and then vary the guess to make the line in Figure
Linear Models for Regression
Linear Models for Regression CSE 4309 Machine Learning Vassilis Athitsos Computer Science and Engineering Department University of Texas at Arlington 1 The Regression Problem Training data: A set of input-output
Bayesian Learning in Undirected Graphical Models
Bayesian Learning in Undirected Graphical Models Zoubin Ghahramani Gatsby Computational Neuroscience Unit University College London, UK http://www.gatsby.ucl.ac.uk/ Work with: Iain Murray and Hyun-Chul
Machine Learning Basics: Maximum Likelihood Estimation
Machine Learning Basics: Maximum Likelihood Estimation Sargur N. srihari@cedar.buffalo.edu This is part of lecture slides on Deep Learning: http://www.cedar.buffalo.edu/~srihari/cse676 1 Topics 1. Learning
Chapter 17: Undirected Graphical Models
Chapter 17: Undirected Graphical Models The Elements of Statistical Learning Biaobin Jiang Department of Biological Sciences Purdue University bjiang@purdue.edu October 30, 2014 Biaobin Jiang (Purdue)
Efficient Variational Inference in Large-Scale Bayesian Compressed Sensing
Efficient Variational Inference in Large-Scale Bayesian Compressed Sensing George Papandreou and Alan Yuille Department of Statistics University of California, Los Angeles ICCV Workshop on Information
8 Error analysis: jackknife & bootstrap
8 Error analysis: jackknife & bootstrap As discussed before, it is no problem to calculate the expectation values and statistical error estimates of normal observables from Monte Carlo. However, often