Rejection Sampling Variational Inference Karan Grewal CSC2547 / - PowerPoint PPT Presentation

Nov 26, 2022 •488 likes •623 views

Rejection Sampling Variational Inference Karan Grewal CSC2547 / STA4273 Overview Variational Inference Interested in computing posterior , but it is often intractable parametrize a variational family of distributions to

Rejection Sampling Variational Inference Karan Grewal CSC2547 / STA4273
Overview
Variational Inference • Interested in computing posterior , but it is often intractable • parametrize a variational family of distributions to approximate true posterior • Maximize Evidence Lower Bound (ELBO):
Rejection Sampling • Want to sample from , parametrize a proposal distribution s.t. • Accept sample with probability source: https://people.eecs.berkeley.edu/~jordan/courses/260-spring10/lectures/lecture17.pdf
Reparameterized Rejection Sampler • Problem: what if we want our variational family to follow a distribution that requires rejection sampling to approximate? • Rejection sampling causes discontinuities
Example: Gamma Distribution source: http://www.epixanalytics.com/ • To sample from , sample from and divide by , the acceptance probability is dependent on
Reparameterized Rejection Sampler 1. Reparameterize : 2. Find marginal distribution of accepted sample :
Reparameterized Rejection Sampler 3. Rewrite ELBO:
Related Work • Automatic Differentiation Variational Inference (ADVI) - fit with Gaussian posterior; cannot learn a Gamma or Dirichlet posterior • Black-Box Variational Inference (BBVI) - sample from to approximate gradient • Generalized Reparameterization Gradient (G-REP) - find a distribution that makes dependent on choice of variational family
Results • model = sparse gamma Deep Exponential Family source: https://arxiv.org/pdf/1610.05683.pdf
Future Work • Combining Rejection Sampling Variational Inference with Metropolis-Hastings • Metropolis-Hastings: Acquire a sequence of samples from a distribution that is difficult to sample from directly; use rejection sampling
Supplementary: Gradient Derivation

Download Presentation

Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Sampling Methods Oliver Schulte - CMPT 419/726 Bishop PRML Ch. 11 Sampling Rejection Sampling

Sampling Rejection Sampling Importance Sampling Markov Chain Monte Carlo Sampling Methods Oliver Schulte - CMPT 419/726 Bishop PRML Ch. 11 Sampling Rejection Sampling Importance Sampling Markov Chain Monte Carlo Recall Inference For

573 views • 41 slides

Variational Inference for GPs: Presenters Group1: Stochastic variational inference. Slides 2 - 28

Variational Inference for GPs: Presenters Group1: Stochastic variational inference. Slides 2 - 28 Chaoqi Wang Sana Tonekaboni Will Grathwohl Group2: Variational inference for GPs. Slides 29 - 57 Trefor Evans Kingsley Chang Shems Saleh James

1.32k views • 98 slides

Stein Variational Newton & other Sampling-Based Inference Methods Robert Scheichl

Stein Variational Newton & other Sampling-Based Inference Methods Robert Scheichl Interdisciplinary Center for Scientific Computing & Institute of Applied Mathematics Universit at Heidelberg Collaborators: G. Detommaso (Bath); T.

970 views • 78 slides

Bayes net wrapup Exact inference algorithms Use to compute P(X1, ..., Xn) or P(X1, ..., Xn

Bayes net wrapup Exact inference algorithms Use to compute P(X1, ..., Xn) or P(X1, ..., Xn | Y1, ..., Ym) Approximate inference algorithms Direct sampling Rejection sampling Likelihood weighting Direct Sampling To

567 views • 5 slides

CS480/680 Machine Learning Lecture 11: February 11 th , 2020 Variational Inference Zahra

CS480/680 Machine Learning Lecture 11: February 11 th , 2020 Variational Inference Zahra Sheikhbahaee VARIATIONAL ALGORITHMS FOR APPROXIMATE BAYESIAN INFERENCE (Beal 2003, chapter 2) Variational Inference: A Review for Statisticians (Blei et al.

713 views • 28 slides

Approximate inference: Sampling methods Probabilistic Graphical Models Sharif University of

Approximate inference: Sampling methods Probabilistic Graphical Models Sharif University of Technology Spring 2018 Soleymani Approximate inference Approximate inference techniques Deterministic approximation Variational algorithms

1.95k views • 97 slides

Sampling Methods CMSC 678 UMBC Outline Recap Monte Carlo methods Sampling Techniques Uniform

Approximate Inference: Sampling Methods CMSC 678 UMBC Outline Recap Monte Carlo methods Sampling Techniques Uniform sampling Importance Sampling Rejection Sampling Metropolis-Hastings Gibbs sampling Example: Collapsed Gibbs Sampler for

1.03k views • 71 slides

Deep Variational Inference FLARE Reading Group Presentation Wesley Tansey 9/28/2016 What is

Deep Variational Inference FLARE Reading Group Presentation Wesley Tansey 9/28/2016 What is Variational Inference? What is Variational Inference? p*(x) Want to estimate some distribution, p*(x) What is Variational Inference?

684 views • 52 slides

Sampling Methods CMSC 691 UMBC (Some) Learning Techniques MAP/MLE: Point estimation, basic EM

Approximate Inference: Sampling Methods CMSC 691 UMBC (Some) Learning Techniques MAP/MLE: Point estimation, basic EM Variational Inference: Functional Optimization Sampling/Monte Carlo today Outline Monte Carlo methods Sampling

985 views • 71 slides

Lecture Variational 13 Inference Panini Kaushal Scribes : - Margulies Smedeuranh Niklas

Lecture Variational 13 Inference Panini Kaushal Scribes : - Margulies Smedeuranh Niklas Variational Inference Approximate by posterior Idea maximizing , bound lower Ptt variational fly ply ? ) a , , ) " 9) * =

709 views • 15 slides

Variational Inference for Bayes vMF Mixture Hanxiao Liu September 23, 2014 1 / 14 Variational

Variational Inference for Bayes vMF Mixture Hanxiao Liu September 23, 2014 1 / 14 Variational Inference Review Lower bound the likelihood L ( ; X ) = E q log p ( X | ) log p ( X , Z | ) q ( Z ) = E q + E q log q (

310 views • 14 slides

Fast and Simple Natural-Gradient Variational Inference with Mixture of Exponential-family

Fast and Simple Natural-Gradient Variational Inference with Mixture of Exponential-family Approximations Wu Lin (UBC) June 11, 2019 Joint work with Mohammad Emtiyaz Khan (AIP, RIKEN) and Mark Schmidt (UBC) 1 / 7 Variational Inference (VI) VI

119 views • 7 slides

Approximate inference (Ch. 14) Likelihood Weighting P(b|a) 1 P(a) 0.5 A B P(b|a) 0.2 In

Approximate inference (Ch. 14) Likelihood Weighting P(b|a) 1 P(a) 0.5 A B P(b|a) 0.2 In LW, say we generated 2 samples: [a] : w = 1, [a], w=0.2 If we did rejection sampling, we need about 5 a to actually get a b, so 10

645 views • 33 slides

Variational Inference CMSC 691 UMBC Goal: Posterior Inference Hyperparameters Unknown

Approximate Inference: Variational Inference CMSC 691 UMBC Goal: Posterior Inference Hyperparameters Unknown parameters Data: p ( | ) Likelihood model: p( | ) (Some) Learning Techniques MAP/MLE: Point

1.09k views • 81 slides

Approximate Inference 9.520 Class 19 Ruslan Salakhutdinov BCS and CSAIL, MIT 1 Plan 1.

Approximate Inference 9.520 Class 19 Ruslan Salakhutdinov BCS and CSAIL, MIT 1 Plan 1. Introduction/Notation. 2. Examples of successful Bayesian models. 3. Laplace and Variational Inference. 4. Basic Sampling Algorithms. 5. Markov chain

833 views • 45 slides

Neural Variational Inference and Learning Andriy Mnih, Karol Gregor 22 June 2014 1 / 14

Neural Variational Inference and Learning Andriy Mnih, Karol Gregor 22 June 2014 1 / 14 Introduction Training directed latent variable models is difficult because inference in them is intractable. Both MCMC and traditional variational

322 views • 14 slides

Sampling and Monte Carlo Integration Michael Gutmann Probabilistic Modelling and Reasoning

Sampling and Monte Carlo Integration Michael Gutmann Probabilistic Modelling and Reasoning (INFR11134) School of Informatics, University of Edinburgh Spring semester 2018 Recap Learning and inference often involves intractable integrals, e.g.

520 views • 41 slides

System Acceptance and Regression System, Acceptance, and Regression Testing (c) 2007 Mauro

System Acceptance and Regression System, Acceptance, and Regression Testing (c) 2007 Mauro Pezz & Michal Young Ch 22, slide 1 Learning objectives Learning objectives Distinguish system and acceptance testing Distinguish system

495 views • 35 slides

Paxos Made Simple John Nguyen Slides adapted from Leslie Lamport and Thomas Marshall Problem

Paxos Made Simple John Nguyen Slides adapted from Leslie Lamport and Thomas Marshall Problem How to agree on a value in a distributed system that tolerate non-malicious failures? Problem Distributed consensus problem Group of

662 views • 19 slides

Introduction Amith Pulla QA Manger at Intel Involved in software testing strategies and

11/1/2013 Amith Pulla, Intel Corp. Twitter: @pamith Sowmya Purushotham Clinicient Inc. Introduction Amith Pulla QA Manger at Intel Involved in software testing strategies and processes Works on sales and marketing applications

591 views • 9 slides

CSci 8980: Advanced Topics in Graphical Models MCMC, Gibbs Sampling Instructor: Arindam Banerjee

Basics MCMC Gibbs Sampling Auxiliary Variable Samplers CSci 8980: Advanced Topics in Graphical Models MCMC, Gibbs Sampling Instructor: Arindam Banerjee September 27, 2007 Basics MCMC Gibbs Sampling Auxiliary Variable Samplers Problems

1.86k views • 147 slides

Probabilistic & Unsupervised Learning Sampling Methods Maneesh Sahani

Probabilistic & Unsupervised Learning Sampling Methods Maneesh Sahani maneesh@gatsby.ucl.ac.uk Gatsby Computational Neuroscience Unit, and MSc ML/CSML, Dept Computer Science University College London Term 1, Autumn 2013 Sampling For

1.12k views • 80 slides

1 Ex. 1 The mean salt content of a certain type of potato chips is supposed to be 2.0mg. The salt

10.4 Inference as Decision Tests of significance assess the strength of evidence against the null hypothesis. The Pvalue is a probability computed under the assumption that H 0 is true. Using a level of significance gives us a value at which

379 views • 5 slides

Introduction to MCMC DB Breakfast 09/30/2011 Guozhang Wang Motivation: Statistical

Introduction to MCMC DB Breakfast 09/30/2011 Guozhang Wang Motivation: Statistical Inference Joint Distribution Sleeps Well Playground Pleasant dinner Posterior Estimation Sunny Bike Ride Productive day Graphical Models

482 views • 21 slides