Multiple Speaker Tracking with the Factorial von Mises- Fisher Filter
|
|
|
- Lilian Hicks
- 5 years ago
- Views:
Transcription
1 Multiple Speaker Tracking with the Factorial von Mises- Fisher Filter IEEE International Workshop on Machine Learning for Signal Processing Sept 21-24, 2014 Reims, France Johannes Traa, Paris Smaragdis University of Illinois at Urbana-Champaign
2 Outline Motivation Sequential Bayesian Inference Linear Dynamical System o Kalman Filter Directional Statistics o von Mises-Fisher distribution o 3D Rotations Spherical Dynamical System o Particle Filter o von Mises-Fisher Filter (vmff) o Factorial vmff (FvMFF) Experiments
3 Motivation Tracking on the sphere o Human-computer interfaces with compact arrays
4 Motivation Sequential Bayesian Inference o Powerful framework for tracking Traditional techniques o Kalman Filter Ignores topology of sphere o Particle Filter Computationally intensive Proposed method o von Mises-Fisher Filter Accurate Deterministic
5 Sequential Bayesian Inference Dynamic Bayesian Network (DBN) o State transition o Measurement x t p (x t x t 1 ) y t p (y t x t ) x t 1 x t x t+1 y t 1 y t y t+1
6 Sequential Bayesian Inference Bayesian Filtering Equations (BFE) o Predict (convolution) p (x t y 1:t 1 ) = o Correct (Bayes rule) Z p (x t x t 1 ) p (x t 1 y 1:t 1 ) d x t 1 p (x t y 1:t ) / p (y t x t ) p (x t y 1:t 1 ) Predict x t 1 x t Correct y t
7 Linear Dynamical System (LDS) Probabilistic model Kalman Filter o Optimal on-line inference for LDS x t N (Ax t 1, x ) y t N (Bx t, y ) x t 1 x t x t+1 y t 1 y t y t+1
8 Kalman Filter KF ignores unique topology of DOA manifold o 3D state tracking o Posterior lies off of manifold
9 Directional Statistics von-mises Fisher distribution o Unit Sphere S 2 = x : x 2 R 3, kxk 2 =1 o Probability density function p (x µ,apple)= apple 4 sinh (apple) eapple x > µ
10 Directional Statistics Rotations on the sphere o Axis (unit vector) a a o Angle o Rotation matrix R (a, )= a 3 a 2 a 3 0 a 1 a 2 a sin ( )+ I aa > cos ( )+aa > o Rotation = linear transformation x 0 = R (a, ) x = R ( a) x
11 Spherical Dynamical System (SDS) Probabilistic Model o DOA state transition o Rotation state transition o Measurement x t x t 1, r t 1 vmf (R (r t 1 ) x t 1,apple x ) r t r t 1 N (Ar t 1, r ) y t x t vmf (x t,apple y ) o Rotation vector: r = a o Full state vector: s t = apple xt r t
12 Particle Filter Approximate inference for the SDS o Stochastic o Sequential variant of Monte Carlo o Approximate BFEs with particles (weighted point estimates) S t = n s (l) t o,w (l) t o Maintain particle representation of filtered state distribution p (s t y 1:t ) LX l=1 w (l) t s (l) t
13 von Mises- Fisher Filter (vmff) Factored representation p (s t 1 y 1:t 1 ) = vmf x t 1 bµ t 1, bapple t 1 N r t 1 b t 1, b t 1 Predict step Position Rotation o DOA state à approximate via convolution of 2D wrapped Normals Convolution p (x t y 1:t 1 ) = Z S 2 p (x t s t 1 ) p (x t 1 y 1:t 1 ) d x t 1 Mean Concentration bµ t = R b t 1 bµ t 1 A bapple t A (bapple t 1 ) A (bapple x ) A 1/ 2 r =0 A (apple) = 1 tanh (apple) 1 apple Position noise Rotation noise o Rotation state à regular KF prediction
14 von Mises- Fisher Filter (vmff) Correct step o DOA state à closed-form solution for vmf o Rotation state à approximate via auxiliary observation Bayes rule p (r t y 1:t ) / p (y t r t ) p (r t y 1:t 1 ) Emission density (not explicitly defined in SDS) Auxiliary observation: rotation vector required for bµ t = y t y r t = cos 1 bµ t 1 y t bµ t 1 y t kbµ t 1 y t k 2 Degree of rotation Axis of rotation
15 Factorial vmff (FvMFF) Probabilistic Data Association (PDA) o Probabilistic assignment of observations to speakers o EM-like de-coupling of correct steps for the speakers o Include component to handle clutter Outlier distribution Source 2 Source 1
16 Experiments Accuracy o Comparison between: 3D Kalman filter (KF) Particle filter on SDS (vmfpf) o 50 particles Proposed method (vmff) o Average angular error: E = 1 T TX cos 1 t=1 True DOA x > t bµ t Mean of filtered distribution Error (radians) Error (radians) Error (radians) k x = 100 KF vmfpf vmff k y k x = 200 KF vmfpf vmff k y k x = 500 KF vmfpf vmff k y
17 Experiments Number of particles and run time o Particle filter matches vmff performance with 150 particles o However, it runs 60x more slowly Error (radians) vmfpf computation time (milliseconds per iteration) KF vmfpf vmff # particles apple x = 200,apple y = 30
18 Experiments Measurement extraction Microphone 1 Microphone M Time domain x (1) t [1...N] x (M) t [1...N] Discrete Fourier Transform Frequency domain X (1) 1:N,t X (M) 1:N,t Inter- channel features Inter- Channel Time Differences 1,t N 2,t Map ITDs to DOAs DOA measurements y 1,t... yn 2,t
19 Experiments Multiple speaker tracking o Square array with M =4 microphones (side length = 2 centimeters) o 2- to 3-second sentences from TSP corpus o Speakers moved around array o ~ 0 db mixture o T 60 reverb time: 100 milliseconds True vmff 1 vmff 2 o Successful tracking requires gating procedure to avoid model mismatch
20 Thank you
PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 13: SEQUENTIAL DATA
PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 13: SEQUENTIAL DATA Contents in latter part Linear Dynamical Systems What is different from HMM? Kalman filter Its strength and limitation Particle Filter
Networks. Dynamic. Bayesian. A Whirlwind Tour. Johannes Traa. Computational Audio Lab, UIUC
Dynamic Bayesian Networks A Whirlwind Tour Johannes Traa Computational Audio Lab, UIUC Sequential data is everywhere Speech waveform Bush s approval rating EEG brain signals Financial trends What s a DBN?
Sensor Fusion: Particle Filter
Sensor Fusion: Particle Filter By: Gordana Stojceska stojcesk@in.tum.de Outline Motivation Applications Fundamentals Tracking People Advantages and disadvantages Summary June 05 JASS '05, St.Petersburg,
Linear Dynamical Systems
Linear Dynamical Systems Sargur N. srihari@cedar.buffalo.edu Machine Learning Course: http://www.cedar.buffalo.edu/~srihari/cse574/index.html Two Models Described by Same Graph Latent variables Observations
Approximate Inference Part 1 of 2
Approximate Inference Part 1 of 2 Tom Minka Microsoft Research, Cambridge, UK Machine Learning Summer School 2009 http://mlg.eng.cam.ac.uk/mlss09/ Bayesian paradigm Consistent use of probability theory
Approximate Inference Part 1 of 2
Approximate Inference Part 1 of 2 Tom Minka Microsoft Research, Cambridge, UK Machine Learning Summer School 2009 http://mlg.eng.cam.ac.uk/mlss09/ 1 Bayesian paradigm Consistent use of probability theory
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
Part 1: Expectation Propagation
Chalmers Machine Learning Summer School Approximate message passing and biomedicine Part 1: Expectation Propagation Tom Heskes Machine Learning Group, Institute for Computing and Information Sciences Radboud
Parallel Particle Filter in Julia
Parallel Particle Filter in Julia Gustavo Goretkin December 12, 2011 1 / 27 First a disclaimer The project in a sentence. workings 2 / 27 First a disclaimer First a disclaimer The project in a sentence.
Lecture 6: Multiple Model Filtering, Particle Filtering and Other Approximations
Lecture 6: Multiple Model Filtering, Particle Filtering and Other Approximations Department of Biomedical Engineering and Computational Science Aalto University April 28, 2010 Contents 1 Multiple Model
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
Lecture 2: From Linear Regression to Kalman Filter and Beyond
Lecture 2: From Linear Regression to Kalman Filter and Beyond Department of Biomedical Engineering and Computational Science Aalto University January 26, 2012 Contents 1 Batch and Recursive Estimation
Machine Learning Overview
Machine Learning Overview Sargur N. Srihari University at Buffalo, State University of New York USA 1 Outline 1. What is Machine Learning (ML)? 2. Types of Information Processing Problems Solved 1. Regression
Expectation propagation for signal detection in flat-fading channels
Expectation propagation for signal detection in flat-fading channels Yuan Qi MIT Media Lab Cambridge, MA, 02139 USA yuanqi@media.mit.edu Thomas Minka CMU Statistics Department Pittsburgh, PA 15213 USA
Bayesian Methods in Positioning Applications
Bayesian Methods in Positioning Applications Vedran Dizdarević v.dizdarevic@tugraz.at Graz University of Technology, Austria 24. May 2006 Bayesian Methods in Positioning Applications p.1/21 Outline Problem
Sequence labeling. Taking collective a set of interrelated instances x 1,, x T and jointly labeling them
HMM, MEMM and CRF 40-957 Special opics in Artificial Intelligence: Probabilistic Graphical Models Sharif University of echnology Soleymani Spring 2014 Sequence labeling aking collective a set of interrelated
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 11 Project
Minimum message length estimation of mixtures of multivariate Gaussian and von Mises-Fisher distributions
Minimum message length estimation of mixtures of multivariate Gaussian and von Mises-Fisher distributions Parthan Kasarapu & Lloyd Allison Monash University, Australia September 8, 25 Parthan Kasarapu
Variational inference
Simon Leglaive Télécom ParisTech, CNRS LTCI, Université Paris Saclay November 18, 2016, Télécom ParisTech, Paris, France. Outline Introduction Probabilistic model Problem Log-likelihood decomposition EM
Sensor Tasking and Control
Sensor Tasking and Control Sensing Networking Leonidas Guibas Stanford University Computation CS428 Sensor systems are about sensing, after all... System State Continuous and Discrete Variables The quantities
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
Lecture 2: From Linear Regression to Kalman Filter and Beyond
Lecture 2: From Linear Regression to Kalman Filter and Beyond January 18, 2017 Contents 1 Batch and Recursive Estimation 2 Towards Bayesian Filtering 3 Kalman Filter and Bayesian Filtering and Smoothing
Towards inference for skewed alpha stable Levy processes
Towards inference for skewed alpha stable Levy processes Simon Godsill and Tatjana Lemke Signal Processing and Communications Lab. University of Cambridge www-sigproc.eng.cam.ac.uk/~sjg Overview Motivation
Gaussian Process Approximations of Stochastic Differential Equations
Gaussian Process Approximations of Stochastic Differential Equations Cédric Archambeau Dan Cawford Manfred Opper John Shawe-Taylor May, 2006 1 Introduction Some of the most complex models routinely run
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),
Human Pose Tracking I: Basics. David Fleet University of Toronto
Human Pose Tracking I: Basics David Fleet University of Toronto CIFAR Summer School, 2009 Looking at People Challenges: Complex pose / motion People have many degrees of freedom, comprising an articulated
Approximating high-dimensional posteriors with nuisance parameters via integrated rotated Gaussian approximation (IRGA)
Approximating high-dimensional posteriors with nuisance parameters via integrated rotated Gaussian approximation (IRGA) Willem van den Boom Department of Statistics and Applied Probability National University
The Kalman Filter ImPr Talk
The Kalman Filter ImPr Talk Ged Ridgway Centre for Medical Image Computing November, 2006 Outline What is the Kalman Filter? State Space Models Kalman Filter Overview Bayesian Updating of Estimates Kalman
output dimension input dimension Gaussian evidence Gaussian Gaussian evidence evidence from t +1 inputs and outputs at time t x t+2 x t-1 x t+1
To appear in M. S. Kearns, S. A. Solla, D. A. Cohn, (eds.) Advances in Neural Information Processing Systems. Cambridge, MA: MIT Press, 999. Learning Nonlinear Dynamical Systems using an EM Algorithm Zoubin
Data Fusion Kalman Filtering Self Localization
Data Fusion Kalman Filtering Self Localization Armando Jorge Sousa http://www.fe.up.pt/asousa asousa@fe.up.pt Faculty of Engineering, University of Porto, Portugal Department of Electrical and Computer
27 : Distributed Monte Carlo Markov Chain. 1 Recap of MCMC and Naive Parallel Gibbs Sampling
10-708: Probabilistic Graphical Models 10-708, Spring 2014 27 : Distributed Monte Carlo Markov Chain Lecturer: Eric P. Xing Scribes: Pengtao Xie, Khoa Luu In this scribe, we are going to review the Parallel
Diversity-Promoting Bayesian Learning of Latent Variable Models
Diversity-Promoting Bayesian Learning of Latent Variable Models Pengtao Xie 1, Jun Zhu 1,2 and Eric Xing 1 1 Machine Learning Department, Carnegie Mellon University 2 Department of Computer Science and
Markov chain Monte Carlo methods for visual tracking
Markov chain Monte Carlo methods for visual tracking Ray Luo rluo@cory.eecs.berkeley.edu Department of Electrical Engineering and Computer Sciences University of California, Berkeley Berkeley, CA 94720
Lecture 5 : Sparse Models
Lecture 5 : Sparse Models Homework 3 discussion (Nima) Sparse Models Lecture - Reading : Murphy, Chapter 13.1, 13.3, 13.6.1 - Reading : Peter Knee, Chapter 2 Paolo Gabriel (TA) : Neural Brain Control After
Expectation Maximization (EM)
Expectation Maximization (EM) The EM algorithm is used to train models involving latent variables using training data in which the latent variables are not observed (unlabeled data). This is to be contrasted
RECURSIVE OUTLIER-ROBUST FILTERING AND SMOOTHING FOR NONLINEAR SYSTEMS USING THE MULTIVARIATE STUDENT-T DISTRIBUTION
1 IEEE INTERNATIONAL WORKSHOP ON MACHINE LEARNING FOR SIGNAL PROCESSING, SEPT. 3 6, 1, SANTANDER, SPAIN RECURSIVE OUTLIER-ROBUST FILTERING AND SMOOTHING FOR NONLINEAR SYSTEMS USING THE MULTIVARIATE STUDENT-T
PROBABILITY DISTRIBUTIONS. J. Elder CSE 6390/PSYC 6225 Computational Modeling of Visual Perception
PROBABILITY DISTRIBUTIONS Credits 2 These slides were sourced and/or modified from: Christopher Bishop, Microsoft UK Parametric Distributions 3 Basic building blocks: Need to determine given Representation:
Bayesian Networks Inference with Probabilistic Graphical Models
4190.408 2016-Spring Bayesian Networks Inference with Probabilistic Graphical Models Byoung-Tak Zhang intelligence Lab Seoul National University 4190.408 Artificial (2016-Spring) 1 Machine Learning? Learning
CSC487/2503: Foundations of Computer Vision. Visual Tracking. David Fleet
CSC487/2503: Foundations of Computer Vision Visual Tracking David Fleet Introduction What is tracking? Major players: Dynamics (model of temporal variation of target parameters) Measurements (relation
SLAM Techniques and Algorithms. Jack Collier. Canada. Recherche et développement pour la défense Canada. Defence Research and Development Canada
SLAM Techniques and Algorithms Jack Collier Defence Research and Development Canada Recherche et développement pour la défense Canada Canada Goals What will we learn Gain an appreciation for what SLAM
Dynamic Data Modeling, Recognition, and Synthesis. Rui Zhao Thesis Defense Advisor: Professor Qiang Ji
Dynamic Data Modeling, Recognition, and Synthesis Rui Zhao Thesis Defense Advisor: Professor Qiang Ji Contents Introduction Related Work Dynamic Data Modeling & Analysis Temporal localization Insufficient
2D Image Processing (Extended) Kalman and particle filter
2D Image Processing (Extended) Kalman and particle filter Prof. Didier Stricker Dr. Gabriele Bleser Kaiserlautern University http://ags.cs.uni-kl.de/ DFKI Deutsches Forschungszentrum für Künstliche Intelligenz
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
3. ESTIMATION OF SIGNALS USING A LEAST SQUARES TECHNIQUE
3. ESTIMATION OF SIGNALS USING A LEAST SQUARES TECHNIQUE 3.0 INTRODUCTION The purpose of this chapter is to introduce estimators shortly. More elaborated courses on System Identification, which are given
Linear Dynamical Systems (Kalman filter)
Linear Dynamical Systems (Kalman filter) (a) Overview of HMMs (b) From HMMs to Linear Dynamical Systems (LDS) 1 Markov Chains with Discrete Random Variables x 1 x 2 x 3 x T Let s assume we have discrete
MMSE-Based Filtering for Linear and Nonlinear Systems in the Presence of Non-Gaussian System and Measurement Noise
MMSE-Based Filtering for Linear and Nonlinear Systems in the Presence of Non-Gaussian System and Measurement Noise I. Bilik 1 and J. Tabrikian 2 1 Dept. of Electrical and Computer Engineering, University
Missing Data and Dynamical Systems
U NIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN CS598PS Machine Learning for Signal Processing Missing Data and Dynamical Systems 12 October 2017 Today s lecture Dealing with missing data Tracking and linear
an introduction to bayesian inference
with an application to network analysis http://jakehofman.com january 13, 2010 motivation would like models that: provide predictive and explanatory power are complex enough to describe observed phenomena
Probabilistic Graphical Models
Probabilistic Graphical Models Brown University CSCI 2950-P, Spring 2013 Prof. Erik Sudderth Lecture 13: Learning in Gaussian Graphical Models, Non-Gaussian Inference, Monte Carlo Methods Some figures
Probabilistic Robotics
University of Rome La Sapienza Master in Artificial Intelligence and Robotics Probabilistic Robotics Prof. Giorgio Grisetti Course web site: http://www.dis.uniroma1.it/~grisetti/teaching/probabilistic_ro
Partially Observable Markov Decision Processes (POMDPs)
Partially Observable Markov Decision Processes (POMDPs) Sachin Patil Guest Lecture: CS287 Advanced Robotics Slides adapted from Pieter Abbeel, Alex Lee Outline Introduction to POMDPs Locally Optimal Solutions
ECE276A: Sensing & Estimation in Robotics Lecture 10: Gaussian Mixture and Particle Filtering
ECE276A: Sensing & Estimation in Robotics Lecture 10: Gaussian Mixture and Particle Filtering Lecturer: Nikolay Atanasov: natanasov@ucsd.edu Teaching Assistants: Siwei Guo: s9guo@eng.ucsd.edu Anwesan Pal:
Organization. I MCMC discussion. I project talks. I Lecture.
Organization I MCMC discussion I project talks. I Lecture. Content I Uncertainty Propagation Overview I Forward-Backward with an Ensemble I Model Reduction (Intro) Uncertainty Propagation in Causal Systems
A Variance Modeling Framework Based on Variational Autoencoders for Speech Enhancement
A Variance Modeling Framework Based on Variational Autoencoders for Speech Enhancement Simon Leglaive 1 Laurent Girin 1,2 Radu Horaud 1 1: Inria Grenoble Rhône-Alpes 2: Univ. Grenoble Alpes, Grenoble INP,
Machine Learning in Simple Networks. Lars Kai Hansen
Machine Learning in Simple Networs Lars Kai Hansen www.imm.dtu.d/~lh Outline Communities and lin prediction Modularity Modularity as a combinatorial optimization problem Gibbs sampling Detection threshold
Source localization and separation for binaural hearing aids
Source localization and separation for binaural hearing aids Mehdi Zohourian, Gerald Enzner, Rainer Martin Listen Workshop, July 218 Institute of Communication Acoustics Outline 1 Introduction 2 Binaural
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
Convergence of Particle Filtering Method for Nonlinear Estimation of Vortex Dynamics
Convergence of Particle Filtering Method for Nonlinear Estimation of Vortex Dynamics Meng Xu Department of Mathematics University of Wyoming February 20, 2010 Outline 1 Nonlinear Filtering Stochastic Vortex
The University of Auckland Applied Mathematics Bayesian Methods for Inverse Problems : why and how Colin Fox Tiangang Cui, Mike O Sullivan (Auckland),
The University of Auckland Applied Mathematics Bayesian Methods for Inverse Problems : why and how Colin Fox Tiangang Cui, Mike O Sullivan (Auckland), Geoff Nicholls (Statistics, Oxford) fox@math.auckland.ac.nz
PROBABILISTIC REASONING OVER TIME
PROBABILISTIC REASONING OVER TIME In which we try to interpret the present, understand the past, and perhaps predict the future, even when very little is crystal clear. Outline Time and uncertainty Inference:
Discriminant Analysis with High Dimensional. von Mises-Fisher distribution and
Athens Journal of Sciences December 2014 Discriminant Analysis with High Dimensional von Mises - Fisher Distributions By Mario Romanazzi This paper extends previous work in discriminant analysis with von
Review: Probabilistic Matrix Factorization. Probabilistic Matrix Factorization (PMF)
Case Study 4: Collaborative Filtering Review: Probabilistic Matrix Factorization Machine Learning for Big Data CSE547/STAT548, University of Washington Emily Fox February 2 th, 214 Emily Fox 214 1 Probabilistic
Posterior Cramer-Rao Lower Bound for Mobile Tracking in Mixed Line-of-Sight/Non Line-of-Sight Conditions
Posterior Cramer-Rao Lower Bound for Mobile Tracking in Mixed Line-of-Sight/Non Line-of-Sight Conditions Chen Liang 1,2, Wu Lenan 2, Robert Piché 1 1 Tampere University of Technology, Finland 2 Southeast
Auxiliary Particle Methods
Auxiliary Particle Methods Perspectives & Applications Adam M. Johansen 1 adam.johansen@bristol.ac.uk Oxford University Man Institute 29th May 2008 1 Collaborators include: Arnaud Doucet, Nick Whiteley
Rao-Blackwellized Particle Filter for Multiple Target Tracking
Rao-Blackwellized Particle Filter for Multiple Target Tracking Simo Särkkä, Aki Vehtari, Jouko Lampinen Helsinki University of Technology, Finland Abstract In this article we propose a new Rao-Blackwellized
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
Introduction to Reinforcement Learning. CMPT 882 Mar. 18
Introduction to Reinforcement Learning CMPT 882 Mar. 18 Outline for the week Basic ideas in RL Value functions and value iteration Policy evaluation and policy improvement Model-free RL Monte-Carlo and
EVALUATING SYMMETRIC INFORMATION GAP BETWEEN DYNAMICAL SYSTEMS USING PARTICLE FILTER
EVALUATING SYMMETRIC INFORMATION GAP BETWEEN DYNAMICAL SYSTEMS USING PARTICLE FILTER Zhen Zhen 1, Jun Young Lee 2, and Abdus Saboor 3 1 Mingde College, Guizhou University, China zhenz2000@21cn.com 2 Department
DETECTION theory deals primarily with techniques for
ADVANCED SIGNAL PROCESSING SE Optimum Detection of Deterministic and Random Signals Stefan Tertinek Graz University of Technology turtle@sbox.tugraz.at Abstract This paper introduces various methods for
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?
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
Lagrangian Data Assimilation and Manifold Detection for a Point-Vortex Model. David Darmon, AMSC Kayo Ide, AOSC, IPST, CSCAMM, ESSIC
Lagrangian Data Assimilation and Manifold Detection for a Point-Vortex Model David Darmon, AMSC Kayo Ide, AOSC, IPST, CSCAMM, ESSIC Background Data Assimilation Iterative process Forecast Analysis Background
Autonomous Mobile Robot Design
Autonomous Mobile Robot Design Topic: Particle Filter for Localization Dr. Kostas Alexis (CSE) These slides relied on the lectures from C. Stachniss, and the book Probabilistic Robotics from Thurn et al.
Introduction to Graphical Models
Introduction to Graphical Models The 15 th Winter School of Statistical Physics POSCO International Center & POSTECH, Pohang 2018. 1. 9 (Tue.) Yung-Kyun Noh GENERALIZATION FOR PREDICTION 2 Probabilistic
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
Stochastic Analogues to Deterministic Optimizers
Stochastic Analogues to Deterministic Optimizers ISMP 2018 Bordeaux, France Vivak Patel Presented by: Mihai Anitescu July 6, 2018 1 Apology I apologize for not being here to give this talk myself. I injured
Variational Methods in Bayesian Deconvolution
PHYSTAT, SLAC, Stanford, California, September 8-, Variational Methods in Bayesian Deconvolution K. Zarb Adami Cavendish Laboratory, University of Cambridge, UK This paper gives an introduction to the
Introduction to Systems Analysis and Decision Making Prepared by: Jakub Tomczak
Introduction to Systems Analysis and Decision Making Prepared by: Jakub Tomczak 1 Introduction. Random variables During the course we are interested in reasoning about considered phenomenon. In other words,
Robotics. Mobile Robotics. Marc Toussaint U Stuttgart
Robotics Mobile Robotics State estimation, Bayes filter, odometry, particle filter, Kalman filter, SLAM, joint Bayes filter, EKF SLAM, particle SLAM, graph-based SLAM Marc Toussaint U Stuttgart DARPA Grand
Monte Carlo in Bayesian Statistics
Monte Carlo in Bayesian Statistics Matthew Thomas SAMBa - University of Bath m.l.thomas@bath.ac.uk December 4, 2014 Matthew Thomas (SAMBa) Monte Carlo in Bayesian Statistics December 4, 2014 1 / 16 Overview
Winter 2019 Math 106 Topics in Applied Mathematics. Lecture 8: Importance Sampling
Winter 2019 Math 106 Topics in Applied Mathematics Data-driven Uncertainty Quantification Yoonsang Lee (yoonsang.lee@dartmouth.edu) Lecture 8: Importance Sampling 8.1 Importance Sampling Importance sampling
Probabilistic Machine Learning
Probabilistic Machine Learning Bayesian Nets, MCMC, and more Marek Petrik 4/18/2017 Based on: P. Murphy, K. (2012). Machine Learning: A Probabilistic Perspective. Chapter 10. Conditional Independence Independent
Bayesian Social Learning with Random Decision Making in Sequential Systems
Bayesian Social Learning with Random Decision Making in Sequential Systems Yunlong Wang supervised by Petar M. Djurić Department of Electrical and Computer Engineering Stony Brook University Stony Brook,
Lecture Outline. Target Tracking: Lecture 3 Maneuvering Target Tracking Issues. Maneuver Illustration. Maneuver Illustration. Maneuver Detection
REGLERTEKNIK Lecture Outline AUTOMATIC CONTROL Target Tracking: Lecture 3 Maneuvering Target Tracking Issues Maneuver Detection Emre Özkan emre@isy.liu.se Division of Automatic Control Department of Electrical
Target Tracking and Classification using Collaborative Sensor Networks
Target Tracking and Classification using Collaborative Sensor Networks Xiaodong Wang Department of Electrical Engineering Columbia University p.1/3 Talk Outline Background on distributed wireless sensor
Convergence Rates of Kernel Quadrature Rules
Convergence Rates of Kernel Quadrature Rules Francis Bach INRIA - Ecole Normale Supérieure, Paris, France ÉCOLE NORMALE SUPÉRIEURE NIPS workshop on probabilistic integration - Dec. 2015 Outline Introduction
Imprecise Filtering for Spacecraft Navigation
Imprecise Filtering for Spacecraft Navigation Tathagata Basu Cristian Greco Thomas Krak Durham University Strathclyde University Ghent University Filtering for Spacecraft Navigation The General Problem
Learning with Noisy Labels. Kate Niehaus Reading group 11-Feb-2014
Learning with Noisy Labels Kate Niehaus Reading group 11-Feb-2014 Outline Motivations Generative model approach: Lawrence, N. & Scho lkopf, B. Estimating a Kernel Fisher Discriminant in the Presence of
Chapter 4 Dynamic Bayesian Networks Fall Jin Gu, Michael Zhang
Chapter 4 Dynamic Bayesian Networks 2016 Fall Jin Gu, Michael Zhang Reviews: BN Representation Basic steps for BN representations Define variables Define the preliminary relations between variables Check
Directional Statistics
Directional Statistics Kanti V. Mardia University of Leeds, UK Peter E. Jupp University of St Andrews, UK I JOHN WILEY & SONS, LTD Chichester New York Weinheim Brisbane Singapore Toronto Contents Preface
PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 2: PROBABILITY DISTRIBUTIONS
PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 2: PROBABILITY DISTRIBUTIONS Parametric Distributions Basic building blocks: Need to determine given Representation: or? Recall Curve Fitting Binary Variables
Dynamic Multipath Estimation by Sequential Monte Carlo Methods
Dynamic Multipath Estimation by Sequential Monte Carlo Methods M. Lentmaier, B. Krach, P. Robertson, and T. Thiasiriphet German Aerospace Center (DLR) Slide 1 Outline Multipath problem and signal model
9 Multi-Model State Estimation
Technion Israel Institute of Technology, Department of Electrical Engineering Estimation and Identification in Dynamical Systems (048825) Lecture Notes, Fall 2009, Prof. N. Shimkin 9 Multi-Model State
A Tree Search Approach to Target Tracking in Clutter
12th International Conference on Information Fusion Seattle, WA, USA, July 6-9, 2009 A Tree Search Approach to Target Tracking in Clutter Jill K. Nelson and Hossein Roufarshbaf Department of Electrical
Patterns of Scalable Bayesian Inference Background (Session 1)
Patterns of Scalable Bayesian Inference Background (Session 1) Jerónimo Arenas-García Universidad Carlos III de Madrid jeronimo.arenas@gmail.com June 14, 2017 1 / 15 Motivation. Bayesian Learning principles
Gaussian Process Optimization with Mutual Information
Gaussian Process Optimization with Mutual Information Emile Contal 1 Vianney Perchet 2 Nicolas Vayatis 1 1 CMLA Ecole Normale Suprieure de Cachan & CNRS, France 2 LPMA Université Paris Diderot & CNRS,
Factor Analysis and Kalman Filtering (11/2/04)
CS281A/Stat241A: Statistical Learning Theory Factor Analysis and Kalman Filtering (11/2/04) Lecturer: Michael I. Jordan Scribes: Byung-Gon Chun and Sunghoon Kim 1 Factor Analysis Factor analysis is used
Hidden Markov Models. Aarti Singh Slides courtesy: Eric Xing. Machine Learning / Nov 8, 2010
Hidden Markov Models Aarti Singh Slides courtesy: Eric Xing Machine Learning 10-701/15-781 Nov 8, 2010 i.i.d to sequential data So far we assumed independent, identically distributed data Sequential data
Multi-fidelity sensitivity analysis
Multi-fidelity sensitivity analysis Loic Le Gratiet 1,2, Claire Cannamela 2 & Bertrand Iooss 3 1 Université Denis-Diderot, Paris, France 2 CEA, DAM, DIF, F-91297 Arpajon, France 3 EDF R&D, 6 quai Watier,
Lagrangian Data Assimilation and Its Application to Geophysical Fluid Flows
Lagrangian Data Assimilation and Its Application to Geophysical Fluid Flows Laura Slivinski June, 3 Laura Slivinski (Brown University) Lagrangian Data Assimilation June, 3 / 3 Data Assimilation Setup: