Intelligent Systems I
|
|
|
- Abigayle Gregory
- 5 years ago
- Views:
Transcription
1 Intelligent Systems I 00 INTRODUCTION Stefan Harmeling & Philipp Hennig 24. October 2013 Max Planck Institute for Intelligent Systems Dptmt. of Empirical Inference
2 Which Card? Opening Experiment
3 Which Card? Opening Experiment 50% 66% something else don t know yet
4 Inference Reasoning under uncertainty Definition (Inference) An inference problem requires statements about the value of an unobserved (latent) variable x based on observations y which are related to x, but not sufficient to fully determine x. This requires a notion of uncertainty.
5 Inference in real life source: wikipedia
6 Inference in real life Luke Fildes, 1891
7 Inference in real life Den Haag, 2006
8 Inference in real life CERN, 1997
9 Inference & Intelligence Reasoning under uncertainty Intelligence [ Mainstream Science on Intelligence, WSJ, 13 Dec. 1994] A very general mental capability that, among other things, involves the ability to reason, plan, solve problems, think abstractly, comprehend complex ideas, learn quickly and learn from experience Definition (Intelligence, for our purposes) An intelligent system is an artifact that collects information about the world discovers (infers) a structured model of the world acts to influence the world
10 Inference & Intelligence Reasoning under uncertainty Intelligence [ Mainstream Science on Intelligence, WSJ, 13 Dec. 1994] A very general mental capability that, among other things, involves the ability to reason, plan, solve problems, think abstractly, comprehend complex ideas, learn quickly and learn from experience Definition (Intelligence, for our purposes) An intelligent system is an artifact that collects information about the world discovers (infers) a structured model of the world acts to influence the world last semester this course next semester
11 How intelligent are we? humans are not always good in inference tasks We need a mathematical description of inference!
12 Probability Theory The logic of uncertainty p(x = x): probability for X = x. short: p(x) product rule (definition conditional probability) p(x, y) = p(x)p(y x) = p(y)p(x y) sum rule Y = y 1,..., y n, X = x 1,..., x m p(x) = p(x, y 1 ) + + p(x, y n ) = p(x, y i ) Corollary: Bayes theorem i=1,...,n p(x i y) = p(x i)p(y x i ) j p(y x j)p(x j ) posterior = prior likelihood evidence in words: The probability for hypothesis x i is the probability for the observed data y under x i, compared to that probability under all hypotheses.
13 Bayes theorem in action p(c 1 ) = 1 /3 p(c 2 ) = 1 /3 p(c 3 ) = 1 /3 p(w c 1 ) = 0 p(r c 1 ) = 1 p(w c 2 ) = 1 /2 p(r c 2 ) = 1 /2 p(w c 3 ) = 1 p(r c 3 ) = 0 c 1 c 2 c 3
14 Contents and goals of this course a coherent picture of intelligent systems connection between Aristotelian / Boolean logic and probability theory graphical models: a structural language for probabilistic computations inference on functions supervised learning {(xi, y i)} f : X R N regression {(xi, c i)} f : X N classification inference on structure {xi} p(x) unsupervised learning models (Gaussian processes, Support Vector Machines, Neural Networks,... ) algorithms (integration, optimization, sampling,... )
15 Is this a machine learning course? Related fields: Statistics Machine learning Scientific inference (in physics, biology, social sciences,... ) numerical mathematics (optimization, integration,... ) control engineering (systems identification) a systems view Intelligent systems consist of interacting parts, in contact with the world require a joint language (probability) linking different parts of the system. We will aim for a computational view emphasizing modularization and abstraction ( probabilistic programming) finite time imposes limits on performance of inference. We will study the way in which learning can fail, the assumptions required for its success, and how generality interacts with efficiency.
16 Summary reasoning and acting under uncertainty intelligence is the ability to reason and act in an uncertain world. an intelligent system observes the world, infers its structure, then acts to effect change. probability theory is the mathematical language of inference.
17 Admin Stuff things to write down Slides: Mailing List: Lecturers: Tutors: Tutorials: date to fix Feedback: return at end of each lecture Exercises: need 30% correct to be admitted to exam Final grade: 100% exam Break: would you prefer 2 45 minutes or 90 minutes?
18 Some Literature but this course is not based explicitly on any of them Free online: David J C MacKay Cambridge, 2003 Information Theory, Inference, and Learning Algorithms David Barber Cambridge, 2012 Bayesian Reasoning and Machine Learning Carl E Rasmussen & Christopher K I Williams MIT, 2006 Gaussian Processes for Machine Learning Non-free: Judea Pearl Morgan Kaufmann, 1988 Probabilistic Reasoning in Intelligent Systems Christopher Bishop Springer, 2007 Pattern Recognition and Machine Learning Bernhard Schölkopf & Alexander J Smola MIT, 2001 Learning with Kernels Edwin T Jaynes & G Larry Bretthorst Cambridge, 2003 Probability Theory the Logic of Science
Probabilistic Graphical Models for Image Analysis - Lecture 1
Probabilistic Graphical Models for Image Analysis - Lecture 1 Alexey Gronskiy, Stefan Bauer 21 September 2018 Max Planck ETH Center for Learning Systems Overview 1. Motivation - Why Graphical Models 2.
9/12/17. Types of learning. Modeling data. Supervised learning: Classification. Supervised learning: Regression. Unsupervised learning: Clustering
Types of learning Modeling data Supervised: we know input and targets Goal is to learn a model that, given input data, accurately predicts target data Unsupervised: we know the input only and want to make
Learning from Data. Amos Storkey, School of Informatics. Semester 1. amos/lfd/
Semester 1 http://www.anc.ed.ac.uk/ amos/lfd/ Introduction Welcome Administration Online notes Books: See website Assignments Tutorials Exams Acknowledgement: I would like to that David Barber and Chris
Tutorial on Gaussian Processes and the Gaussian Process Latent Variable Model
Tutorial on Gaussian Processes and the Gaussian Process Latent Variable Model (& discussion on the GPLVM tech. report by Prof. N. Lawrence, 06) Andreas Damianou Department of Neuro- and Computer Science,
DD Advanced Machine Learning
Modelling Carl Henrik {chek}@csc.kth.se Royal Institute of Technology November 4, 2015 Who do I think you are? Mathematically competent linear algebra multivariate calculus Ok programmers Able to extend
STAT 518 Intro Student Presentation
STAT 518 Intro Student Presentation Wen Wei Loh April 11, 2013 Title of paper Radford M. Neal [1999] Bayesian Statistics, 6: 475-501, 1999 What the paper is about Regression and Classification Flexible
Bayesian Machine Learning
Bayesian Machine Learning Andrew Gordon Wilson ORIE 6741 Lecture 4 Occam s Razor, Model Construction, and Directed Graphical Models https://people.orie.cornell.edu/andrew/orie6741 Cornell University September
Probabilistic Models for Learning Data Representations. Andreas Damianou
Probabilistic Models for Learning Data Representations Andreas Damianou Department of Computer Science, University of Sheffield, UK IBM Research, Nairobi, Kenya, 23/06/2015 Sheffield SITraN Outline Part
PILCO: A Model-Based and Data-Efficient Approach to Policy Search
PILCO: A Model-Based and Data-Efficient Approach to Policy Search (M.P. Deisenroth and C.E. Rasmussen) CSC2541 November 4, 2016 PILCO Graphical Model PILCO Probabilistic Inference for Learning COntrol
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
Machine Learning. Bayesian Regression & Classification. Marc Toussaint U Stuttgart
Machine Learning Bayesian Regression & Classification learning as inference, Bayesian Kernel Ridge regression & Gaussian Processes, Bayesian Kernel Logistic Regression & GP classification, Bayesian Neural
CSci 8980: Advanced Topics in Graphical Models Gaussian Processes
CSci 8980: Advanced Topics in Graphical Models Gaussian Processes Instructor: Arindam Banerjee November 15, 2007 Gaussian Processes Outline Gaussian Processes Outline Parametric Bayesian Regression Gaussian
Lecture 3. Linear Regression II Bastian Leibe RWTH Aachen
Advanced Machine Learning Lecture 3 Linear Regression II 02.11.2015 Bastian Leibe RWTH Aachen http://www.vision.rwth-aachen.de/ leibe@vision.rwth-aachen.de This Lecture: Advanced Machine Learning Regression
Introduction to Bayesian Learning. Machine Learning Fall 2018
Introduction to Bayesian Learning Machine Learning Fall 2018 1 What we have seen so far What does it mean to learn? Mistake-driven learning Learning by counting (and bounding) number of mistakes PAC learnability
Probability. Machine Learning and Pattern Recognition. Chris Williams. School of Informatics, University of Edinburgh. August 2014
Probability Machine Learning and Pattern Recognition Chris Williams School of Informatics, University of Edinburgh August 2014 (All of the slides in this course have been adapted from previous versions
CSC321 Lecture 18: Learning Probabilistic Models
CSC321 Lecture 18: Learning Probabilistic Models Roger Grosse Roger Grosse CSC321 Lecture 18: Learning Probabilistic Models 1 / 25 Overview So far in this course: mainly supervised learning Language modeling
Machine Learning Lecture 1
Many slides adapted from B. Schiele Machine Learning Lecture 1 Introduction 18.04.2016 Bastian Leibe RWTH Aachen http://www.vision.rwth-aachen.de/ leibe@vision.rwth-aachen.de Organization Lecturer Prof.
Lecture Machine Learning (past summer semester) If at least one English-speaking student is present.
Advanced Machine Learning Lecture 1 Organization Lecturer Prof. Bastian Leibe (leibe@vision.rwth-aachen.de) Introduction 20.10.2015 Bastian Leibe Visual Computing Institute RWTH Aachen University http://www.vision.rwth-aachen.de/
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. Lecture 11: Gaussian Processes. Department of Statistics
STA414/2104 Lecture 11: Gaussian Processes Department of Statistics www.utstat.utoronto.ca Delivered by Mark Ebden with thanks to Russ Salakhutdinov Outline Gaussian Processes Exam review Course evaluations
Computational Cognitive Science
Computational Cognitive Science Lecture 9: A Bayesian model of concept learning Chris Lucas School of Informatics University of Edinburgh October 16, 218 Reading Rules and Similarity in Concept Learning
Multivariate Bayesian Linear Regression MLAI Lecture 11
Multivariate Bayesian Linear Regression MLAI Lecture 11 Neil D. Lawrence Department of Computer Science Sheffield University 21st October 2012 Outline Univariate Bayesian Linear Regression Multivariate
Probabilistic & Unsupervised Learning
Probabilistic & Unsupervised Learning Gaussian Processes Maneesh Sahani maneesh@gatsby.ucl.ac.uk Gatsby Computational Neuroscience Unit, and MSc ML/CSML, Dept Computer Science University College London
ECE-271B. Nuno Vasconcelos ECE Department, UCSD
ECE-271B Statistical ti ti Learning II Nuno Vasconcelos ECE Department, UCSD The course the course is a graduate level course in statistical learning in SLI we covered the foundations of Bayesian or generative
Probability models for machine learning. Advanced topics ML4bio 2016 Alan Moses
Probability models for machine learning Advanced topics ML4bio 2016 Alan Moses What did we cover in this course so far? 4 major areas of machine learning: Clustering Dimensionality reduction Classification
Regression. Machine Learning and Pattern Recognition. Chris Williams. School of Informatics, University of Edinburgh.
Regression Machine Learning and Pattern Recognition Chris Williams School of Informatics, University of Edinburgh September 24 (All of the slides in this course have been adapted from previous versions
Machine Learning
Machine Learning 10-601 Tom M. Mitchell Machine Learning Department Carnegie Mellon University August 30, 2017 Today: Decision trees Overfitting The Big Picture Coming soon Probabilistic learning MLE,
PATTERN RECOGNITION AND MACHINE LEARNING
PATTERN RECOGNITION AND MACHINE LEARNING Chapter 1. Introduction Shuai Huang April 21, 2014 Outline 1 What is Machine Learning? 2 Curve Fitting 3 Probability Theory 4 Model Selection 5 The curse of dimensionality
Machine Learning (CS 567) Lecture 2
Machine Learning (CS 567) Lecture 2 Time: T-Th 5:00pm - 6:20pm Location: GFS118 Instructor: Sofus A. Macskassy (macskass@usc.edu) Office: SAL 216 Office hours: by appointment Teaching assistant: Cheol
COURSE INTRODUCTION. J. Elder CSE 6390/PSYC 6225 Computational Modeling of Visual Perception
COURSE INTRODUCTION COMPUTATIONAL MODELING OF VISUAL PERCEPTION 2 The goal of this course is to provide a framework and computational tools for modeling visual inference, motivated by interesting examples
Course 395: Machine Learning
Course 395: Machine Learning Lecturers: Maja Pantic (maja@doc.ic.ac.uk) Stavros Petridis (sp104@doc.ic.ac.uk) Goal (Lectures): To present basic theoretical concepts and key algorithms that form the core
An Introduction to Statistical and Probabilistic Linear Models
An Introduction to Statistical and Probabilistic Linear Models Maximilian Mozes Proseminar Data Mining Fakultät für Informatik Technische Universität München June 07, 2017 Introduction In statistical learning
Introduction Generalization Overview of the main methods Resources. Pattern Recognition. Bertrand Thirion and John Ashburner
Definitions Classification and Regression Curse of Dimensionality Some key concepts Definitions Classification and Regression Curse of Dimensionality supervised learning: The data comes with additional
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
GWAS V: Gaussian processes
GWAS V: Gaussian processes Dr. Oliver Stegle Christoh Lippert Prof. Dr. Karsten Borgwardt Max-Planck-Institutes Tübingen, Germany Tübingen Summer 2011 Oliver Stegle GWAS V: Gaussian processes Summer 2011
NPFL108 Bayesian inference. Introduction. Filip Jurčíček. Institute of Formal and Applied Linguistics Charles University in Prague Czech Republic
NPFL108 Bayesian inference Introduction Filip Jurčíček Institute of Formal and Applied Linguistics Charles University in Prague Czech Republic Home page: http://ufal.mff.cuni.cz/~jurcicek Version: 21/02/2014
Gaussian Process Regression
Gaussian Process Regression 4F1 Pattern Recognition, 21 Carl Edward Rasmussen Department of Engineering, University of Cambridge November 11th - 16th, 21 Rasmussen (Engineering, Cambridge) Gaussian Process
Intro to Probability. Andrei Barbu
Intro to Probability Andrei Barbu Some problems Some problems A means to capture uncertainty Some problems A means to capture uncertainty You have data from two sources, are they different? Some problems
ADVANCED MACHINE LEARNING ADVANCED MACHINE LEARNING. Non-linear regression techniques Part - II
1 Non-linear regression techniques Part - II Regression Algorithms in this Course Support Vector Machine Relevance Vector Machine Support vector regression Boosting random projections Relevance vector
Chapter 04: Exact Inference in Bayesian Networks
LEARNING AND INFERENCE IN GRAPHICAL MODELS Chapter 04: Exact Inference in Bayesian Networks Dr. Martin Lauer University of Freiburg Machine Learning Lab Karlsruhe Institute of Technology Institute of Measurement
Introduction to Machine Learning. Introduction to ML - TAU 2016/7 1
Introduction to Machine Learning Introduction to ML - TAU 2016/7 1 Course Administration Lecturers: Amir Globerson (gamir@post.tau.ac.il) Yishay Mansour (Mansour@tau.ac.il) Teaching Assistance: Regev Schweiger
Bayesian Linear Regression [DRAFT - In Progress]
![Bayesian Linear Regression [DRAFT - In Progress]](/thumbs/92/109828713.jpg "Bayesian Linear Regression [DRAFT - In Progress]")
Bayesian Linear Regression [DRAFT - In Progress] David S. Rosenberg Abstract Here we develop some basics of Bayesian linear regression. Most of the calculations for this document come from the basic theory
DEPARTMENT OF COMPUTER SCIENCE Autumn Semester MACHINE LEARNING AND ADAPTIVE INTELLIGENCE
Data Provided: None DEPARTMENT OF COMPUTER SCIENCE Autumn Semester 203 204 MACHINE LEARNING AND ADAPTIVE INTELLIGENCE 2 hours Answer THREE of the four questions. All questions carry equal weight. Figures
Intelligent Systems: Reasoning and Recognition. Reasoning with Bayesian Networks
Intelligent Systems: Reasoning and Recognition James L. Crowley ENSIMAG 2 / MoSIG M1 Second Semester 2016/2017 Lesson 13 24 march 2017 Reasoning with Bayesian Networks Naïve Bayesian Systems...2 Example
Expectation Propagation for Approximate Bayesian Inference
Expectation Propagation for Approximate Bayesian Inference José Miguel Hernández Lobato Universidad Autónoma de Madrid, Computer Science Department February 5, 2007 1/ 24 Bayesian Inference Inference Given
Statistical Techniques in Robotics (16-831, F12) Lecture#21 (Monday November 12) Gaussian Processes
Statistical Techniques in Robotics (16-831, F12) Lecture#21 (Monday November 12) Gaussian Processes Lecturer: Drew Bagnell Scribe: Venkatraman Narayanan 1, M. Koval and P. Parashar 1 Applications of Gaussian
CS-E3210 Machine Learning: Basic Principles
CS-E3210 Machine Learning: Basic Principles Lecture 4: Regression II slides by Markus Heinonen Department of Computer Science Aalto University, School of Science Autumn (Period I) 2017 1 / 61 Today s introduction
CS 6375 Machine Learning
CS 6375 Machine Learning Nicholas Ruozzi University of Texas at Dallas Slides adapted from David Sontag and Vibhav Gogate Course Info. Instructor: Nicholas Ruozzi Office: ECSS 3.409 Office hours: Tues.
Neutron inverse kinetics via Gaussian Processes
Neutron inverse kinetics via Gaussian Processes P. Picca Politecnico di Torino, Torino, Italy R. Furfaro University of Arizona, Tucson, Arizona Outline Introduction Review of inverse kinetics techniques
Intelligent Systems I
1, Intelligent Systems I 12 SAMPLING METHODS THE LAST THING YOU SHOULD EVER TRY Philipp Hennig & Stefan Harmeling Max Planck Institute for Intelligent Systems 23. January 2014 Dptmt. of Empirical Inference
Bayesian Deep Learning
Bayesian Deep Learning Mohammad Emtiyaz Khan AIP (RIKEN), Tokyo http://emtiyaz.github.io emtiyaz.khan@riken.jp June 06, 2018 Mohammad Emtiyaz Khan 2018 1 What will you learn? Why is Bayesian inference
Machine Learning. Bayes Basics. Marc Toussaint U Stuttgart. Bayes, probabilities, Bayes theorem & examples
Machine Learning Bayes Basics Bayes, probabilities, Bayes theorem & examples Marc Toussaint U Stuttgart So far: Basic regression & classification methods: Features + Loss + Regularization & CV All kinds
20: Gaussian Processes
10-708: Probabilistic Graphical Models 10-708, Spring 2016 20: Gaussian Processes Lecturer: Andrew Gordon Wilson Scribes: Sai Ganesh Bandiatmakuri 1 Discussion about ML Here we discuss an introduction
Logistic Regression Review Fall 2012 Recitation. September 25, 2012 TA: Selen Uguroglu
Logistic Regression Review 10-601 Fall 2012 Recitation September 25, 2012 TA: Selen Uguroglu!1 Outline Decision Theory Logistic regression Goal Loss function Inference Gradient Descent!2 Training Data
CMU-Q Lecture 24:
CMU-Q 15-381 Lecture 24: Supervised Learning 2 Teacher: Gianni A. Di Caro SUPERVISED LEARNING Hypotheses space Hypothesis function Labeled Given Errors Performance criteria Given a collection of input
Gaussian Processes. 1 What problems can be solved by Gaussian Processes?
Statistical Techniques in Robotics (16-831, F1) Lecture#19 (Wednesday November 16) Gaussian Processes Lecturer: Drew Bagnell Scribe:Yamuna Krishnamurthy 1 1 What problems can be solved by Gaussian Processes?
Latent Dirichlet Allocation Introduction/Overview
Latent Dirichlet Allocation Introduction/Overview David Meyer 03.10.2016 David Meyer http://www.1-4-5.net/~dmm/ml/lda_intro.pdf 03.10.2016 Agenda What is Topic Modeling? Parametric vs. Non-Parametric Models
Learning Gaussian Process Models from Uncertain Data
Learning Gaussian Process Models from Uncertain Data Patrick Dallaire, Camille Besse, and Brahim Chaib-draa DAMAS Laboratory, Computer Science & Software Engineering Department, Laval University, Canada
Recall from last time: Conditional probabilities. Lecture 2: Belief (Bayesian) networks. Bayes ball. Example (continued) Example: Inference problem
Recall from last time: Conditional probabilities Our probabilistic models will compute and manipulate conditional probabilities. Given two random variables X, Y, we denote by Lecture 2: Belief (Bayesian)
Day 5: Generative models, structured classification
Day 5: Generative models, structured classification Introduction to Machine Learning Summer School June 18, 2018 - June 29, 2018, Chicago Instructor: Suriya Gunasekar, TTI Chicago 22 June 2018 Linear regression
Statistical Techniques in Robotics (16-831, F12) Lecture#20 (Monday November 12) Gaussian Processes
Statistical Techniques in Robotics (6-83, F) Lecture# (Monday November ) Gaussian Processes Lecturer: Drew Bagnell Scribe: Venkatraman Narayanan Applications of Gaussian Processes (a) Inverse Kinematics
Nonparameteric Regression:
Nonparameteric Regression: Nadaraya-Watson Kernel Regression & Gaussian Process Regression Seungjin Choi Department of Computer Science and Engineering Pohang University of Science and Technology 77 Cheongam-ro,
The Variational Gaussian Approximation Revisited
The Variational Gaussian Approximation Revisited Manfred Opper Cédric Archambeau March 16, 2009 Abstract The variational approximation of posterior distributions by multivariate Gaussians has been much
Gaussian Process Dynamical Models Jack M Wang, David J Fleet, Aaron Hertzmann, NIPS 2005
Gaussian Process Dynamical Models Jack M Wang, David J Fleet, Aaron Hertzmann, NIPS 2005 Presented by Piotr Mirowski CBLL meeting, May 6, 2009 Courant Institute of Mathematical Sciences, New York University
Machine Learning and Bayesian Inference
Machine Learning and Bayesian Inference Dr Sean Holden Computer Laboratory, Room FC6 Telephone extension 63725 Email: sbh11@cl.cam.ac.uk www.cl.cam.ac.uk/ sbh11/ Copyright c Sean Holden 22-17. 1 Artificial
Probability and (Bayesian) Data Analysis
Department of Statistics The University of Auckland https://www.stat.auckland.ac.nz/ brewer/ Where to get everything To get all of the material (slides, code, exercises): git clone --recursive https://github.com/eggplantbren/madrid
Probabilistic Graphical Models Lecture 20: Gaussian Processes
Probabilistic Graphical Models Lecture 20: Gaussian Processes Andrew Gordon Wilson www.cs.cmu.edu/~andrewgw Carnegie Mellon University March 30, 2015 1 / 53 What is Machine Learning? Machine learning algorithms
Logistic Regression. Machine Learning Fall 2018
Logistic Regression Machine Learning Fall 2018 1 Where are e? We have seen the folloing ideas Linear models Learning as loss minimization Bayesian learning criteria (MAP and MLE estimation) The Naïve Bayes
Introduction to Gaussian Processes
Introduction to Gaussian Processes Neil D. Lawrence GPSS 10th June 2013 Book Rasmussen and Williams (2006) Outline The Gaussian Density Covariance from Basis Functions Basis Function Representations Constructing
Probabilistic latent variable models for distinguishing between cause and effect
Probabilistic latent variable models for distinguishing between cause and effect Joris M. Mooij joris.mooij@tuebingen.mpg.de Oliver Stegle oliver.stegle@tuebingen.mpg.de Dominik Janzing dominik.janzing@tuebingen.mpg.de
Probabilistic Graphical Models
Probabilistic Graphical Models Introduction. Basic Probability and Bayes Volkan Cevher, Matthias Seeger Ecole Polytechnique Fédérale de Lausanne 26/9/2011 (EPFL) Graphical Models 26/9/2011 1 / 28 Outline
Parametric Unsupervised Learning Expectation Maximization (EM) Lecture 20.a
Parametric Unsupervised Learning Expectation Maximization (EM) Lecture 20.a Some slides are due to Christopher Bishop Limitations of K-means Hard assignments of data points to clusters small shift of a
Cheng Soon Ong & Christian Walder. Canberra February June 2018
Cheng Soon Ong & Christian Walder Research Group and College of Engineering and Computer Science Canberra February June 218 Outlines Overview Introduction Linear Algebra Probability Linear Regression 1
Statistical and Learning Techniques in Computer Vision Lecture 2: Maximum Likelihood and Bayesian Estimation Jens Rittscher and Chuck Stewart
Statistical and Learning Techniques in Computer Vision Lecture 2: Maximum Likelihood and Bayesian Estimation Jens Rittscher and Chuck Stewart 1 Motivation and Problem In Lecture 1 we briefly saw how histograms
Inference of Cause and Effect with Unsupervised Inverse Regression
Inference of Cause and Effect with Unsupervised Inverse Regression Eleni Sgouritsa Dominik Janzing Philipp Hennig Bernhard Schölkopf Max Planck Institute for Intelligent Systems, Tübingen, Germany {eleni.sgouritsa,
CS Lecture 18. Topic Models and LDA
CS 6347 Lecture 18 Topic Models and LDA (some slides by David Blei) Generative vs. Discriminative Models Recall that, in Bayesian networks, there could be many different, but equivalent models of the same
Nonparametric Bayesian Methods (Gaussian Processes)
[70240413 Statistical Machine Learning, Spring, 2015] Nonparametric Bayesian Methods (Gaussian Processes) Jun Zhu dcszj@mail.tsinghua.edu.cn http://bigml.cs.tsinghua.edu.cn/~jun State Key Lab of Intelligent
GWAS IV: Bayesian linear (variance component) models
GWAS IV: Bayesian linear (variance component) models Dr. Oliver Stegle Christoh Lippert Prof. Dr. Karsten Borgwardt Max-Planck-Institutes Tübingen, Germany Tübingen Summer 2011 Oliver Stegle GWAS IV: Bayesian
Gaussian Mixture Models, Expectation Maximization
Gaussian Mixture Models, Expectation Maximization Instructor: Jessica Wu Harvey Mudd College The instructor gratefully acknowledges Andrew Ng (Stanford), Andrew Moore (CMU), Eric Eaton (UPenn), David Kauchak
Generative Clustering, Topic Modeling, & Bayesian Inference
Generative Clustering, Topic Modeling, & Bayesian Inference INFO-4604, Applied Machine Learning University of Colorado Boulder December 12-14, 2017 Prof. Michael Paul Unsupervised Naïve Bayes Last week
Generative Learning. INFO-4604, Applied Machine Learning University of Colorado Boulder. November 29, 2018 Prof. Michael Paul
Generative Learning INFO-4604, Applied Machine Learning University of Colorado Boulder November 29, 2018 Prof. Michael Paul Generative vs Discriminative The classification algorithms we have seen so far
Pattern Recognition and Machine Learning. Learning and Evaluation of Pattern Recognition Processes
Pattern Recognition and Machine Learning James L. Crowley ENSIMAG 3 - MMIS Fall Semester 2016 Lesson 1 5 October 2016 Learning and Evaluation of Pattern Recognition Processes Outline Notation...2 1. The
Advanced Introduction to Machine Learning CMU-10715
Advanced Introduction to Machine Learning CMU-10715 Gaussian Processes Barnabás Póczos http://www.gaussianprocess.org/ 2 Some of these slides in the intro are taken from D. Lizotte, R. Parr, C. Guesterin
Machine Learning. Gaussian Mixture Models. Zhiyao Duan & Bryan Pardo, Machine Learning: EECS 349 Fall
Machine Learning Gaussian Mixture Models Zhiyao Duan & Bryan Pardo, Machine Learning: EECS 349 Fall 2012 1 The Generative Model POV We think of the data as being generated from some process. We assume
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
PMR Introduction. Probabilistic Modelling and Reasoning. Amos Storkey. School of Informatics, University of Edinburgh
PMR Introduction Probabilistic Modelling and Reasoning Amos Storkey School of Informatics, University of Edinburgh Amos Storkey PMR Introduction School of Informatics, University of Edinburgh 1/50 Outline
Course Introduction. Probabilistic Modelling and Reasoning. Relationships between courses. Dealing with Uncertainty. Chris Williams.
Course Introduction Probabilistic Modelling and Reasoning Chris Williams School of Informatics, University of Edinburgh September 2008 Welcome Administration Handout Books Assignments Tutorials Course
Bayesian network modeling. 1
Bayesian network modeling http://springuniversity.bc3research.org/ 1 Probabilistic vs. deterministic modeling approaches Probabilistic Explanatory power (e.g., r 2 ) Explanation why Based on inductive
Introduc)on to Bayesian methods (con)nued) - Lecture 16
Introduc)on to Bayesian methods (con)nued) - Lecture 16 David Sontag New York University Slides adapted from Luke Zettlemoyer, Carlos Guestrin, Dan Klein, and Vibhav Gogate Outline of lectures Review of
PROBABILITY AND INFERENCE
PROBABILITY AND INFERENCE Progress Report We ve finished Part I: Problem Solving! Part II: Reasoning with uncertainty Part III: Machine Learning 1 Today Random variables and probabilities Joint, marginal,
CSC2541 Lecture 2 Bayesian Occam s Razor and Gaussian Processes
CSC2541 Lecture 2 Bayesian Occam s Razor and Gaussian Processes Roger Grosse Roger Grosse CSC2541 Lecture 2 Bayesian Occam s Razor and Gaussian Processes 1 / 55 Adminis-Trivia Did everyone get my e-mail
COMP90051 Statistical Machine Learning
COMP90051 Statistical Machine Learning Semester 2, 2017 Lecturer: Trevor Cohn 2. Statistical Schools Adapted from slides by Ben Rubinstein Statistical Schools of Thought Remainder of lecture is to provide
Uncertain Inference and Artificial Intelligence
March 3, 2011 1 Prepared for a Purdue Machine Learning Seminar Acknowledgement Prof. A. P. Dempster for intensive collaborations on the Dempster-Shafer theory. Jianchun Zhang, Ryan Martin, Duncan Ermini
Model Selection for Gaussian Processes
Institute for Adaptive and Neural Computation School of Informatics,, UK December 26 Outline GP basics Model selection: covariance functions and parameterizations Criteria for model selection Marginal
Learning in Bayesian Networks
Learning in Bayesian Networks Florian Markowetz Max-Planck-Institute for Molecular Genetics Computational Molecular Biology Berlin Berlin: 20.06.2002 1 Overview 1. Bayesian Networks Stochastic Networks
Statistical learning. Chapter 20, Sections 1 4 1
Statistical learning Chapter 20, Sections 1 4 Chapter 20, Sections 1 4 1 Outline Bayesian learning Maximum a posteriori and maximum likelihood learning Bayes net learning ML parameter learning with complete
Introduction to Probability and Statistics (Continued)
Introduction to Probability and Statistics (Continued) Prof. icholas Zabaras Center for Informatics and Computational Science https://cics.nd.edu/ University of otre Dame otre Dame, Indiana, USA Email:
John Ashburner. Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, 12 Queen Square, London WC1N 3BG, UK.
FOR MEDICAL IMAGING John Ashburner Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, 12 Queen Square, London WC1N 3BG, UK. PIPELINES V MODELS PROBABILITY THEORY MEDICAL IMAGE COMPUTING