Discrete Optimization for Vision and Learning. Who? How? M. Pawan Kumar Associate Professor Ecole Centrale Paris Nikos Komodakis Associate Professor Ecole.

Slides:



Advertisements
Similar presentations
Solving Markov Random Fields using Second Order Cone Programming Relaxations M. Pawan Kumar Philip Torr Andrew Zisserman.
Advertisements

Convex Programming Brookes Vision Reading Group. Huh? What is convex ??? What is programming ??? What is convex programming ???
1 LP Duality Lecture 13: Feb Min-Max Theorems In bipartite graph, Maximum matching = Minimum Vertex Cover In every graph, Maximum Flow = Minimum.
Learning with Inference for Discrete Graphical Models Nikos Komodakis Pawan Kumar Nikos Paragios Ramin Zabih (presenter)
Semi-supervised Learning Rong Jin. Semi-supervised learning  Label propagation  Transductive learning  Co-training  Active learning.
ICCV 2007 tutorial Part III Message-passing algorithms for energy minimization Vladimir Kolmogorov University College London.
Discrete Optimization in Computer Vision Nikos Komodakis Ecole des Ponts ParisTech, LIGM Traitement de l’information et vision artificielle.
1 EL736 Communications Networks II: Design and Algorithms Class8: Networks with Shortest-Path Routing Yong Liu 10/31/2007.
Discrete Optimization Shi-Chung Chang. Discrete Optimization Lecture #1 Today: Reading Assignments 1.Chapter 1 and the Appendix of [Pas82] 2.Chapter 1.
1 s-t Graph Cuts for Binary Energy Minimization  Now that we have an energy function, the big question is how do we minimize it? n Exhaustive search is.
Learning with Inference for Discrete Graphical Models Nikos Komodakis Pawan Kumar Nikos Paragios Ramin Zabih (presenter)
Introduction to Linear and Integer Programming Lecture 7: Feb 1.
Math443/543 Mathematical Modeling and Optimization
Improved Moves for Truncated Convex Models M. Pawan Kumar Philip Torr.
Minimum Cost Flow Lecture 5: Jan 25. Problems Recap Bipartite matchings General matchings Maximum flows Stable matchings Shortest paths Minimum spanning.
Relaxations and Moves for MAP Estimation in MRFs M. Pawan Kumar STANFORDSTANFORD Vladimir KolmogorovPhilip TorrDaphne Koller.
Linear Programming – Max Flow – Min Cut Orgad Keller.
Multiplicative Bounds for Metric Labeling M. Pawan Kumar École Centrale Paris École des Ponts ParisTech INRIA Saclay, Île-de-France Joint work with Phil.
Ranking with High-Order and Missing Information M. Pawan Kumar Ecole Centrale Paris Aseem BehlPuneet DokaniaPritish MohapatraC. V. Jawahar.
Math – Getting Information from the Graph of a Function 1.
Polyhedral Optimization Lecture 1 – Part 1 M. Pawan Kumar Slides available online
CS223 Algorithms D-Term 2013 Instructor: Mohamed Eltabakh WPI, CS Introduction Slide 1.
ISE420 Algorithmic Operations Research Asst.Prof.Dr. Arslan M. Örnek Industrial Systems Engineering.
1 ESI 6417 Linear Programming and Network Optimization Fall 2003 Ravindra K. Ahuja 370 Weil Hall, Dept. of ISE
Robotics Daniel Vasicek 2012/04/15.
Computational Geometry Piyush Kumar (Lecture 5: Linear Programming) Welcome to CIS5930.
Ranking with High-Order and Missing Information M. Pawan Kumar Ecole Centrale Paris Aseem BehlPuneet KumarPritish MohapatraC. V. Jawahar.
Multiplicative Bounds for Metric Labeling M. Pawan Kumar École Centrale Paris Joint work with Phil Torr, Daphne Koller.
Rounding-based Moves for Metric Labeling M. Pawan Kumar Center for Visual Computing Ecole Centrale Paris.
1 Network Coding and its Applications in Communication Networks Alex Sprintson Computer Engineering Group Department of Electrical and Computer Engineering.
Learning a Small Mixture of Trees M. Pawan Kumar Daphne Koller Aim: To efficiently learn a.
Review for E&CE Find the minimal cost spanning tree for the graph below (where Values on edges represent the costs). 3 Ans. 18.
Modeling Latent Variable Uncertainty for Loss-based Learning Daphne Koller Stanford University Ben Packer Stanford University M. Pawan Kumar École Centrale.
Route Planning Texas Transfer Corp (TTC) Case 1. Linear programming Example: Woodcarving, Inc. Manufactures two types of wooden toys  Soldiers sell for.
Algorithms for MAP estimation in Markov Random Fields Vladimir Kolmogorov University College London.
Discrete Optimization Lecture 3 – Part 1 M. Pawan Kumar Slides available online
Fast and accurate energy minimization for static or time-varying Markov Random Fields (MRFs) Nikos Komodakis (Ecole Centrale Paris) Nikos Paragios (Ecole.
Probabilistic Inference Lecture 5 M. Pawan Kumar Slides available online
Discrete Optimization Lecture 2 – Part 2 M. Pawan Kumar Slides available online
CSCI-256 Data Structures & Algorithm Analysis Lecture Note: Some slides by Kevin Wayne. Copyright © 2005 Pearson-Addison Wesley. All rights reserved. 25.
Discrete Optimization Lecture 1 M. Pawan Kumar Slides available online
Discrete Optimization Lecture 4 – Part 1 M. Pawan Kumar
LINEAR PROGRAMMING 3.4 Learning goals represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret.
MAP Estimation in Binary MRFs using Bipartite Multi-Cuts Sashank J. Reddi Sunita Sarawagi Sundar Vishwanathan Indian Institute of Technology, Bombay TexPoint.
DEPARTMENT/SEMESTER ME VII Sem COURSE NAME Operation Research Manav Rachna College of Engg.
Review for E&CE Find the minimal cost spanning tree for the graph below (where Values on edges represent the costs). 3 Ans. 18.
Energy-efficient Scheduling policy for collaborative execution in mobile cloud computing INFOCOM '13.
ENGM 631 Maximum Flow Solutions. Maximum Flow Models (Flow, Capacity) (0,3) (2,2) (5,7) (0,8) (3,6) (6,8) (3,3) (4,4) (4,10)
Rounding-based Moves for Metric Labeling M. Pawan Kumar École Centrale Paris INRIA Saclay, Île-de-France.
Introduction of BP & TRW-S
Learning a Region-based Scene Segmentation Model
Graph Theory and Optimization
CIS 700 Advanced Machine Learning for NLP Inference Applications
Efficiently Selecting Regions for Scene Understanding
The Shortest Augmenting Path Algorithm for the Maximum Flow Problem
Graph Partitioning Problems
Lecture 19-Problem Solving 4 Incremental Method
8.4 Linear Programming p
Unit-4: Dynamic Programming
Spanning Tree Algorithms
Primal-Dual Algorithm
Discrete Inference and Learning
The Shortest Augmenting Path Algorithm for the Maximum Flow Problem
The Shortest Augmenting Path Algorithm for the Maximum Flow Problem
Lecture 6 Dynamic Programming
and 6.855J Dijkstra’s Algorithm
Introduction to Maximum Flows
Lecture 19 Linear Program
The Minimum Cost Spanning Tree Problem
Introduction to Maximum Flows
Presentation transcript:

Discrete Optimization for Vision and Learning

Who? How? M. Pawan Kumar Associate Professor Ecole Centrale Paris Nikos Komodakis Associate Professor Ecole des Ponts 7 lectures. 1 exam. All in English.

Where? When? Starts on 16 th January, 09h45 – 13h00

Why? How can I change the scenery?

Why? Where is my car? car road grass tree sky

Why? Where are my arms? My legs?

What? Input x Output y Energy of y

What? Energy Minimization Obtain output y with minimum energy Learning Obtain energy using training samples Energy of y

Syllabus Dynamic Programming –e.g. Shortest paths, Belief propagation Submodularity –e.g. Max flow, Min cut Convex Relaxations –e.g. Linear and semidefinite programming Parameter Estimation –e.g. SVM, Maximum likelihood Two equations (reparameterization) !!

Analysis Which algorithm is most efficient? Which algorithm is most accurate? What algorithm should I use?

Offered in 2014 as an MVA course University of Crete, Greece Ecole Centrale Paris – Coursera – Previous Courses

Evaluation Programming assignments –Graph Cuts –LP Relaxation One written exam –Half “easy” questions –Half “difficult” theoretical questions –“Missing information in publications”

Questions? Look at our research and previous courses –Search ‘Nikos Komodakis’ –Search ‘M. Pawan Kumar’ Send us an