Diverse M-Best Solutions in Markov Random Fields

Much effort has been directed at algorithms for obtaining the highest probability (MAP) configuration in probabilistic (random field) models. In many situations, one could benefit from additional high-probability solutions. Current methods for computing the M most probable configurations produce solutions that tend to be very similar to the MAP solution and each other. This is often an undesirable property. In this paper we propose an algorithm for the Diverse M-Best problem, which involves finding a diverse set of highly probable solutions under a discrete probabilistic model. Given a dissimilarity function measuring closeness of two solutions, our formulation involves maximizing a linear combination of the probability and dissimilarity to previous solutions. Our formulation generalizes the M-Best MAP problem and we show that for certain families of dissimilarity functions we can guarantee that these solutions can be found as easily as the MAP solution.

[1]  E. Lawler.  A PROCEDURE FOR COMPUTING THE K BEST SOLUTIONS TO DISCRETE OPTIMIZATION PROBLEMS AND ITS APPLICATION TO THE SHORTEST PATH PROBLEM , 1972 .

[2]  Naum Zuselevich Shor,et al.  Minimization Methods for Non-Differentiable Functions , 1985, Springer Series in Computational Mathematics.

[3]  Jean-Louis Golmard,et al.  An algorithm directly finding the K most probable configurations in Bayesian networks , 1994, Int. J. Approx. Reason..

[4]  D. Nilsson,et al.  An efficient algorithm for finding the M most probable configurationsin probabilistic expert systems , 1998, Stat. Comput..

[5]  Marie-Pierre Jolly,et al.  Interactive Graph Cuts for Optimal Boundary and Region Segmentation of Objects in N-D Images , 2001, ICCV.

[6]  Y.Y. Boykov,et al.  Interactive graph cuts for optimal boundary & region segmentation of objects in N-D images , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[7]  Harry Shum,et al.  Image segmentation by data driven Markov chain Monte Carlo , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[8]  Olga Veksler,et al.  Fast Approximate Energy Minimization via Graph Cuts , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  M. Guignard.  Lagrangean relaxation , 2003 .

[10]  Y. Weiss,et al.  Finding the M Most Probable Configurations using Loopy Belief Propagation , 2003, NIPS 2003.

[11]  Vladimir Kolmogorov,et al.  What energy functions can be minimized via graph cuts? , 2002, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  Vladimir Kolmogorov,et al.  An experimental comparison of min-cut/max- flow algorithms for energy minimization in vision , 2001, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Andrew Blake,et al.  "GrabCut" , 2004, ACM Trans. Graph..

[14]  Adrian Barbu,et al.  Generalizing Swendsen-Wang to sampling arbitrary posterior probabilities , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  P. Kohli,et al.  Efficiently solving dynamic Markov random fields using graph cuts , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[16]  Alexei A. Efros,et al.  Geometric context from a single image , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[17]  Thomas Hofmann,et al.  Large Margin Methods for Structured and Interdependent Output Variables , 2005, J. Mach. Learn. Res..

[18]  Yair Weiss,et al.  Globally optimal solutions for energy minimization in stereo vision using reweighted belief propagation , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[19]  S. Sathiya Keerthi,et al.  Large scale semi-supervised linear SVMs , 2006, SIGIR.

[20]  Jianguo Zhang,et al.  The PASCAL Visual Object Classes Challenge , 2006 .

[21]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[22]  Nikos Komodakis,et al.  MRF Optimization via Dual Decomposition: Message-Passing Revisited , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[23]  Léon Bottou,et al.  The Tradeoffs of Large Scale Learning , 2007, NIPS.

[24]  Tomás Werner,et al.  A Linear Programming Approach to Max-Sum Problem: A Review , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[25]  Richard Szeliski,et al.  A Comparative Study of Energy Minimization Methods for Markov Random Fields with Smoothness-Based Priors , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[26]  Michael I. Jordan,et al.  Graphical Models, Exponential Families, and Variational Inference , 2008, Found. Trends Mach. Learn..

[27]  Thorsten Joachims,et al.  Predicting diverse subsets using structural SVMs , 2008, ICML '08.

[28]  Michael J. Black,et al.  Fields of Experts , 2009, International Journal of Computer Vision.

[29]  Pushmeet Kohli,et al.  Measuring uncertainty in graph cut solutions , 2008, Comput. Vis. Image Underst..

[30]  Pushmeet Kohli,et al.  Minimizing sparse higher order energy functions of discrete variables , 2009, 2009 IEEE Conference on Computer Vision and Pattern Recognition.

[31]  Amir Globerson,et al.  An LP View of the M-best MAP problem , 2009, NIPS.

[32]  N. Komodakis,et al.  Beyond pairwise energies: Efficient optimization for higher-order MRFs , 2009, 2009 IEEE Conference on Computer Vision and Pattern Recognition.

[33]  Pushmeet Kohli,et al.  Associative hierarchical CRFs for object class image segmentation , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[34]  Sebastian Nowozin,et al.  Global connectivity potentials for random field models , 2009, 2009 IEEE Conference on Computer Vision and Pattern Recognition.

[35]  Pushmeet Kohli,et al.  Graph Cut Based Inference with Co-occurrence Statistics , 2010, ECCV.

[36]  Pushmeet Kohli,et al.  Energy minimization for linear envelope MRFs , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[37]  Richard S. Zemel,et al.  HOP-MAP: Efficient Message Passing with High Order Potentials , 2010, AISTATS.

[38]  Rahul Gupta,et al.  Collective Inference for Extraction MRFs Coupled with Symmetric Clique Potentials , 2010, J. Mach. Learn. Res..

[39]  Cristian Sminchisescu,et al.  Object recognition as ranking holistic figure-ground hypotheses , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[40]  Thomas Deselaers,et al.  ClassCut for Unsupervised Class Segmentation , 2010, ECCV.

[41]  Arthur M. Geoffrion,et al.  Lagrangian Relaxation for Integer Programming , 2010, 50 Years of Integer Programming.

[42]  George Papandreou,et al.  Perturb-and-MAP random fields: Using discrete optimization to learn and sample from energy models , 2011, 2011 International Conference on Computer Vision.

[43]  Matthew B. Blaschko.  Branch and Bound Strategies for Non-maximal Suppression in Object Detection , 2011, EMMCVPR.

[44]  R. Dechter,et al.  Inference Schemes for M Best Solutions for Soft CSPs , 2011 .

[45]  Rina Dechter,et al.  Bucket and Mini-bucket Schemes for M Best Solutions over Graphical Models , 2011, GKR.

[46]  Yi Yang,et al.  Articulated pose estimation with flexible mixtures-of-parts , 2011, CVPR 2011.

[47]  Deva Ramanan,et al.  N-best maximal decoders for part models , 2011, 2011 International Conference on Computer Vision.

[48]  Song-Chun Zhu,et al.  C^4: Exploring Multiple Solutions in Graphical Models by Cluster Sampling , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[49]  Pushmeet Kohli,et al.  On Detection of Multiple Object Instances Using Hough Transforms , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[50]  Stefan Woltran,et al.  Graph Structures for Knowledge Representation and Reasoning , 2012, Lecture Notes in Computer Science.

[51]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .