相关论文: Tighter relaxations for MAP-MRF optimization via S…

Linear Programming (LP) relaxations have become powerful tools for finding the most probable (MAP) configuration in graphical models. These relaxations can be solved efficiently using message-passing algorithms such as belief propagation…

We consider the MAP-inference problem for graphical models, which is a valued constraint satisfaction problem defined on real numbers with a natural summation operation. We propose a family of relaxations (different from the famous…

We describe a new technique for computing lower-bounds on the minimum energy configuration of a planar Markov Random Field (MRF). Our method successively adds large numbers of constraints and enforces consistency over binary projections of…

Dual decomposition provides a tractable framework for designing algorithms for finding the most probable (MAP) configuration in graphical models. However, for many real-world inference problems, the typical decomposition has a large…

Dense conditional random fields (CRFs) have become a popular framework for modelling several problems in computer vision such as stereo correspondence and multi-class semantic segmentation. By modelling long-range interactions, dense CRFs…

In this paper, we study a nonconvex continuous relaxation of MAP inference in discrete Markov random fields (MRFs). We show that for arbitrary MRFs, this relaxation is tight, and a discrete stationary point of it can be easily reached by a…

Graphical models with High Order Potentials (HOPs) have received considerable interest in recent years. While there are a variety of approaches to inference in these models, nearly all of them amount to solving a linear program (LP)…

The Matching Augmentation Problem (MAP) has recently received significant attention as an important step towards better approximation algorithms for finding cheap $2$-edge connected subgraphs. This has culminated in a…

In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global…

We develop a general framework for MAP estimation in discrete and Gaussian graphical models using Lagrangian relaxation techniques. The key idea is to reformulate an intractable estimation problem as one defined on a more tractable graph,…

We consider the task of obtaining the maximum a posteriori estimate of discrete pairwise random fields with arbitrary unary potentials and semimetric pairwise potentials. For this problem, we propose an accurate hierarchical move making…

We develop a unified framework to characterize the power of higher-level algorithms for the constraint satisfaction problem (CSP), such as $k$-consistency, the Sherali-Adams LP hierarchy, and the affine IP hierarchy. As a result,…

Maximum a posteriori (MAP) inference is a fundamental computational paradigm for statistical inference. In the setting of graphical models, MAP inference entails solving a combinatorial optimization problem to find the most likely…

LP relaxation-based message passing algorithms provide an effective tool for MAP inference over Probabilistic Graphical Models. However, different LP relaxations often have different objective functions and variables of differing…

Maximum a posteriori (MAP) inference over discrete Markov random fields is a fundamental task spanning a wide spectrum of real-world applications, which is known to be NP-hard for general graphs. In this paper, we propose a novel…

Spectral Clustering as a relaxation of the normalized/ratio cut has become one of the standard graph-based clustering methods. Existing methods for the computation of multiple clusters, corresponding to a balanced $k$-cut of the graph, are…

We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…

MAP inference for general energy functions remains a challenging problem. While most efforts are channeled towards improving the linear programming (LP) based relaxation, this work is motivated by the quadratic programming (QP) relaxation.…

The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice.…

The relaxation complexity rc(X) of the set of integer points X contained in a polyhedron is the minimal number of inequalities needed to formulate a linear optimization problem over X without using auxiliary variables. Besides its relevance…