Related papers: On MAP Inference by MWSS on Perfect Graphs
We propose a model for recoverable robust optimization with commitment. Given a combinatorial optimization problem and uncertainty about elements that may fail, we ask for a robust solution that, after the failing elements are revealed, can…
Partially observable Markov decision processes (POMDPs) with continuous state and observation spaces have powerful flexibility for representing real-world decision and control problems but are notoriously difficult to solve. Recent online…
We consider move-making algorithms for energy minimization of multi-label Markov Random Fields (MRFs). Since this is not a tractable problem in general, a commonly used heuristic is to minimize over subsets of labels and variables in an…
A 2-packing set for an undirected, weighted graph G=(V,E,w) is a subset S of the vertices V such that any two vertices are not adjacent and have no common neighbors. The Maximum Weight 2-Packing Set problem that asks for a 2-packing set of…
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…
We study the Maximum Bipartite Subgraph (MBS) problem, which is defined as follows. Given a set $S$ of $n$ geometric objects in the plane, we want to compute a maximum-size subset $S'\subseteq S$ such that the intersection graph of the…
This study formulates the IR target detection as a binary classification problem of each pixel. Each pixel is associated with a label which indicates whether it is a target or background pixel. The optimal label set for all the pixels of an…
Bayesian inference for models with intractable likelihoods, such as Markov random fields, poses a fundamental computational challenge due to the tradeoff between inferential accuracy and computational cost. Various MCMC methods have been…
The Maximum Weighted Independent Set (MWIS) problem, which considers a graph with weights assigned to nodes and seeks to discover the "heaviest" independent set, that is, a set of nodes with maximum total weight so that no two nodes in the…
Gaussian Markov random fields (GMRFs) are probabilistic graphical models widely used in spatial statistics and related fields to model dependencies over spatial structures. We establish a formal connection between GMRFs and convolutional…
The maximum a posteriori (MAP) configuration of binary variable models with submodular graph-structured energy functions can be found efficiently and exactly by graph cuts. Max-product belief propagation (MP) has been shown to be suboptimal…
In this paper, we consider the problem of recovering random graph signals from nonlinear measurements. We formulate the maximum a-posteriori probability (MAP) estimator, which results in a nonconvex optimization problem. Conventional…
Weighted model counting (WMC) consists of computing the weighted sum of all satisfying assignments of a propositional formula. WMC is well-known to be #P-hard for exact solving, but admits a fully polynomial randomized approximation scheme…
We consider the problem of jointly estimating the parameters as well as the structure of binary valued Markov Random Fields, in contrast to earlier work that focus on one of the two problems. We formulate the problem as a maximization of…
In this letter, we propose an algorithm for learning a sparse weighted graph by estimating its adjacency matrix under the assumption that the observed signals vary smoothly over the nodes of the graph. The proposed algorithm is based on the…
A matching $M$ is a $\mathscr{P}$-matching if the subgraph induced by the endpoints of the edges of $M$ satisfies property $\mathscr{P}$. As examples, for appropriate choices of $\mathscr{P}$, the problems Induced Matching, Uniquely…
We study a general class of convex submodular optimization problems with indicator variables. Many applications such as the problem of inferring Markov random fields (MRFs) with a sparsity or robustness prior can be naturally modeled in…
One powerful technique to solve NP-hard optimization problems in practice is branch-and-reduce search---which is branch-and-bound that intermixes branching with reductions to decrease the input size. While this technique is known to be very…
This paper presents a new anytime algorithm for the marginal MAP problem in graphical models. The algorithm is described in detail, its complexity and convergence rate are studied, and relations to previous theoretical results for the…
Discrete Markov random fields are undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is often computationally challenging because…