Related papers: ReMAP: Neural Reparameterization for Scalable MAP …

Recovering jointly sparse signals in the multiple measurement vectors (MMV) setting is a fundamental problem in machine learning, but traditional methods often require careful parameter tuning or prior knowledge of the sparsity of the…

Finding the most likely (MAP) configuration of a Markov random field (MRF) is NP-hard in general. A promising, recent technique is to reduce the problem to finding a maximum weight stable set (MWSS) on a derived weighted graph, which if…

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…

The marginal maximum a posteriori probability (MAP) estimation problem, which calculates the mode of the marginal posterior distribution of a subset of variables with the remaining variables marginalized, is an important inference problem…

We consider the energy minimization problem for undirected graphical models, also known as MAP-inference problem for Markov random fields which is NP-hard in general. We propose a novel polynomial time algorithm to obtain a part of its…

This paper is concerned with the problem of exact MAP inference in general higher-order graphical models by means of a traditional linear programming relaxation approach. In fact, the proof that we have developed in this paper is a rather…

Modern instance-based model-agnostic explanation methods (LIME, SHAP, L2X) are of great use in data-heavy industries for model diagnostics, and for end-user explanations. These methods generally return either a weighting or subset of input…

Multi-label submodular Markov Random Fields (MRFs) have been shown to be solvable using max-flow based on an encoding of the labels proposed by Ishikawa, in which each variable $X_i$ is represented by $\ell$ nodes (where $\ell$ is the…

The growing reliance on artificial intelligence in safety- and security-critical applications is raising concerns about the robustness of neural networks to erroneous or adversarial input. Certification is a methodology for ensuring model…

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…

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…

We develop and analyze methods for computing provably optimal {\em maximum a posteriori} (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex…

UMAP is a non-parametric graph-based dimensionality reduction algorithm using applied Riemannian geometry and algebraic topology to find low-dimensional embeddings of structured data. The UMAP algorithm consists of two steps: (1) Compute a…

Energy minimization algorithms, such as graph cuts, enable the computation of the MAP solution under certain probabilistic models such as Markov random fields. However, for many computer vision problems, the MAP solution under the model is…

Fine-grained visual reasoning remains a core challenge for multimodal large language models (MLLMs). The recently introduced ReasonMap highlights this gap by showing that even advanced MLLMs struggle with spatial reasoning in structured and…

We propose a novel compact linear programming (LP) relaxation for binary sub-modular MRF in the context of object segmentation. Our model is obtained by linearizing an $l_1^+$-norm derived from the quadratic programming (QP) form of the MRF…

We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…

By leveraging differentiable dynamics, Reparameterization Policy Gradient (RPG) achieves high sample efficiency. However, current approaches are hindered by two critical limitations: the under-utilization of computationally expensive…

We present a new local approximation algorithm for computing Maximum a Posteriori (MAP) and log-partition function for arbitrary exponential family distribution represented by a finite-valued pair-wise Markov random field (MRF), say $G$.…

This article presents a new search algorithm for the NP-hard problem of optimizing functions of binary variables that decompose according to a graphical model. It can be applied to models of any order and structure. The main novelty is a…