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Are we using the right potential functions in the Conditional Random Field models that are popular in the Vision community? Semantic segmentation and other pixel-level labelling tasks have made significant progress recently due to the deep…

Semidefinite programming (SDP) is widely acknowledged as one of the most effective methods for deriving the tightest lower bounds of the optimal power flow (OPF) problems. In this paper, an enhanced semidefinite relaxation model that…

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…

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…

Robots typically possess sensors of different modalities, such as colour cameras, inertial measurement units, and 3D laser scanners. Often, solving a particular problem becomes easier when more than one modality is used. However, while…

Frank-Wolfe (FW) algorithms have been often proposed over the last few years as efficient solvers for a variety of optimization problems arising in the field of Machine Learning. The ability to work with cheap projection-free iterations and…

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…

While the literature has been fairly dense in the areas of scene understanding and semantic labeling there have been few works that make use of motion cues to embellish semantic performance and vice versa. In this paper, we address the…

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,…

In this short paper we bridge two seemingly unrelated sparse approximation topics: continuous sparse coding and low-rank approximations. We show that for a specific choice of continuous dictionary, linear systems with nuclear-norm…

In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the…

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…

Low-Rank Factorization (LRF) is a widely adopted technique for compressing deep neural networks (DNNs). However, it faces several challenges, including optimal rank selection, a vast design space, long fine-tuning times, and limited…

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…

With the potential to find global solutions, significant research interest has focused on convex relaxations of the non-convex OPF problem. Recently, "moment-based" relaxations from the Lasserre hierarchy for polynomial optimization have…

We address the problem of semantic segmentation using deep learning. Most segmentation systems include a Conditional Random Field (CRF) to produce a structured output that is consistent with the image's visual features. Recent deep learning…

We develop new accelerated first-order algorithms in the Frank-Wolfe (FW) family for minimizing smooth convex functions over compact convex sets, with a focus on two prominent constraint classes: (1) polytopes and (2) matrix domains given…

Most previous learning-based graph matching algorithms solve the \textit{quadratic assignment problem} (QAP) by dropping one or more of the matching constraints and adopting a relaxed assignment solver to obtain sub-optimal correspondences.…

The matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in…

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…