Related papers: Tightening MRF Relaxations with Planar Subproblems
In many applications, we need algorithms which can align partially overlapping point sets and are invariant to the corresponding transformations. In this work, a method possessing such properties is realized by minimizing the objective of…
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…
Inference in general Markov random fields (MRFs) is NP-hard, though identifying the maximum a posteriori (MAP) configuration of pairwise MRFs with submodular cost functions is efficiently solvable using graph cuts. Marginal inference,…
We study the problem of inferring sparse time-varying Markov random fields (MRFs) with different discrete and temporal regularizations on the parameters. Due to the intractability of discrete regularization, most approaches for solving this…
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…
We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…
A vertex cover on a graph is a set of vertices in which each edge of the graph is adjacent to at least one vertex in the set. The Minimal Vertex Cover (MVC) Problem concerns finding vertex covers with a smallest cardinality. The MVC problem…
Deep Neural Networks have achieved remarkable success relying on the developing availability of GPUs and large-scale datasets with increasing network depth and width. However, due to the expensive computation and intensive memory,…
Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…
The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization…
In this article a topology optimization method is developed, which is aware of material uncertainties. The uncertainties are handled in a worst-case sense, i.e. the worst possible material distribution over a given uncertainty set is taken…
We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of an LP relaxation of ultrametric rounding. To solve this LP efficiently we introduce a dual cutting plane scheme that uses minimum cost perfect…
Learning neural fields has been an active topic in deep learning research, focusing, among other issues, on finding more compact and easy-to-fit representations. In this paper, we introduce a novel low-rank representation termed Tensor…
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…
We provide theory for computing the lower semi-continuous convex envelope of functionals of the type f(x) plus an l2 misfit, and discuss applications to various non-convex optimization problems. The latter term is a data fit term whereas f…
We consider an effective new method for solving trust-region and norm-regularization problems that arise as subproblems in many optimization applications. We show that the solutions to such subproblems effectively lie in a…
A new Levenberg--Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described. Various versions of the LM method have been proposed, their main differences being in the choice of a damping…
Proper regularization is critical for speeding up training, improving generalization performance, and learning compact models that are cost efficient. We propose and analyze regularized gradient descent algorithms for learning shallow…
Markov random fields (MRFs) have been widely used as prior models in various inverse problems such as tomographic reconstruction. While MRFs provide a simple and often effective way to model the spatial dependencies in images, they suffer…