Related papers: Generalized sequential tree-reweighted message pas…
Due to its broad applications in practice, the minimum spanning tree problem and its all kinds of variations have been studied extensively during the last decades, for which a host of efficient exact and heuristic algorithms have been…
Nonnegative matrix factorization (NMF) is a linear dimensionality technique for nonnegative data with applications such as image analysis, text mining, audio source separation and hyperspectral unmixing. Given a data matrix $M$ and a…
To fully uncover the great potential of deep neural networks (DNNs), various learning algorithms have been developed to improve the model's generalization ability. Recently, sharpness-aware minimization (SAM) establishes a generic scheme…
Considering the worst-case scenario, junction tree algorithm remains the most general solution for exact MAP inference with polynomial run-time guarantees. Unfortunately, its main tractability assumption requires the treewidth of a…
While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…
A randomized algorithm for computing a data sparse representation of a given rank structured matrix $A$ (a.k.a. an $H$-matrix) is presented. The algorithm draws on the randomized singular value decomposition (RSVD), and operates under the…
Most algorithms for decentralized learning employ a consensus or diffusion mechanism to drive agents to a common solution of a global optimization problem. Generally this takes the form of linear averaging, at a rate of contraction…
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…
A popular approach to the MAP inference problem in graphical models is to minimize an upper bound obtained from a dual linear programming or Lagrangian relaxation by (block-)coordinate descent. This is also known as convex/convergent…
We consider a class of linear programs on graphs with total variation regularization and a budgetary constraint. For these programs, we give a characterization of basic solutions in terms of rooted spanning forests with orientation on the…
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…
We study the crossing-minimization problem in a layered graph drawing of planar-embedded rooted trees whose leaves have a given total order on the first layer, which adheres to the embedding of each individual tree. The task is then to…
Maximum weight matching is one of the most fundamental combinatorial optimization problems with a wide range of applications in data mining and bioinformatics. Developing distributed weighted matching algorithms is challenging due to the…
In this paper, randomized gossip-type matrix-weighted consensus algorithms are proposed for both leaderless and leader-follower topologies. First, we introduce the notion of expected matrix-weighted network, which captures the…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
Marginal MAP problems are notoriously difficult tasks for graphical models. We derive a general variational framework for solving marginal MAP problems, in which we apply analogues of the Bethe, tree-reweighted, and mean field…
The complexity of a reasoning task over a graphical model is tied to the induced width of the underlying graph. It is well-known that the conditioning (assigning values) on a subset of variables yields a subproblem of the reduced complexity…
Maximum a posteriori (MAP) inference in discrete-valued Markov random fields is a fundamental problem in machine learning that involves identifying the most likely configuration of random variables given a distribution. Due to the…
This paper proposes the matrix-weighted consensus algorithm, which is a generalization of the consensus algorithm in the literature. Given a networked dynamical system where the interconnections between agents are weighted by nonnegative…
An important part of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov Random Field. The belief propagation algorithm, which is an exact procedure to compute…