Related papers: Scalable Semidefinite Relaxation for Maximum A Pos…

Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…

We have observed an interesting, yet unexplained, phenomenon: Semidefinite programming (SDP) based relaxations of maximum likelihood estimators (MLE) tend to be tight in recovery problems with noisy data, even when MLE cannot exactly…

Convex relaxation methods are powerful tools for studying the lowest energy of many-body problems. By relaxing the representability conditions for marginals to a set of local constraints, along with a global semidefinite constraint, a…

Safe reinforcement learning has been a promising approach for optimizing the policy of an agent that operates in safety-critical applications. In this paper, we propose an algorithm, SNO-MDP, that explores and optimizes Markov decision…

The sensor network localization, SNL, problem in embedding dimension r, consists of locating the positions of wireless sensors, given only the distances between sensors that are within radio range and the positions of a subset of the…

Computing the conditional mode of a distribution, better known as the $\mathit{maximum\ a\ posteriori}$ (MAP) assignment, is a fundamental task in probabilistic inference. However, MAP estimation is generally intractable, and remains hard…

In this paper, we propose some new semidefinite relaxations for a class of nonconvex complex quadratic programming problems, which widely appear in the areas of signal processing and power system. By deriving new valid constraints to the…

Spike-and-Slab Deep Learning (SS-DL) is a fully Bayesian alternative to Dropout for improving generalizability of deep ReLU networks. This new type of regularization enables provable recovery of smooth input-output maps with unknown levels…

Robust Markov decision processes (MDPs) allow to compute reliable solutions for dynamic decision problems whose evolution is modeled by rewards and partially-known transition probabilities. Unfortunately, accounting for uncertainty in the…

Following the great success of Machine Learning (ML), especially Deep Neural Networks (DNNs), in many research domains in 2010s, several ML-based approaches were proposed for detection in large inverse linear problems, e.g., massive MIMO…

We propose a Bayesian image super-resolution (SR) method with a causal Gaussian Markov random field (MRF) prior. SR is a technique to estimate a spatially high-resolution image from given multiple low-resolution images. An MRF model with…

This paper develops a new storage-optimal algorithm that provably solves generic semidefinite programs (SDPs) in standard form. This method is particularly effective for weakly constrained SDPs. The key idea is to formulate an approximate…

Lifted inference reduces the complexity of inference in relational probabilistic models by identifying groups of constants (or atoms) which behave symmetric to each other. A number of techniques have been proposed in the literature for…

We consider a new semidefinite programming (SDP) relaxation of the symmetric traveling salesman problem (TSP) that may be obtained via an SDP relaxation of the more general quadratic assignment problem (QAP). We show that the new relaxation…

We consider the problem of finding the optimal diagonal preconditioner for a positive definite matrix. Although this problem has been shown to be solvable and various methods have been proposed, none of the existing approaches are scalable…

We propose the first general and scalable framework to design certifiable algorithms for robust geometric perception in the presence of outliers. Our first contribution is to show that estimation using common robust costs, such as truncated…

We study T-semidefinite programming (SDP) relaxation for constrained polynomial optimization problems (POPs). T-SDP relaxation for unconstrained POPs was introduced by Zheng, Huang and Hu in 2022. In this work, we propose a T-SDP relaxation…

The traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization. Several semidefinite programming relaxations have been proposed recently that exploit a variety of mathematical structures including, e.g.,…

Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…

In recent years, there has been remarkable progress in the development of so-called certifiable perception methods, which leverage semidefinite, convex relaxations to find global optima of perception problems in robotics. However, many of…