Related papers: Efficient semidefinite-programming-based inference…
We propose a multi-index algorithm for the Monte Carlo (MC) discretization of a linear, elliptic PDE with affine-parametric input. We prove an error vs. work analysis which allows a multi-level finite-element approximation in the physical…
In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…
Key challenges in the analysis of highly multivariate large-scale spatial stochastic processes, where both the number of components (p) and spatial locations (n) can be large, include achieving maximal sparsity in the joint precision…
This paper focuses on the study of a mathematical program with equilibrium constraints, where the objective and the constraint functions are all polynomials. We present a method for finding its global minimizers and global minimum using a…
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…
Inspired by the combination of feedforward and iterative computations in the virtual cortex, and taking advantage of the ability of denoising autoencoders to estimate the score of a joint distribution, we propose a novel approach to…
Many fundamental low-rank optimization problems, such as matrix completion, phase synchronization/retrieval, power system state estimation, and robust PCA, can be formulated as the matrix sensing problem. Two main approaches for solving…
Packing and covering semidefinite programs (SDPs) appear in natural relaxations of many combinatorial optimization problems as well as a number of other applications. Recently, several techniques were proposed, that utilize the particular…
Motivated by applications in wireless communications, this paper develops semidefinite programming (SDP) relaxation techniques for some mixed binary quadratically constrained quadratic programs (MBQCQP) and analyzes their approximation…
Probabilistic circuits (PCs) such as sum-product networks efficiently represent large multi-variate probability distributions. They are preferred in practice over other probabilistic representations such as Bayesian and Markov networks…
The problem of detecting communities in a graph is maybe one the most studied inference problems, given its simplicity and widespread diffusion among several disciplines. A very common benchmark for this problem is the stochastic block…
We introduce fast randomized algorithms for solving semidefinite programming (SDP) relaxations of the partial permutation synchronization (PPS) problem, a core task in multi-image matching with significant relevance to 3D reconstruction.…
We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to…
Robust Markov decision processes (RMDPs) extend standard Markov decision processes (MDPs) to account for uncertainty in the transition probabilities. RMDPs have an uncertainty set that defines a set of possible transition functions, each of…
We consider the structured-output prediction problem through probabilistic approaches and generalize the "perturb-and-MAP" framework to more challenging weighted Hamming losses, which are crucial in applications. While in principle our…
In this paper, we study the estimation of partially linear models for spatial data distributed over complex domains. We use bivariate splines over triangulations to represent the nonparametric component on an irregular two-dimensional…
The Hilbert space of probability mass functions (pmf) is introduced in this thesis. A factorization method for multivariate pmfs is proposed by using the tools provided by the Hilbert space of pmfs. The resulting factorization is special…
This paper deals with the algorithmic aspects of solving feasibility problems of semidefinite programming (SDP), aka linear matrix inequalities (LMI). Since in some SDP instances all feasible solutions have irrational entries, numerical…
Low-rank matrix completion has achieved great success in many real-world data applications. A matrix factorization model that learns latent features is usually employed and, to improve prediction performance, the similarities between latent…
Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…