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In recent years, a rich variety of regularization procedures have been proposed for high dimensional regression problems. However, tuning parameter choice and computational efficiency in ultra-high dimensional problems remain vexing issues.…
In this paper, we study the problem of inferring spatially-varying Gaussian Markov random fields (SV-GMRF) where the goal is to learn a network of sparse, context-specific GMRFs representing network relationships between genes. An important…
Many regression and classification procedures fit a parameterized function $f(x;w)$ of predictor variables $x$ to data $\{x_{i},y_{i}\}_1^N$ based on some loss criterion $L(y,f)$. Often, regularization is applied to improve accuracy by…
Learning a Gaussian Mixture Model (GMM) is hard when the number of parameters is too large given the amount of available data. As a remedy, we propose restricting the GMM to a Gaussian Markov Random Field Mixture Model (GMRF-MM), as well as…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
Markov random fields (MRFs) are invaluable tools across diverse fields, and spatiotemporal MRFs (STMRFs) amplify their effectiveness by integrating spatial and temporal dimensions. However, modeling spatiotemporal data introduces additional…
In dynamic MRI, sufficient time resolution can often only be obtained using imaging protocols which produce undersampled data for each image in the time series. This has led to the popularity of compressed sensing (CS) based image…
In this paper, we present a new variational method for sparse regression using $L_0$ regularization. The variational parameters appear in the approximate model in a way that is similar to Breiman's Garrote model. We refer to this method as…
Markov Decision Processes (MDPs) are a mathematical framework for modeling sequential decision making under uncertainty. The classical approaches for solving MDPs are well known and have been widely studied, some of which rely on…
We investigate different ways of generating approximate solutions to the pairwise Markov random field (MRF) selection problem. We focus mainly on the inverse Ising problem, but discuss also the somewhat related inverse Gaussian problem…
In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…
Large sparse sets of binary transaction data with millions of records and thousands of attributes occur in various domains: customers purchasing products, users visiting web pages, and documents containing words are just three typical…
This paper investigates the optimization problem of an infinite stage discrete time Markov decision process (MDP) with a long-run average metric considering both mean and variance of rewards together. Such performance metric is important…
For many algorithms, parameter tuning remains a challenging and critical task, which becomes tedious and infeasible in a multi-parameter setting. Multi-penalty regularization, successfully used for solving undetermined sparse regression of…
We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this…
Identifying important features linked to a response variable is a fundamental task in various scientific domains. This article explores statistical inference for simulated Markov random fields in high-dimensional settings. We introduce a…
We numerically investigate a mean-field Bayesian approach with the assistance of the Markov chain Monte Carlo method to estimate motion velocity fields and probabilistic models simultaneously in consecutive digital images described by…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
Path planning for multiple robots (MRPP) represents a task of finding non-colliding paths for robots through which they can navigate from their initial positions to specified goal positions. The problem is usually modeled using undirected…
We present a novel statistically-based discretization paradigm and derive a class of maximum a posteriori (MAP) estimators for solving ill-conditioned linear inverse problems. We are guided by the theory of sparse stochastic processes,…