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Creating low dimensional representations of a high dimensional data set is an important component in many machine learning applications. How to cluster data using their low dimensional embedded space is still a challenging problem in…
Many models for sparse regression typically assume that the covariates are known completely, and without noise. Particularly in high-dimensional applications, this is often not the case. This paper develops efficient OMP-like algorithms to…
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)…
Sparse signal recovery from a small number of random measurements is a well known NP-hard to solve combinatorial optimization problem, with important applications in signal and image processing. The standard approach to the sparse signal…
In learned image compression, probabilistic models play an essential role in characterizing the distribution of latent variables. The Gaussian model with mean and scale parameters has been widely used for its simplicity and effectiveness.…
Consider a Bernoulli-Gaussian complex $n$-vector whose components are $V_i = X_i B_i$, with $X_i \sim \Cc\Nc(0,\Pc_x)$ and binary $B_i$ mutually independent and iid across $i$. This random $q$-sparse vector is multiplied by a square random…
In compressed sensing, it is often desirable to consider signals possessing additional structure beyond sparsity. One such structured signal model - which forms the focus of this paper - is the local sparsity in levels class. This class has…
We show that density models describing multiple observables with (i) hard boundaries and (ii) dependence on external parameters may be created using an auto-regressive Gaussian mixture model. The model is designed to capture how observable…
We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like…
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…
We consider the recovery of a low rank and jointly sparse matrix from under sampled measurements of its columns. This problem is highly relevant in the recovery of dynamic MRI data with high spatio-temporal resolution, where each column of…
We analyze the asymptotic performance of sparse signal recovery from noisy measurements. In particular, we generalize some of the existing results for the Gaussian case to subgaussian and other ensembles. An achievable result is presented…
Structured sparsity has recently emerged in statistics, machine learning and signal processing as a promising paradigm for learning in high-dimensional settings. All existing methods for learning under the assumption of structured sparsity…
Statistical inference for stochastic processes has advanced significantly due to applications in diverse fields, but challenges remain in high-dimensional settings where parameters are allowed to grow with the sample size. This paper…
This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This under-complete dictionary learning task can be formulated as a blind separation problem of sparse sources…
High-dimensional vector autoregressive (VAR) models are important tools for the analysis of multivariate time series. This paper focuses on high-dimensional time series and on the different regularized estimation procedures proposed for…
High-dimensional time series datasets are becoming increasingly common in many areas of biological and social sciences. Some important applications include gene regulatory network reconstruction using time course gene expression data, brain…
Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…
This paper studies sequential methods for recovery of sparse signals in high dimensions. When compared to fixed sample size procedures, in the sparse setting, sequential methods can result in a large reduction in the number of samples…
In many statistical modeling problems, such as classification and regression, it is common to encounter sparse and blocky coefficients. Sparse fused Lasso is specifically designed to recover these sparse and blocky structured features,…