Cem Aksoylar

Information-theoretic bounds for adaptive sparse recovery.

We derive an information-theoretic lower bound for sample complexity in sparse recovery problems where inputs can be chosen sequentially and adaptively. This lower bound is in terms of a simple mutual information expression and unifies many different linear and nonlinear observation models. Using this formula we derive bounds for adaptive compressive sensing (CS), group testing and 1-bit CS problems. We show that adaptivity cannot decrease sample complexity in group testing, 1-bit CS and CS with linear sparsity. In contrast, we show there might be mild performance gains for CS in the sublinear regime. Our unified analysis also allows characterization of gains due to adaptivity from a wider perspective on sparse problems.

Sample complexity of salient feature identification for sparse signal processing

Suppose among a set of N covariates X1, X2, ..., XN there is a subset S of covariates that are salient for predicting outcomes Y. Specifically, we assume that when Y is conditioned on {Yk}k∈S it is independent of the other covariates. Our goal is to identify the subset S from data samples of the covariates and the associated outcomes. We first consider the case where the covariates are independent of each other and then generalize the results to the case where the covariates are dependent with symmetric distributions. We present precise mutual information expressions that characterize the sample complexity for accurately identifying the subset S. We then derive sample complexity bounds for interesting scenarios.

Sparse Signal Processing With Linear and Nonlinear Observations: A Unified Shannon-Theoretic Approach

We derive fundamental sample complexity bounds for recovering sparse and structured signals for linear and nonlinear observation models, including sparse regression, group testing, multivariate regression, and problems with missing features. In general, sparse signal processing problems can be characterized in terms of the following Markovian property. We are given a set of

Compressive sensing bounds through a unifying framework for sparse models

N

Clustering and Community Detection With Imbalanced Clusters

variables

Sparse signal processing with linear and non-linear observations: A unified shannon theoretic approach

X_{1},X_{2},\ldots ,X_{N}

{Information-Theoretic Characterization of Sparse Recovery}

, and there is an unknown subset of variables

Sparse Recovery with Linear and Nonlinear Observations: Dependent and Noisy Data

S \subset \{1,\ldots ,N\}

Correction to “Boolean Compressed Sensing and Noisy Group Testing” [Mar 12 1880-1901]

that are relevant for predicting outcomes

Connected Subgraph Detection with Mirror Descent on SDPs.

Y