DeepAI AI Chat
Log In Sign Up

Provable Guarantees for Sparsity Recovery with Deterministic Missing Data Patterns

by   Chuyang Ke, et al.
Purdue University

We study the problem of consistently recovering the sparsity pattern of a regression parameter vector from correlated observations governed by deterministic missing data patterns using Lasso. We consider the case in which the observed dataset is censored by a deterministic, non-uniform filter. Recovering the sparsity pattern in datasets with deterministic missing structure can be arguably more challenging than recovering in a uniformly-at-random scenario. In this paper, we propose an efficient algorithm for missing value imputation by utilizing the topological property of the censorship filter. We then provide novel theoretical results for exact recovery of the sparsity pattern using the proposed imputation strategy. Our analysis shows that, under certain statistical and topological conditions, the hidden sparsity pattern can be recovered consistently with high probability in polynomial time and logarithmic sample complexity.


page 1

page 2

page 3

page 4


FCMI: Feature Correlation based Missing Data Imputation

Processed data are insightful, and crude data are obtuse. A serious thre...

Missing Value Knockoffs

One limitation of the most statistical/machine learning-based variable s...

Covariance Matrix Estimation with Non Uniform and Data Dependent Missing Observations

In this paper we study covariance estimation with missing data. We consi...

Weighted matrix completion from non-random, non-uniform sampling patterns

We study the matrix completion problem when the observation pattern is d...

Pattern graphs: a graphical approach to nonmonotone missing data

We introduce the concept of pattern graphs–directed acyclic graphs repre...

A Theoretical Study of The Effects of Adversarial Attacks on Sparse Regression

This paper analyzes ℓ_1 regularized linear regression under the challeng...