Phase Transition for Support Recovery from Gaussian Linear Measurements

by   Lekshmi Ramesh, et al.

We study the problem of recovering the common k-sized support of a set of n samples of dimension d, using m noisy linear measurements per sample. Most prior work has focused on the case when m exceeds k, in which case n of the order (k/m)log(d/k) is both necessary and sufficient. Thus, in this regime, only the total number of measurements across the samples matter, and there is not much benefit in getting more than k measurements per sample. In the measurement-constrained regime where we have access to fewer than k measurements per sample, we show an upper bound of O((k^2/m^2)log d) on the sample complexity for successful support recovery when m≥ 2log d. Along with the lower bound from our previous work, this shows a sharp phase transition for the sample complexity of this problem around k/m=1. In fact, our proposed algorithm is sample-optimal in both the regimes. It follows that, in the m≪ k regime, multiple measurements from the same sample are more valuable than measurements from different samples.



There are no comments yet.


page 1

page 2

page 3

page 4


Sample-Measurement Tradeoff in Support Recovery under a Subgaussian Prior

Data samples from R^d with a common support of size k are accessed throu...

Sample complexity of population recovery

The problem of population recovery refers to estimating a distribution b...

Network Recovery from Unlabeled Noisy Samples

There is a growing literature on the statistical analysis of multiple ne...

Multiple Support Recovery Using Very Few Measurements Per Sample

In the problem of multiple support recovery, we are given access to line...

Multi-reference alignment in high dimensions: sample complexity and phase transition

Multi-reference alignment entails estimating a signal in ℝ^L from its ci...

Dynamic Sample Complexity for Exact Sparse Recovery using Sequential Iterative Hard Thresholding

In this paper we consider the problem of exact recovery of a fixed spars...

Learning Graphs from Linear Measurements: Fundamental Trade-offs and Applications

We consider a specific graph learning task: reconstructing a symmetric m...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.