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When in Doubt, SWAP: High-Dimensional Sparse Recovery from Correlated Measurements
Divyanshu Vats · Richard Baraniuk

Thu Dec 05 07:00 PM -- 11:59 PM (PST) @ Harrah's Special Events Center, 2nd Floor #None

We consider the problem of accurately estimating a high-dimensional sparse vector using a small number of linear measurements that are contaminated by noise. It is well known that standard computationally tractable sparse recovery algorithms, such as the Lasso, OMP, and their various extensions, perform poorly when the measurement matrix contains highly correlated columns. We develop a simple greedy algorithm, called SWAP, that iteratively swaps variables until a desired loss function cannot be decreased any further. SWAP is surprisingly effective in handling measurement matrices with high correlations. We prove that SWAP can be easily used as a wrapper around standard sparse recovery algorithms for improved performance. We theoretically quantify the statistical guarantees of SWAP and complement our analysis with numerical results on synthetic and real data.

Author Information

Divyanshu Vats (Rice University)
Richard Baraniuk (Rice University)

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