Optimal convex lifted sparse phase retrieval and PCA with an atomic matrix norm regularizer
| Autor: | Andrew D. McRae, Justin Romberg, Mark A. Davenport |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
optimal rates
principal component analysis convex relaxation sparse matrices MathematicsofComputing_NUMERICALANALYSIS noise measurement sparse pca complexity theory Mathematics - Statistics Theory Statistics Theory (math.ST) Library and Information Sciences algorithms phase measurement atomic norm Computer Science Applications signal recovery structured signal FOS: Mathematics standards quadratic measurements bounds optimization sparse phase retrieval Information Systems |
| Popis: | We present novel analysis and algorithms for solving sparse phase retrieval and sparse principal component analysis (PCA) with convex lifted matrix formulations. The key innovation is a new mixed atomic matrix norm that, when used as regularization, promotes low-rank matrices with sparse factors. We show that convex programs with this atomic norm as a regularizer provide near-optimal sample complexity and error rate guarantees for sparse phase retrieval and sparse PCA. While we do not know how to solve the convex programs exactly with an efficient algorithm, for the phase retrieval case we carefully analyze the program and its dual and thereby derive a practical heuristic algorithm. We show empirically that this practical algorithm performs similarly to existing state-of-the-art algorithms. |
| Databáze: | OpenAIRE |
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