Corpus ID: 224803172

# A Continuous-Time Mirror Descent Approach to Sparse Phase Retrieval

@article{Wu2020ACM,
title={A Continuous-Time Mirror Descent Approach to Sparse Phase Retrieval},
author={Fan Wu and Patrick Rebeschini},
journal={ArXiv},
year={2020},
volume={abs/2010.10168}
}
• Published 2020
• Computer Science, Mathematics
• ArXiv
We analyze continuous-time mirror descent applied to sparse phase retrieval, which is the problem of recovering sparse signals from a set of magnitude-only measurements. We apply mirror descent to the unconstrained empirical risk minimization problem (batch setting), using the square loss and square measurements. We provide a convergence analysis of the algorithm in this non-convex setting and prove that, with the hypentropy mirror map, mirror descent recovers any $k$-sparse vector $\mathbf{x… Expand 3 Citations #### Figures from this paper Implicit Regularization in Matrix Sensing via Mirror Descent • Mathematics, Computer Science • ArXiv • 2021 It is shown that gradient descent with full-rank factorized parametrization is a first-order approximation to mirror descent, in which case an explicit characterization of the implicit bias of gradient flow as a by-product is obtained. Expand Implicit Bias of SGD for Diagonal Linear Networks: a Provable Benefit of Stochasticity • Computer Science • ArXiv • 2021 The findings highlight the fact that structured noise can induce better generalisation and they help explain the greater performances observed in practice of stochastic gradient descent over gradient descent. Expand Approximate Message Passing with Spectral Initialization for Generalized Linear Models • Mathematics, Computer Science • AISTATS • 2021 This paper proposes a two-phase artificial AMP algorithm that first produces the spectral estimator, and then closely approximates the iterates of the true AMP, and yields a rigorous characterization of the performance of AMP with spectral initialization in the high-dimensional limit. Expand #### References SHOWING 1-10 OF 69 REFERENCES Optimal Rates of Convergence for Noisy Sparse Phase Retrieval via Thresholded Wirtinger Flow • Mathematics, Computer Science • ArXiv • 2015 A novel thresholded gradient descent algorithm is proposed and it is shown to adaptively achieve the minimax optimal rates of convergence over a wide range of sparsity levels when the a_j's are independent standard Gaussian random vectors, provided that the sample size is sufficiently large compared to the sparsity of$x. Expand
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