Cauchy noise loss for stochastic optimization of random matrix models via free deterministic equivalents
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Based on free probability theory and stochastic optimization, we introduce a new parameter estimation method of random matrix models. Our method is inspired by free deterministic equivalents and iterative methods for computing Cauchy transforms. Moreover, we study an asymptotic property of a generalization gap and show numerical experiments of the optimization. We treat two random matrix models; the compound Wishart model and the information-plus-noise model. In addition, we propose a new rank recovery method for the information-plus-noise model, and experimentally demonstrate that it recovers the true rank even if the rank is not low.
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