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作者：Thepaut, Solene; Verzelen, Nicolas
作者单位：Safran S.A.; INRAE; Universite de Montpellier
摘要：We consider the twin problems of estimating the effective rank and the Schatten norms HAHs of a rectangular p x q matrix A from noisy observations. When s is an even integer, we introduce a polynomial-time estimator of HAHs that achieves the minimax rate (pq)(1/4). Interestingly, this optimal rate does not depend on the underlying rank of the matrix A. When s is not an even integer, the optimal rate is much slower. A simple thresholding estimator of the singular values achieves the rate (q boo...
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作者：Yan, Yuling; Wang, Kaizheng; Rigollet, Philippe
作者单位：University of Wisconsin System; University of Wisconsin Madison; Columbia University; Columbia University; Massachusetts Institute of Technology (MIT)
摘要：Gaussian mixture models form a flexible and expressive parametric family of distributions that has found a variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a computational perspective. Currently, only moment-based methods enjoy theoretical guarantees while likelihood-based methods are dominated by heuristics such as Expectation-Maximization that are known to fail in simple examples. In this work, we propose a new algorithm to compute the n...
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作者：Katsevich, Anya; Rigollet, Philippe
作者单位：Massachusetts Institute of Technology (MIT)
摘要：The main computational challenge in Bayesian inference is to compute integrals against a high-dimensional posterior distribution. In the past decades, variational inference (VI) has emerged as a tractable approximation to these integrals, and a viable alternative to the more established paradigm of Markov chain Monte Carlo. However, little is known about the approximation accuracy of VI. In this work, we bound the TV error and the mean and covariance approximation error of Gaussian VI in terms...
