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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：Chetelat, Didier
作者单位：Universite de Montreal; Polytechnique Montreal
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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...
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作者：Li, Jiaqi; Chen, Likai; Wang, Weining; Wu, Wei biao
作者单位：Washington University (WUSTL); University of Groningen; University of Chicago
摘要：We propose an inference method for detecting multiple change points inhigh-dimensional time series, targeting dense or spatially clustered signals.Our method aggregates moving sum (MOSUM) statistics cross-sectionallyby an2-norm and maximizes them over time. We further introduce anovel Two-Way MOSUM, which utilizes spatial-temporal moving regionsto search for breaks, with the added advantage of enhancing testing powerwhen breaks occur in only a few groups. The limiting distribution of an2-aggre...
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作者：Marandon, Ariane; Lei, Lihua; Mary, David; Roquain, Etienne
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Stanford University; Universite Cote d'Azur; Observatoire de la Cote d'Azur
摘要：This paper studies the semisupervised novelty detection problem where a set of typical measurements is available to the researcher. Motivated by recent advances in multiple testing and conformal inference, we propose AdaDetect, a flexible method that is able to wrap around any probabilistic classification algorithm and control the false discovery rate (FDR) on detected novelties in finite samples without any distributional assumption other than exchangeability. In contrast to classical FDR-con...
