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作者：Mourtada, Jaouad
作者单位：Institut Polytechnique de Paris; ENSAE Paris
摘要：We consider random-design linear prediction and related questions on the lower tail of random matrices. It is known that, under boundedness constraints, the minimax risk is of order d/n in dimension d with n samples. Here, we study the minimax expected excess risk over the full linear class, depending on the distribution of covariates. First, the least squares estimator is exactly minimax optimal in the well-specified case, for every distribution of covariates. We express the minimax risk in t...
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作者：Wei, Yun; Nguyen, XuanLong
作者单位：University of Michigan System; University of Michigan; University of Michigan System; University of Michigan
摘要：Mixtures of product distributions are a powerful device for learning about heterogeneity within data populations. In this class of latent structure models, de Finetti's mixing measure plays the central role for describing the uncertainty about the latent parameters representing heterogeneity. In this paper, posterior contraction theorems for de Finetti's mixing measure arising from finite mixtures of product distributions will be established; under the setting the number of exchangeable sequen...
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作者：Koltchinskii, Vladimir
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：Let X-(n) be an observation sampled from a distribution P(theta)((n) )with an unknown parameter theta, theta being a vector in a Banach space E (most often, a high-dimensional space of dimension d). We study the problem of estimation of f (theta) for a functional f : E bar right arrow R of some smoothness s > 0 based on an observation X-(n) similar to P-theta((n)). Assuming that there exists an estimator (theta) over cap (n) = (theta) over cap (n) (X-(n)) of parameter theta such that root n((t...
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作者：Koskela, Jere; Jenkins, Paul A.; Johansen, Adam M.; Spano, Dario
作者单位：University of Warwick
