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作者：Cai, T. Tony; Liu, Weidong; Zhou, Harrison H.
作者单位：University of Pennsylvania; Shanghai Jiao Tong University; Shanghai Jiao Tong University; Yale University
摘要：Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of sparse precision matrices in the high dimensional setting. Optimal rates of convergence are established for a range of matrix norm losses. A fully data driven estimator based on adaptive constrained l(1) minimization is proposed and its rate of convergence is obtained over a collection of parameter spaces. The estimator, called ACLIME, is e...
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作者：Cai, Tony; Kim, Donggyu; Wang, Yazhen; Yuan, Ming; Zhou, Harrison H.
作者单位：University of Pennsylvania; University of Wisconsin System; University of Wisconsin Madison; Yale University
摘要：Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this paper, we study estimation of high-dimensional density matrices based on Pauli measurements. In particular, under appropriate notion of sparsity, we establish the minimax optimal rates of convergence for estimation of the density matrix under both the spectral and Frobenius norm losses; and show how...
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作者：Bonhomme, Stephane; Jochmans, Koen; Robin, Jean-Marc
作者单位：University of Chicago; Institut d'Etudes Politiques Paris (Sciences Po); University of London; University College London
摘要：A constructive proof of identification of multilinear decompositions of multiway arrays is presented. It can be applied to show identification in a variety of multivariate latent structures. Examples are finite-mixture models and hidden Markov models. The key step to show identification is the joint diagonalization of a set of matrices in the same nonorthogonal basis. An estimator of the latent-structure model may then be based on a sample version of this joint-diagonalization problem. Algorit...
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作者：Chen, Yen-Chi; Genovese, Christopher R.; Tibshirani, Ryan J.; Wasserman, Larry
作者单位：Carnegie Mellon University
摘要：Modal regression estimates the local modes of the distribution of Y given X = x, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usual regression methods. We study a simple nonparametric method for modal regression, based on a kernel density estimate (KDE) of the joint distribution of Y and X. We derive asymptotic error bounds for this method, and propose techniques for constructing confidence sets and prediction sets. The latter is use...
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作者：Luedtke, Alexander R.; van der Laan, Mark J.
作者单位：University of California System; University of California Berkeley
摘要：We consider challenges that arise in the estimation of the mean outcome under an optimal individualized treatment strategy defined as the treatment rule that maximizes the population mean outcome, where the candidate treatment rules are restricted to depend on baseline covariates. We prove a necessary and sufficient condition for the pathwise differentiability of the optimal value, a key condition needed to develop a regular and asymptotically linear (RAL) estimator of the optimal value. The s...
