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作者：Duchi, John C.; Ruan, Feng
作者单位：Stanford University; Northwestern University
摘要：We identify fundamental tradeoffs between statistical utility and privacy under local models of privacy in which data is kept private even from the statistician, providing instance-specific bounds for private estimation and learning problems by developing the local minimax risk. In contrast to approaches based on worst-case (minimax) error, which are conservative, this allows us to evaluate the difficulty of individual problem instances and delineate the possibilities for adaptation in private...
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作者：Dudeja, Rishabh; Hsu, Daniel
作者单位：University of Wisconsin System; University of Wisconsin Madison; Columbia University
摘要：Tensor PCA is a stylized statistical inference problem introduced by Montanari and Richard to study the computational difficulty of estimating an unknown parameter from higher-order moment tensors. Unlike its matrix counterpart, Tensor PCA exhibits a statistical-computational gap, that is, a sample size regime where the problem is information-theoretically solvable but conjectured to be computationally hard. This paper derives computational lower bounds on the run -time of memory bounded algor...
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作者：Luo, Yuetian; Zhang, Anru r.
作者单位：University of Chicago; Duke University; Duke University
摘要：We study the tensor-on-tensor regression, where the goal is to connect tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without prior knowledge of its intrinsic rank. We propose the Riemethods and cope with the challenge of unknown rank by studying the effect of rank over-parameterization. We provide the first convergence guarantee for the general tensor-on-tensor regression by showing that RGD and RGN respectively converge linearly and quadratically to a st...
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作者：Lyu, Ziyang; Sisson, S. A.; Welsh, A. H.
作者单位：University of New South Wales Sydney; University of New South Wales Sydney; Australian National University
摘要：This paper presents asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators within a two-way crossed mixed effect model, when the number of rows, columns, and the number of observations per cell tend to infinity. The relative growth rate for the number of rows, columns, and cells is unrestricted, whether considered pairwise or collectively. Under very mild conditions (which include moment conditions instead of requiring normality for either the random ...
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作者：Montanari, Andrea; Wu, Yuchen
作者单位：Stanford University; Stanford University; University of Pennsylvania
摘要：We consider the problem of estimating the factors of a low-rank n x d matrix, when this is corrupted by additive Gaussian noise. A special example of our setting corresponds to clustering mixtures of Gaussians with equal (known) covariances. Simple spectral methods do not take into account the distribution of the entries of these factors and are therefore often suboptimal. Here, we characterize the asymptotics of the minimum estimation error under the assumption that the distribution of the en...
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作者：Perez-Ortiz, Muriel Felipe; Lardy, Tyron; Heide, Rianne; Gruenwald, Peter D.
作者单位：Eindhoven University of Technology; Leiden University - Excl LUMC; Leiden University; Vrije Universiteit Amsterdam
摘要：We study worst-case-growth-rate-optimal (GROW) e-statistics for hypothesis testing between two group models. It is known that under a mild condition on the action of the underlying group G on the data, there exists a maximally invariant statistic. We show that among all e-statistics, invariant or not, the likelihood ratio of the maximally invariant statistic is GROW, both in the absolute and in the relative sense, and that an anytime-valid test can be based on it. The GROW e-statistic is equal...
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作者：Ascolani, Filippo; Zanella, Giacomo
作者单位：Duke University; Bocconi University
摘要：Gibbs samplers are popular algorithms to approximate posterior distributions arising from Bayesian hierarchical models. Despite their popularity and good empirical performance, however, there are still relatively few quantitative results on their convergence properties, for example, much less than for gradient-based sampling methods. In this work, we analyse the behaviour of total variation mixing times of Gibbs samplers targeting hierarchical models using tools from Bayesian asymptotics. We o...
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作者：Cai, Changxiao; Cai, T. Tony; Li, Hongzhe
作者单位：University of Michigan System; University of Michigan; University of Pennsylvania; University of Pennsylvania
摘要：Motivated by a range of applications, we study in this paper the problem of transfer learning for nonparametric contextual multi-armed bandits under the covariate shift model, where we have data collected from source bandits before the start of the target bandit learning. The minimax rate of convergence for the cumulative regret is established and a novel transfer learning algorithm that attains the minimax regret is proposed. The results quantify the contribution of the data from the source d...
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作者：Bao, Zhigang; Hu, Jiang; Xu, Xiaocong; Zhang, Xiaozhuo
作者单位：University of Hong Kong; Northeast Normal University - China; Hong Kong University of Science & Technology
摘要：A fundamental concept in multivariate statistics, the sample correlation matrix, is often used to infer the correlation/dependence structure among random variables, when the population mean and covariance are unknown. A natural block extension of it, the sample block correlation matrix, is proposed to take on the same role, when random variables are generalized to random subvectors. In this paper, we establish a spectral theory of the sample block correlation matrices and apply it to group ind...
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作者：Wang, Yuhao; Shah, Rajen d.
作者单位：Tsinghua University; University of Cambridge
摘要：We consider estimation of average treatment effects given observational data with high-dimensional pretreatment variables. Existing methods for this problem typically assume some form of sparsity for the regression functions. In this work, we introduce a debiased inverse propensity score weighting (DIPW) scheme for average treatment effect estimation that delivers root nconsistent estimates when the propensity score follows a sparse logistic regression model; the outcome regression functions a...
