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作者：Bilodeau, Blair; Foster, Dylan J.; Roy, Daniel M.
作者单位：University of Toronto; Microsoft
摘要：We consider the task of estimating a conditional density using i.i.d. sam-ples from a joint distribution, which is a fundamental problem with applica-tions in both classification and uncertainty quantification for regression. For joint density estimation, minimax rates have been characterized for general density classes in terms of uniform (metric) entropy, a well-studied notion of statistical capacity. When applying these results to conditional density es-timation, the use of uniform entropy-...
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作者：Celentano, Michael; Fan, Zhou; Mei, Song
作者单位：University of California System; University of California Berkeley; Yale University
摘要：We study mean-field variational Bayesian inference using the TAP approach, for Z2-synchronization as a prototypical example of a high -dimensional Bayesian model. We show that for any signal strength & lambda; > 1 (the weak-recovery threshold), there exists a unique local minimizer of the TAP free energy functional near the mean of the Bayes posterior law. Furthermore, the TAP free energy in a local neighborhood of this minimizer is strongly con-vex. Consequently, a natural-gradient/mirror-des...
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作者：Finke, Axel; Thiery, Alexandre H.
作者单位：Loughborough University; National University of Singapore
摘要：The iterated conditional sequential Monte Carlo (i-CSMC) algorithm from Andrieu, Doucet and Holenstein (J. R. Stat. Soc. Ser. B Stat. Methodol. 72 (2010) 269-342) is an MCMC approach for efficiently sampling from the joint posterior distribution of the T latent states in challenging time-series models, for example, in nonlinear or non-Gaussian state-space models. It is also the main ingredient in particle Gibbs samplers which infer unknown model parameters alongside the latent states. In this ...
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作者：Awan, Jordan; Vadhan, Salil
作者单位：Purdue University System; Purdue University
摘要：f-DP has recently been proposed as a generalization of differential pri-vacy allowing a lossless analysis of composition, post-processing, and pri-vacy amplification via subsampling. In the setting of f-DP, we propose the concept of a canonical noise distribution (CND), the first mechanism de-signed for an arbitrary f-DP guarantee. The notion of CND captures whether an additive privacy mechanism perfectly matches the privacy guarantee of a given f . We prove that a CND always exists, and give ...
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作者：Ma, Cong; Pathak, Reese; Wainwright, Martin J.
作者单位：University of Chicago; University of California System; University of California Berkeley; Massachusetts Institute of Technology (MIT)
摘要：We study the covariate shift problem in the context of nonparametric regression over a reproducing kernel Hilbert space (RKHS). We focus on two natural families of covariate shift problems defined using the likelihood ratios between the source and target distributions. When the likelihood ratios are uniformly bounded, we prove that the kernel ridge regression (KRR) estimator with a carefully chosen regularization parameter is minimax rate-optimal (up to a log factor) for a large family of RKHS...
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作者：Mei, By Tianxing; Wang, Chen; Yao, Jianfeng
作者单位：University of Hong Kong; The Chinese University of Hong Kong, Shenzhen
摘要：We analyze the singular values of a large p x n data matrix Xn = (xn1, . . . ,xnn), where the columns {xnj } are independent p-dimensional vec-tors, possibly with different distributions. Assuming that the covariance ma-trices Enj = Cov(xnj) of the column vectors can be asymptotically simulta-neously diagonalized, with appropriately converging spectra, we establish a limiting spectral distribution (LSD) for the singular values of Xn when both dimensions p and n grow to infinity in comparable m...
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作者：Butucea, Cristina; Rohde, Angelika; Steinberger, Lukas
作者单位：Institut Polytechnique de Paris; ENSAE Paris; University of Freiburg; University of Vienna
摘要：Local differential privacy has recently received increasing attention from the statistics community as a valuable tool to protect the privacy of individual data owners without the need of a trusted third party. Similar to the classical notion of randomized response, the idea is that data owners randomize their true information locally and only release the perturbed data. Many different protocols for such local perturbation procedures can be designed. In most estimation problems studied in the ...
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作者：Barber, Rina Foygel; Candes, Emmanuel J.; Ramdas, Aaditya; Tibshirani, Ryan J.
作者单位：University of Chicago; Stanford University; Carnegie Mellon University
摘要：Conformal prediction is a popular, modern technique for providing valid predictive inference for arbitrary machine learning models. Its validity relies on the assumptions of exchangeability of the data, and symmetry of the given model fitting algorithm as a function of the data. However, exchangeability is often violated when predictive models are deployed in practice. For example, if the data distribution drifts over time, then the data points are no longer ex-changeable; moreover, in such se...
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作者：Bellec, Pierre C.; Zhang, Cun-Hui
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：New upper bounds are developed for the L2 distance between & xi;/ Var[& xi;]1/2 and linear and quadratic functions of z & SIM; N(0, In) for random vari-ables of the form & xi; = z ⠃f (z) - div f (z). The linear approximation yields a central limit theorem when the squared norm of f (z) dominates the squared Frobenius norm of backward difference f (z) in expectation.Applications of this normal approximation are given for the asymptotic normality of debiased estimators in linear regression with...
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作者：Berrett, Thomas B.; Samworth, Richard J.
作者单位：University of Warwick; University of Cambridge
摘要：We consider the estimation of two-sample integral functionals, of the type that occur naturally, for example, when the object of interest is a diver-gence between unknown probability densities. Our first main result is that, in wide generality, a weighted nearest neighbour estimator is efficient, in the sense of achieving the local asymptotic minimax lower bound. Moreover, we also prove a corresponding central limit theorem, which facilitates the con-struction of asymptotically valid confidenc...
