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作者：Andrieu, Christophe; Lee, Anthony; Power, Sam; Wang, Andi Q.
作者单位：University of Bristol
摘要：We investigate the use of a certain class of functional inequalities known as weak Poincare inequalities to bound convergence of Markov chains to equilibrium. We show that this enables the straightforward and transpar-ent derivation of subgeometric convergence bounds for methods such as the Independent Metropolis-Hastings sampler and pseudo-marginal methods for intractable likelihoods, the latter being subgeometric in many practical settings. These results rely on novel quantitative comparison...
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作者：Liao, Peng; Qi, Zhengling; Wan, Runzhe; Klasnja, Predrag; Murphy, Susan A.
作者单位：Harvard University; George Washington University; Amazon.com; University of Michigan System; University of Michigan
摘要：We consider the batch (off-line) policy learning problem in the infinite horizon Markov decision process. Motivated by mobile health applications, we focus on learning a policy that maximizes the long-term average reward. We propose a doubly robust estimator for the average reward and show that it achieves semiparametric efficiency. Further, we develop an optimization algorithm to compute the optimal policy in a parameterized stochastic policy class. The performance of the estimated policy is ...
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作者：Shi, Hongjian; Hallin, Marc; Drton, Mathias; Han, Fang
作者单位：Technical University of Munich; Universite Libre de Bruxelles; Universite Libre de Bruxelles; University of Washington; University of Washington Seattle
摘要：Rank correlations have found many innovative applications in the last decade. In particular, suitable rank correlations have been used for consistent tests of independence between pairs of random variables. Using ranks is especially appealing for continuous data as tests become distribution-free. However, the traditional concept of ranks relies on ordering data and is, thus, tied to univariate observations. As a result, it has long remained unclear how one may construct distribution-free yet c...
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作者：Zhong, Qixian; Mueller, Jonas; Wang, Jane-Ling
作者单位：Xiamen University; Amazon.com; University of California System; University of California Davis
摘要：While deep learning approaches to survival data have demonstrated empirical success in applications, most of these methods are difficult to interpret and mathematical understanding of them is lacking. This paper studies the partially linear Cox model, where the nonlinear component of the model is implemented using a deep neural network. The proposed approach is flexible and able to circumvent the curse of dimensionality, yet it facilitates interpretability of the effects of treatment covariate...
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作者：Mccormack, Andrew; Hoff, Peter
作者单位：Duke University
摘要：The Frechet mean is a useful description of location for a probability distribution on a metric space that is not necessarily a vector space. This article considers simultaneous estimation of multiple Frechet means from a decision-theoretic perspective, and in particular, the extent to which the unbiased estimator of a Frechet mean can be dominated by a generalization of the James-Stein shrinkage estimator. It is shown that if the metric space satisfies a nonpositive curvature condition, then ...
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作者：Zhang, Qihao; Lahiri, Soumendra N.; Nordman, Daniel J.
作者单位：Iowa State University; Washington University (WUSTL)
摘要：Block-based resampling estimators have been intensively investigated for weakly dependent time processes, which has helped to inform imple-mentation (e.g., best block sizes). However, little is known about resampling performance and block sizes under strong or long-range dependence. To es-tablish guideposts in block selection, we consider a broad class of strongly dependent time processes, formed by a transformation of a stationary long -memory Gaussian series, and examine block-based resampli...
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作者：Chen, Pinhan; Gao, Chao; Zhang, Anderson Y.
作者单位：University of Chicago; University of Pennsylvania
摘要：Given partially observed pairwise comparison data generated by the Bradley-Terry-Luce (BTL) model, we study the problem of top-k ranking. That is, to optimally identify the set of top-k players. We derive the minimax rate with respect to a normalized Hamming loss. This provides the first result in the literature that characterizes the partial recovery error in terms of the proportion of mistakes for top-k ranking. We also derive the optimal signal to noise ratio condition for the exact recover...
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作者：Kirchner, Kristin; Bolin, David
作者单位：Delft University of Technology; King Abdullah University of Science & Technology
摘要：Optimal linear prediction (aka. kriging) of a random field {Z(x)}(x is an element of X )indexed by a compact metric space (X, d(X)) can be obtained if the mean value function m : chi -> R and the covariance function Q: X x X -> R of Z are known. We consider the problem of predicting the value of Z (x*) at some location x* is an element of X based on observations at locations {x(j)}(j=1)(n), which accumulate at x* as n -> infinity (or, more generally, predicting phi(Z) based on {phi(j)(Z)}(j=i)...
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作者：Han, Qiyang; Sen, Bodhisattva; Shen, Yandi
作者单位：Rutgers University System; Rutgers University New Brunswick; Columbia University; University of Washington; University of Washington Seattle
摘要：In the Gaussian sequence model Y = mu + xi, we study the likelihood ratio test (LRT) for testing H-0 : mu = mu(0) versus H-1 : mu is an element of K, where mu(0) is an element of K, and K is a closed convex set in R-n. In particular, we show that under the null hypothesis, normal approximation holds for the log-likelihood ratio statistic for a general pair (mu(0), K), in the high-dimensional regime where the estimation error of the associated least squares estimator diverges in an appropriate ...
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作者：Barber, Rina Foygel; Drton, Mathias; Sturma, Nils; Weihs, Luca
作者单位：University of Chicago; Technical University of Munich
摘要：We consider linear structural equation models with latent variables and develop a criterion to certify whether the direct causal effects between the ob-servable variables are identifiable based on the observed covariance matrix. Linear structural equation models assume that both observed and latent vari-ables solve a linear equation system featuring stochastic noise terms. Each model corresponds to a directed graph whose edges represent the direct ef-fects that appear as coefficients in the eq...
