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作者：Jiao, Yuling; Kang, Lican; Liu, Jin; Liu, Xiliang; Yang, Jerry zhijian
作者单位：Wuhan University; Wuhan University; The Chinese University of Hong Kong, Shenzhen; Wuhan University; Wuhan University; Wuhan University
摘要：In this paper, we consider deep approximate policy iteration (DAPI) with the Bellman residual minimization in reinforcement learning. In each iteration of DAPI, we apply convolutional neural networks (CNNs) with ReLU activation, called ReLU CNNs, to estimate the fixed point of the Bellman equation by minimizing an unbiased minimax loss. To bound the estimation error in each iteration, we control the statistical and approximation errors using the tools of the empirical process theory with depen...
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作者：Chong, Carsten H.; Delerue, Thomas; Mies, Fabian
作者单位：Hong Kong University of Science & Technology; Delft University of Technology
摘要：Consider the sum Y = B + B(H) of a Brownian motion B and an independent fractional Brownian motion B(H) with Hurst parameter H is an element of (0, 1). Even though B(H) is not a semimartingale, it was shown by Cheridito (Bernoulli 7 (2001) 913-934) that Y is a semimartingale if H > 3/4. Moreover, Y is locally equivalent to B in this case, so H cannot be consistently estimated from local observations of Y. This paper pivots on another unexpected feature in this model: if B and B(H) become corre...
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作者：Shen, Yinan; Li, Jingyang; Cai, Jian-feng; Xia, Dong
作者单位：Hong Kong University of Science & Technology
摘要：High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs, especially since the robust loss functions are usually nonsmooth. More recently, computationally fast nonconvex approaches via subgradient descent are proposed, which, unfortunately, fail to deliver a statistically consistent estimator even under sub-Gaussian n...
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作者：Leanthous, C.; Eorgiadis, A. G.; Epski, O., V
作者单位：Maynooth University; Trinity College Dublin; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We deal with the problem of the adaptive estimation of the L-2-norm of a probability density on R-d, d >= 1, from independent observations. The unknown density is assumed to be uniformly bounded and to belong to the union of balls in the isotropic/anisotropic Nikolskii's spaces. We will show that the optimally adaptive estimators over the collection of considered functional classes do no exist. Also, in the framework of an abstract density model we present several generic lower bounds related ...
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作者：Li, Xiang; Ruan, Feng; Wang, Huiyuan; Long, Qi; Su, Weijie J.
作者单位：University of Pennsylvania; Northwestern University
摘要：Since ChatGPT was introduced in November 2022, embedding (nearly) unnoticeable statistical signals into text generated by large language models (LLMs), also known as watermarking, has been used as a principled approach to provable detection of LLM-generated text from its human-written counterpart. In this paper, we introduce a general and flexible framework for reasoning about the statistical efficiency of watermarks and designing powerful detection rules. Inspired by the hypothesis testing fo...
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作者：Barigozzi, Matteo; LA Vecchia, Davide; Liu, Hang
作者单位：Institut Polytechnique de Paris; ENSAE Paris; University of Geneva; Chinese Academy of Sciences; University of Science & Technology of China, CAS
摘要：Motivated by the need for analysing large spatio-temporal panel data, we introduce a novel nonparametric methodology for n-dimensional random fields observed across S spatial locations and T time periods. We call it general spatio-temporal factor model (GSTFM). First, we provide the probabilistic and mathematical underpinning needed for the representation of a random field as the sum of two components: the common component (driven by a small number q of latent factors) and the idiosyncratic co...
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作者：Igollet, Philippe; Tromme, Austin j.
作者单位：Massachusetts Institute of Technology (MIT); Institut Polytechnique de Paris; ENSAE Paris
摘要：We study the sample complexity of entropic optimal transport in high diadvance the state of the art by establishing dimension-free, parametric rates for estimating various quantities of interest, including the entropic regression function, which is a natural analog to the optimal transport map. As an application, we propose a practical model for transfer learning based on entropic optimal transport and establish parametric rates of convergence for nonparametric regression and classification.
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作者：Fan, Yingying; Gao, Lan; Lv, Jinchi
作者单位：University of Southern California; University of Tennessee System; University of Tennessee Knoxville
摘要：We investigate the robustness of the model-X knockoffs framework with respect to the misspecified or estimated feature distribution. We achieve such a goal by theoretically studying the feature selection performance of a practically implemented knockoffs algorithm, which we name as the approximate knockoffs (ARK) procedure, under the measures of the false discovery rate (FDR) and k-familywise error rate (k-FWER). The approximate knockoffs procedure differs from the model-X knockoffs procedure ...
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作者：Lin, Licong; Khamaru, Koulik; Wainwright, Martin J.
作者单位：University of California System; University of California Berkeley; Rutgers University System; Rutgers University New Brunswick; Massachusetts Institute of Technology (MIT)
摘要：Many standard estimators, when applied to adaptively collected data, fail to be asymptotically normal, thereby complicating the construction of confidence intervals. We address this challenge in a semiparametric context: estimating the parameter vector of a generalized linear regression model contaminated by a nonparametric nuisance component. We construct suitably weighted estimating equations that account for adaptivity in data collection and provide conditions under which the associated est...
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作者：Shi, Lei; Wang, Jingshen; Ding, Peng
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：Ever since the seminal work of R. A. Fisher and F. Yates, factorial designs have been an important experimental tool to simultaneously estimate the effects of multiple treatment factors. In factorial designs, the number of treatment combinations grows exponentially with the number of treatment factors, which motivates the forward selection strategy based on the sparsity, hierarchy and heredity principles for factorial effects. Although this strategy is intuitive and has been widely used in pra...
