-
作者：Ghorbani, Behrooz; Mei, Song; Misiakiewicz, Theodor; Montanari, Andrea
作者单位：Stanford University; Stanford University; Stanford University
摘要：We consider the problem of learning an unknown function f(star) on the d-dimensional sphere with respect to the square loss, given i.i.d. samples {(y(i), x(i))}(i <= n) where x(i) is a feature vector uniformly distributed on the sphere and y(i) = f(star)(x(i)) + epsilon(i). We study two popular classes of models that can be regarded as linearizations of two-layers neural networks around a random initialization: the random features model of Rahimi-Recht (RF); the neural tangent model of Jacot-G...
-
作者：Azadkia, Mona; Chatterjee, Sourav
作者单位：Stanford University
摘要：We propose a coefficient of conditional dependence between two random variables Y and Z given a set of other variables X-1, ..., X-p, based on an i.i.d. sample. The coefficient has a long list of desirable properties, the most important of which is that under absolutely no distributional assumptions, it converges to a limit in [0, 1], where the limit is 0 if and only if Y and Z are conditionally independent given X-1, ..., X-p, and is 1 if and only if Y is equal to a measurable function of Z g...
-
作者：de Chaumaray, Marie du Roy; Marbac, Matthieu; Patilea, Valentin
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Rennes; Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI)
摘要：The empirical likelihood inference is extended to a class of semiparametric models for stationary, weakly dependent series. A partially linear single-index regression is used for the conditional mean of the series given its past, and the present and past values of a vector of covariates. A parametric model for the conditional variance of the series is added to capture further nonlinear effects. We propose suitable moment equations which characterize the mean and variance model. We derive an em...
-
作者：Luedtke, Alex; Bibaut, Aurelien; van der Laan, Mark
作者单位：University of Washington; University of Washington Seattle; University of California System; University of California Berkeley
-
作者：Brecheteau, Claire; Fischer, Aurelie; Levrard, Clement
作者单位：Universite Rennes 2; Universite de Rennes; Universite Paris Cite
摘要：Clustering with Bregman divergences encompasses a wide family of clustering procedures that are well suited to mixtures of distributions from exponential families (J. Mach. Learn. Res. 6 (2005) 1705-1749). However, these techniques are highly sensitive to noise. To address the issue of clustering data with possibly adversarial noise, we introduce a robustified version of Bregman clustering based on a trimming approach. We investigate its theoretical properties, showing for instance that our es...
-
作者：Andrieu, Christophe; Livingstone, Samuel
作者单位：University of Bristol; University of London; University College London
摘要：Historically time-reversibility of the transitions or processes underpinning Markov chain Monte Carlo methods (MCMC) has played a key role in their development, while the self-adjointness of associated operators together with the use of classical functional analysis techniques on Hilbert spaces have led to powerful and practically successful tools to characterise and compare their performance. Similar results for algorithms relying on nonreversible Markov processes are scarce. We show that for...
-
作者：Duchi, John C.; Namkoong, Hongseok
作者单位：Stanford University; Columbia University
摘要：A common goal in statistics and machine learning is to learn models that can perform well against distributional shifts, such as latent heterogeneous subpopulations, unknown covariate shifts or unmodeled temporal effects. We develop and analyze a distributionally robust stochastic optimization (DRO) framework that learns a model providing good performance against perturbations to the data-generating distribution. We give a convex formulation for the problem, providing several convergence guara...
-
作者：Imbens, Guido; Menzel, Konrad
作者单位：Stanford University; Stanford University; New York University
摘要：The bootstrap, introduced by The Jackknife, the Bootstrap and Other Resampling Plans ((1982), SIAM), has become a very popular method for estimating variances and constructing confidence intervals. A key insight is that one can approximate the properties of estimators by using the empirical distribution function of the sample as an approximation for the true distribution function. This approach views the uncertainty in the estimator as coming exclusively from sampling uncertainty. We argue tha...
-
作者：Ding, Xiucai; Yang, Fan
作者单位：Duke University; University of Pennsylvania
摘要：We study a class of separable sample covariance matrices of the form (Q) over tilde (1) := (A) over tilde X-1/2 (B) over tilde BX*(B) over tilde (1/2). Here, (A) over tilde and (B) over tilde are positive definite matrices whose spectrums consist of bulk spectrums plus several spikes, that is, larger eigenvalues that are separated from the bulks. Conceptually, we call (Q) over tilde (1) a spiked separable covariance matrix model. On the one hand, this model includes the spiked covariance matri...
-
作者：Bao, Zhigang; Ding, Xiucai; Wang, Ke
作者单位：Hong Kong University of Science & Technology; University of California System; University of California Davis
摘要：In this paper, we study the matrix denoising model Y = S + X, where S is a low rank deterministic signal matrix and X is a random noise matrix, and both are M x n. In the scenario that M and n are comparably large and the signals are supercritical, we study the fluctuation of the outlier singular vectors of Y, under fully general assumptions on the structure of S and the distribution of X. More specifically, we derive the limiting distribution of angles between the principal singular vectors o...
