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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：Oh, Eun Jeong; Qian, Min; Cheung, Ying Kuen
作者单位：Columbia University
摘要：A dynamic treatment regime (DTR) is a sequence of decision rules, one per stage of intervention, that maps up-to-date patient information to a recommended treatment. Discovering an appropriate DTR for a given disease is a challenging issue especially when a large set of prognostic variables are observed. To address this problem, we propose penalized regression-based learning methods with l(1) penalty to estimate the optimal DTR that would maximize the expected outcome if implemented. We also p...
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作者：Goodman, Jesse
作者单位：University of Auckland
摘要：The saddlepoint approximation gives an approximation to the density of a random variable in terms of its moment generating function. When the underlying random variable is itself the sum of n unobserved i.i.d. terms, the basic classical result is that the relative error in the density is of order 1/ n. If instead the approximation is interpreted as a likelihood and maximised as a function of model parameters, the result is an approximation to the maximum likelihood estimate (MLE) that can be m...
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作者：Javanmard, Adel; Soltanolkotabi, Mahdi
作者单位：University of Southern California; University of Southern California
摘要：Despite the wide empirical success of modern machine learning algorithms and models in a multitude of applications, they are known to be highly susceptible to seemingly small indiscernible perturbations to the input data known as adversarial attacks. A variety of recent adversarial training procedures have been proposed to remedy this issue. Despite the success of such procedures at increasing accuracy on adversarially perturbed inputs or robust accuracy, these techniques often reduce accuracy...
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作者：Abbe, Emmanuel; Fan, Jianqing; Wang, Kaizheng
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Princeton University; Columbia University; Columbia University
摘要：Principal Component Analysis (PCA) is a powerful tool in statistics and machine learning. While existing study of PCA focuses on the recovery of principal components and their associated eigenvalues, there are few precise characterizations of individual principal component scores that yield low-dimensional embedding of samples. That hinders the analysis of various spectral methods. In this paper, we first develop an l(p) perturbation theory for a hollowed version of PCA in Hilbert spaces which...
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作者：Li, Shuangning; Wager, Stefan
作者单位：Stanford University; Stanford University
摘要：The network interference model for treatment effect estimation places experimental units at the vertices of an undirected exposure graph, such that treatment assigned to one unit may affect the outcome of another unit if and only if these two units are connected by an edge. This model has recently gained popularity as means of incorporating interference effects into the Neyman-Rubin potential outcomes framework; and several authors have considered estimation of various causal targets, includin...
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作者：Austern, Morgane; Orbanz, Peter
作者单位：Harvard University; University of London; University College London
摘要：A distributional symmetry is invariance of a distribution under a group of transformations. Exchangeability and stationarity are examples. We explain that a result of ergodic theory implies a law of large numbers for such invariant distributions: If the group satisfies suitable conditions, expectations can be estimated by averaging over subsets of transformations, and these estimators are strongly consistent. We show that, if a mixing condition holds, the averages also satisfy a central limit ...
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作者：Wang, Jingshu; Gui, Lin; Su, Weijie J.; Sabatti, Chiara; Owen, Art B.
作者单位：University of Chicago; University of Pennsylvania; Stanford University
摘要：Replicability is a fundamental quality of scientific discoveries: we are interested in those signals that are detectable in different laboratories, different populations, across time etc. Unlike meta-analysis which accounts for experimental variability but does not guarantee replicability, testing a partial conjunction (PC) null aims specifically to identify the signals that are discovered in multiple studies. In many contemporary applications, for example, comparing multiple high-throughput g...
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作者：Zhu, Banghua; Jiao, Jiantao; Steinhardt, Jacob
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be maliciously corrupted in many other ways, such as systematic measurement errors and missing covariates. We consider corruption in either TV or Wasserstein distance, and show that robust estimation is possible whenever the true population distribution satisfies a property called generalized resilience, which holds under moment or hypercontractive conditions. For TV corr...
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作者：Cai, T. Tony; Pu, Hongming
作者单位：University of Pennsylvania
摘要：We consider d-dimensional stochastic continuum-armed bandits with the expected reward function being additive beta-Holder with sparsity s for 0 < beta < infinity and 1 <= s <= d. The rate of convergence (O) over tilde (s center dot T beta+1/2 beta+1) for the minimax regret is established where T is the number of rounds. In particular, the minimax regret does not depend on d and is linear in s. A novel algorithm is proposed and is shown to be rate-optimal, up to a logarithmic factor of T. The p...
