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作者：Soloff, Jake A.; Guntuboyina, Adityanand; Sen, Bodhisattva
作者单位：University of Chicago; University of California System; University of California Berkeley; Columbia University
摘要：Multivariate, heteroscedastic errors complicate statistical inference in many large-scale denoizing problems. Empirical Bayes is attractive in such settings, but standard parametric approaches rest on assumptions about the form of the prior distribution which can be hard to justify and which introduce unnecessary tuning parameters. We extend the nonparametric maximum-likelihood estimator (NPMLE) for Gaussian location mixture densities to allow for multivariate, heteroscedastic errors. NPMLEs e...
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作者：Siegmund, David
作者单位：Stanford University; Stanford University
摘要：We derive confidence intervals (CIs) and confidence sequences (CSs) for the classical problem of estimating a bounded mean. Our approach generalizes and improves on the celebrated Chernoff method, yielding the best closed-form empirical-Bernstein CSs and CIs (converging exactly to the oracle Bernstein width) as well as non-closed-form betting CSs and CIs. Our method combines new composite nonnegative (super) martingales with Ville's maximal inequality, with strong connections to testing by bet...
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作者：Vovk, Vladimir
作者单位：University of London; Royal Holloway University London
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作者：Waudby-Smith, Ian; Ramdas, Aaditya
作者单位：Carnegie Mellon University; Carnegie Mellon University; Carnegie Mellon University
摘要：We derive confidence intervals (CIs) and confidence sequences (CSs) for the classical problem of estimating a bounded mean. Our approach generalizes and improves on the celebrated Chernoff method, yielding the best closed-form empirical-Bernstein CSs and CIs (converging exactly to the oracle Bernstein width) as well as non-closed-form betting CSs and CIs. Our method combines new composite nonnegative (super)martingales with Ville's maximal inequality, with strong connections to testing by bett...
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作者：Ren, Zhimei; Barber, Rina Foygel
作者单位：University of Pennsylvania; University of Chicago
摘要：Model-X knockoffs is a flexible wrapper method for high-dimensional regression algorithms, which provides guaranteed control of the false discovery rate (FDR). Due to the randomness inherent to the method, different runs of model-X knockoffs on the same dataset often result in different sets of selected variables, which is undesirable in practice. In this article, we introduce a methodology for derandomising model-X knockoffs with provable FDR control. The key insight of our proposed method li...
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作者：Stark, Philip B.
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We derive confidence intervals (CIs) and confidence sequences (CSs) for the classical problem of estimating a bounded mean. Our approach generalizes and improves on the celebrated Chernoff method, yielding the best closed-form empirical-Bernstein CSs and CIs (converging exactly to the oracle Bernstein width) as well as non-closed-form betting CSs and CIs. Our method combines new composite nonnegative (super) martingales with Ville's maximal inequality, with strong connections to testing by bet...
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作者：Waudby-Smith, Ian; Ramdas, Aaditya
作者单位：Carnegie Mellon University; Carnegie Mellon University; Carnegie Mellon University
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作者：Javanmard, Adel; Mehrabi, Mohammad
作者单位：University of Southern California; University of Southern California
摘要：Performance of classifiers is often measured in terms of average accuracy on test data. Despite being a standard measure, average accuracy fails in characterising the fit of the model to the underlying conditional law of labels given the features vector (Y | X), e.g. due to model misspecification, over fitting, and high-dimensionality. In this paper, we consider the fundamental problem of assessing the goodness-of-fit for a general binary classifier. Our framework does not make any parametric ...
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作者：Maullin-Sapey, Thomas; Schwartzman, Armin; Nichols, Thomas E.
作者单位：University of Oxford; University of California System; University of California San Diego; University of California System; University of California San Diego; University of Oxford
摘要：The analysis of excursion sets in imaging data is essential to a wide range of scientific disciplines such as neuroimaging, climatology, and cosmology. Despite growing literature, there is little published concerning the comparison of processes that have been sampled across the same spatial region but which reflect different study conditions. Given a set of asymptotically Gaussian random fields, each corresponding to a sample acquired for a different study condition, this work aims to provide ...
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作者：Waghmare, Kartik G.; Panaretos, Victor M.
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：Let X={Xu}u is an element of U be a real-valued Gaussian process indexed by a set U. We show that X can be viewed as a graphical model with an uncountably infinite graph, where each Xu is a vertex. This graph is characterized by the reproducing property of X's covariance kernel, without restricting U to be finite or countable, allowing the modelling of stochastic processes in continuous time/space. Unlike traditional methods, this characterization is not based on zero entries of an inverse cov...
