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作者：Donnet, Sophie; Rivoirard, Vincent; Rousseau, Judith
作者单位：INRAE; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine
摘要：This paper studies nonparametric estimation of parameters of multivariate Hawkes processes. We consider the Bayesian setting and derive posterior concentration rates. First, rates are derived for L-1-metrics for stochastic intensities of the Hawkes process. We then deduce rates for the L-1-norm of interactions functions of the process. Our results are exemplified by using priors based on piecewise constant functions, with regular or random partitions and priors based on mixtures of Betas distr...
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作者：Rohde, Angelika; Steinberger, Lukas
作者单位：University of Freiburg; University of Vienna
摘要：We study the problem of estimating a functional theta(P) of an unknown probability distribution P is an element of P in which the original iid sample X-1,..., X-n is kept private even from the statistician via an alpha-local differential privacy constraint. Let omega TV denote the modulus of continuity of the functional theta over P with respect to total variation distance. For a large class of loss functions l and a fixed privacy level alpha, we prove that the privatized minimax risk is equiv...
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作者：Dobriban, Edgar
作者单位：University of Pennsylvania
摘要：Researchers often have datasets measuring features xij of samples, such as test scores of students. In factor analysis and PCA, these features are thought to be influenced by unobserved factors, such as skills. Can we determine how many components affect the data? This is an important problem, because decisions made here have a large impact on all downstream data analysis. Consequently, many approaches have been developed. Parallel Analysis is a popular permutation method: it randomly scramble...
