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作者：Hoffmann, Marc; Rousseau, Judith; Schmidt-Hieber, Johannes
作者单位：Universite PSL; Universite Paris-Dauphine; Leiden University - Excl LUMC; Leiden University
摘要：We investigate the problem of deriving posterior concentration rates under different loss functions in nonparametric Bayes. We first provide a lower bound on posterior coverages of shrinking neighbourhoods that relates the metric or loss under which the shrinking neighbourhood is considered, and an intrinsic pre-metric linked to frequentist separation rates. In the Gaussian white noise model, we construct feasible priors based on a spike and slab procedure reminiscent of wavelet thresholding t...
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作者：Zheng, Qi; Peng, Limin; He, Xuming
作者单位：Emory University; University of Michigan System; University of Michigan
摘要：Quantile regression has become a valuable tool to analyze heterogeneous covaraite-response associations that are often encountered in practice. The development of quantile regression methodology for high-dimensional covariates primarily focuses on the examination of model sparsity at a single or multiple quantile levels, which are typically prespecified ad hoc by the users. The resulting models may be sensitive to the specific choices of the quantile levels, leading to difficulties in interpre...
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作者：Lei, Jing; Rinaldo, Alessandro
作者单位：Carnegie Mellon University
摘要：We analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden communities even when the order of the maximum expected degree is as small as log n, with n the number of nodes. This result applies to some popular polynomial time spectral clustering algorithms and is further extended to degree corrected stochastic block mo...
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作者：Chatterjee, Yasachi; Guntuboyina, Adityanand; Sen, Bodhisattva
作者单位：University of Chicago; University of California System; University of California Berkeley; Columbia University
摘要：We consider the problem of estimating an unknown theta is an element of R-n from noisy observations under the constraint that theta belongs to certain convex polyhedral cones in R-n. Under this setting, we prove bounds for the risk of the least squares estimator (LSE). The obtained risk bound behaves differently depending on the true sequence theta which highlights the adaptive behavior of theta. As special cases of our general result, we derive risk bounds for the LSE in univariate isotonic a...
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作者：Schiebinger, Geoffrey; Wainwright, Martin J.; Yu, Bin
作者单位：University of California System; University of California Berkeley
摘要：Clustering of data sets is a standard problem in many areas of science and engineering. The method of spectral clustering is based on embedding the data set using a kernel function, and using the top eigenvectors of the normalized Laplacian to recover the connected components. We study the performance of spectral clustering in recovering the latent labels of i.i.d. samples from a finite mixture of nonparametric distributions. The difficulty of this label recovery problem depends on the overlap...
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作者：Armstrong, Timothy
作者单位：Yale University
摘要：We consider the problem of inference on a regression function at a point when the entire function satisfies a sign or shape restriction under the null. We propose a test that achieves the optimal minimax rate adaptively over a range of Holder classes, up to a log log n term, which we show to be necessary for adaptation. We apply the results to adaptive one-sided tests for the regression discontinuity parameter under a monotonicity restriction, the value of a monotone regression function at the...
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作者：Li, Kang; Zheng, Wei; Ai, Mingyao
作者单位：Peking University; Peking University; Purdue University System; Purdue University; Purdue University in Indianapolis
摘要：The interference model has been widely used and studied in block experiments where the treatment for a particular plot has effects on its neighbor plots. In this paper, we study optimal circular designs for the proportional interference model, in which the neighbor effects of a treatment are proportional to its direct effect. Kiefer's equivalence theorems for estimating both the direct and total treatment effects are developed with respect to the criteria of A, D, E and T. Parallel studies are...
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作者：Lee, Young K.; Mammen, Enno; Nielsen, Jens P.; Park, Byeong U.
作者单位：Kangwon National University; Ruprecht Karls University Heidelberg; City St Georges, University of London; Seoul National University (SNU)
摘要：This paper generalizes recent proposals of density forecasting models and it develops theory for this class of models. In density forecasting, the density of observations is estimated in regions where the density is not observed. Identification of the density in such regions is guaranteed by structural assumptions on the density that allows exact extrapolation. In this paper, the structural assumption is made that the density is a product of one-dimensional functions. The theory is quite gener...
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作者：Chatterjee, Sourav
作者单位：Stanford University
摘要：Consider the problem of estimating the entries of a large matrix, when the observed entries are noisy versions of a small random fraction of the original entries. This problem has received widespread attention in recent times, especially after the pioneering works of Emmanuel Candes and collaborators. This paper introduces a simple estimation procedure, called Universal Singular Value Thresholding (USVT), that works for any matrix that has a little bit of structure. Surprisingly, this simple e...
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作者：Jin, Jiashun
作者单位：Carnegie Mellon University
摘要：Consider a network where the nodes split into K different communities. The community labels for the nodes are unknown and it is of major interest to estimate them (i.e., community detection). Degree Corrected Block Model (DCBM) is a popular network model. How to detect communities with the DCBM is an interesting problem, where the main challenge lies in the degree heterogeneity. We propose a new approach to community detection which we call the Spectral Clustering On Ratios-of-Eigenvectors (SC...
