-
作者：Syring, Nicholas; Martin, Ryan
作者单位：Washington University (WUSTL); North Carolina State University
摘要：Detection of an image boundary when the pixel intensities are measured with noise is an important problem in image segmentation. From a statistical point of view, a challenge is that likelihood-based methods require modeling the pixel intensities inside and outside the image boundary, even though these distributions are typically not of interest. Since misspecification of the pixel intensity distributions can negatively affect inference on the image boundary, it would be desirable to avoid thi...
-
作者：Barber, Rina Foygel; Candes, Emmanuel J.; Samworth, Richard J.
作者单位：University of Chicago; Stanford University; Stanford University; University of Cambridge
摘要：We consider the variable selection problem, which seeks to identify important variables influencing a response Y out of many candidate features X-1, ..., X-p. We wish to do so while offering finite-sample guarantees about the fraction of false positives-selected variables X-j that in fact have no effect on Y after the other features are known. When the number of features p is large (perhaps even larger than the sample size n), and we have no prior knowledge regarding the type of dependence bet...
-
作者：Liang, Tengyuan; Rakhlin, Alexander
作者单位：University of Chicago; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：In the absence of explicit regularization, Kernel Ridgeless Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirically, however, that such interpolated solutions can still generalize well on test data. We isolate a phenomenon of implicit regularization for minimum-norm interpolated solutions which is due to a combination of high dimensionality of the input data, curvature of the kernel function and favorable geometric properties of ...
-
作者：Reiss, Markus; Schmidt-Hieber, Johannes
作者单位：Humboldt University of Berlin; University of Twente
摘要：Given data from a Poisson point process with intensity (x, y) bar right arrow n1( f (x) <= y), frequentist properties for the Bayesian reconstruction of the support boundary function f are derived. We mainly study compound Poisson process priors with fixed intensity proving that the posterior contracts with nearly optimal rate for monotone support boundaries and adapts to Holder smooth boundaries. We then derive a limiting shape result for a compound Poisson process prior and a function space ...
-
作者：Mendelson, Shahar; Zhivotovskiy, Nikita
作者单位：Australian National University; HSE University (National Research University Higher School of Economics)
摘要：Let X be a centered random vector taking values in R-d and let Sigma = E (X circle times X) be its covariance matrix. We show that if X satisfies an L-4 - L-2 norm equivalence (sometimes referred to as the bounded kurtosis assumption), there is a covariance estimator (Sigma) over cap that exhibits almost the same performance one would expect had X been a Gaussian vector. The procedure also improves the current state-of-the-art regarding high probability bounds in the sub-Gaussian case (sharp r...
-
作者：Giordano, Francesco; Lahiri, Soumendra Nath; Parrella, Maria Lucia
作者单位：University of Salerno; North Carolina State University
摘要：We consider nonparametric regression in high dimensions where only a relatively small subset of a large number of variables are relevant and may have nonlinear effects on the response. We develop methods for variable selection, structure discovery and estimation of the true low-dimensional regression function, allowing any degree of interactions among the relevant variables that need not be specified a-priori. The proposed method, called the GRID, combines empirical likelihood based marginal t...
