-
作者：Ingster, Yuri I.; Sapatinas, Theofanis; Suslina, Irina A.
作者单位：Saint Petersburg State Electrotechnical University; University of Cyprus; ITMO University
摘要：Ill-posed inverse problems arise in various scientific fields. We consider the signal detection problem for mildly, severely and extremely ill-posed inverse problems with l(q)-ellipsoids (bodies), q is an element of (0, 2], for Sobolev, analytic and generalized analytic classes of functions under the Gaussian white noise model. We study both rate and sharp asymptotics for the error probabilities in the minimax setup. By construction, the derived tests are, often, nonadaptive. Minimax rate-opti...
-
作者：Loh, Po-Ling; Wainwright, Martin J.
作者单位：University of California System; University of California Berkeley
摘要：Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these issues in the context of high-dimensional sparse linear regression, and propose novel estimators for the cases of noisy, missing and/or dependent data. Many standard approaches to noisy or missing data, such as those using the EM algorithm, lead to optimization p...
-
作者：Zhang, Ting; Wu, Wei Biao
作者单位：University of Iowa; University of Chicago
摘要：We consider parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models. Our asymptotic theory has the useful feature that it can allow dependent, nonstationary error and covariate processes. With a two-stage method, the parametric component can be estimated with a n(1/2)-convergence rate. A simulation-assisted hypothesis testing procedure is proposed for testing significance and parameter constancy. We further propose an information criterion ...
-
作者：Agarwal, Alekh; Negahban, Sahand; Wainwright, Martin J.
作者单位：University of California System; University of California Berkeley; Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley
摘要：We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation (sic) of the sum of an (approximately) low rank matrix Theta(star) with a second matrix Gamma(star) endowed with a complementary form of low-dimensional structure; this set-up includes many statistical models of interest, including factor analysis, multi-task regression and robust covariance estimation. We der...
-
作者：Parry, Matthew; Dawid, A. Philip; Lauritzen, Steffen
作者单位：University of Otago; University of Cambridge; University of Oxford
摘要：We investigate proper scoring rules for continuous distributions on the real line. It is known that the log score is the only such rule that depends on the quoted density only through its value at the outcome that materializes. Here we allow further dependence on a finite number in of derivatives of the density at the outcome, and describe a large class of such m-local proper scoring rules: these exist for all even m but no odd m. We further show that for m >= 2 all such m-local rules can be c...
-
作者：Douc, Randal; Moulines, Eric
作者单位：IMT - Institut Mines-Telecom; IMT Atlantique; Institut Polytechnique de Paris; Telecom SudParis; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; IMT Atlantique
摘要：Let (Y-k)(k is an element of Z) be a stationary sequence on a probability space (Omega, A, P) taking values in a standard Borel space Y. Consider the associated maximum likelihood estimator with respect to a parametrized family of hidden Markov models such that the law of the observations (Y-k)(k is an element of Z) is not assumed to be described by any of the hidden Markov models of this family. In this paper we investigate the consistency of this estimator in such misspecified models under m...
-
作者：Wainwright, Martin J.
作者单位：University of California System; University of California Berkeley
-
作者：Delaigle, Aurore; Hall, Peter
作者单位：University of Melbourne
摘要：We introduce new nonparametric predictors for homogeneous pooled data in the context of group testing for rare abnormalities and show that they achieve optimal rates of convergence. In particular, when the level of pooling is moderate, then despite the cost savings, the method enjoys the same convergence rate as in the case of no pooling. In the setting of over-pooling the convergence rate differs from that of an optimal estimator by no more than a logarithmic factor. Our approach improves on ...
-
作者：Juditsky, Anatoli; Karzan, Fatma Kilinc; Nemirovski, Arkadi; Polyak, Boris
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Carnegie Mellon University; University System of Georgia; Georgia Institute of Technology; V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences; Russian Academy of Sciences
摘要：We introduce a general framework to handle structured models (sparse and block-sparse with possibly overlapping blocks). We discuss new methods for their recovery from incomplete observation, corrupted with deterministic and stochastic noise, using block-l(1) regularization. While the current theory provides promising bounds for the recovery errors under a number of different, yet mostly hard to verify conditions, our emphasis is on verifiable conditions on the problem parameters (sensing matr...
-
作者：Samworth, Richard J.; Yuan, Ming
作者单位：University of Cambridge; University System of Georgia; Georgia Institute of Technology
摘要：Independent Component Analysis (ICA) models are very popular semi-parametric models in which we observe independent copies of a random vector X = AS, where A is a non-singular matrix and S has independent components. We propose a new way of estimating the unmixing matrix W = A(-1) and the marginal distributions of the components of S using nonparametric maximum likelihood. Specifically, we study the projection of the empirical distribution onto the subset of ICA distributions having log-concav...
