6B期

最新文章

• APPROXIMATE l0-PENALIZED ESTIMATION OF PIECEWISE-CONSTANT SIGNALS ON GRAPHS AI翻译
  作者：Fan, Zhou; Guan, Leying
  作者单位：Stanford University
  摘要：We study recovery of piecewise-constant signals on graphs by the estimator minimizing an l(0)-edge-penalized objective. Although exact minimization of this objective may be computationally intractable, we show that the same statistical risk guarantees are achieved by the alpha-expansion algorithm which computes an approximate minimizer in polynomial time. We establish that for graphs with small average vertex degree, these guarantees are minimax rate-optimal over classes of edge-sparse signals...
• NONPARAMETRIC COVARIATE-ADJUSTED RESPONSE-ADAPTIVE DESIGN BASED ON A FUNCTIONAL URN MODEL AI翻译
  作者：Aletti, Giacomo; Ghiglietti, Andrea; Rosenberger, William F.
  作者单位：University of Milan; Catholic University of the Sacred Heart; George Mason University
  摘要：In this paper, we propose a general class of covariate-adjusted response adaptive (CARA) designs based on a new functional urn model. We prove strong consistency concerning the functional urn proportion and the proportion of subjects assigned to the treatment groups, in the whole study and for each covariate profile, allowing the distribution of the responses conditioned on covariates to be estimated nonparametrically. In addition, we establish joint central limit theorems for the above quanti...
• ROBUST LOW-RANK MATRIX ESTIMATION AI翻译
  作者：Elsener, Andreas; van de Geer, Sara
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：Many results have been proved for various nuclear norm penalized estimators of the uniform sampling matrix completion problem. However, most of these estimators are not robust: in most of the cases the quadratic loss function and its modifications are used. We consider robust nuclear norm penalized estimators using two well-known robust loss functions: the absolute value loss and the Huber loss. Under several conditions on the sparsity of the problem (i.e., the rank of the parameter matrix) an...
• ADAPTIVE INVARIANT DENSITY ESTIMATION FOR ERGODIC DIFFUSIONS OVER ANISOTROPIC CLASSES AI翻译
  作者：Strauch, Claudia
  作者单位：University of Mannheim
  摘要：Consider some multivariate diffusion process X = (X-t)(t >= 0) with unique invariant probability measure and associated invariant density rho, and assume that a continuous record of observations X-T = (X-t)(0 <= t <= T) of X is available. Recent results on functional inequalities for symmetric Markov semi groups are used in the statistical analysis of kernel estimators (rho) over cap (T) = (rho) over cap (T) (X-T) of rho. For the basic problem of estimation with respect to sup-norm risk under ...
• RESTRICTED STRONG CONVEXITY IMPLIES WEAK SUBMODULARITY AI翻译
  作者：Elenberg, Ethan R.; Khanna, Rajiv; Dimakis, Alexandros G.; Negahban, Sahand
  作者单位：University of Texas System; University of Texas Austin; Yale University
  摘要：We connect high-dimensional subset selection and submodular maximization. Our results extend the work of Das and Kempe [In ICML (2011) 1057-1064] from the setting of linear regression to arbitrary objective functions. For greedy feature selection, this connection allows us to obtain strong multiplicative performance bounds on several methods without statistical modeling assumptions. We also derive recovery guarantees of this form under standard assumptions. Our work shows that greedy algorithm...
• A NEW SCOPE OF PENALIZED EMPIRICAL LIKELIHOOD WITH HIGH-DIMENSIONAL ESTIMATING EQUATIONS AI翻译
  作者：Chang, Jinyuan; Tang, Cheng Yong; Wu, Tong Tong
  作者单位：Southwestern University of Finance & Economics - China; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University; University of Rochester
  摘要：Statistical methods with empirical likelihood (EL) are appealing and effective especially in conjunction with estimating equations for flexibly and adaptively incorporating data information. It is known that EL approaches encounter difficulties when dealing with high-dimensional problems. To overcome the challenges, we begin our study with investigating high-dimensional EL from a new scope targeting at high-dimensional sparse model parameters. We show that the new scope provides an opportunity...
• PRINCIPAL COMPONENT ANALYSIS FOR FUNCTIONAL DATA ON RIEMANNIAN MANIFOLDS AND SPHERES AI翻译
  作者：Dai, Xiongtao; Mueller, Hans-Georg
  作者单位：University of California System; University of California Davis
  摘要：Functional data analysis on nonlinear manifolds has drawn recent interest. Sphere-valued functional data, which are encountered, for example, as movement trajectories on the surface of the earth are an important special case. We consider an intrinsic principal component analysis for smooth Riemannian manifold-valued functional data and study its asymptotic properties. Riemannian functional principal component analysis (RFPCA) is carried out by first mapping the manifold-valued data through Rie...
• RHO-ESTIMATORS REVISITED: GENERAL THEORY AND APPLICATIONS AI翻译
  作者：Baraud, Yannick; Birge, Lucien
  作者单位：Universite Cote d'Azur; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS)
  摘要：Following Baraud, Birge and Sart [Invent. Math. 207 (2017) 425-517], we pursue our attempt to design a robust universal estimator of the joint distribution of n independent (but not necessarily i.i.d.) observations for an Hellinger-type loss. Given such observations with an unknown joint distribution P and a dominated model Q for P, we build an estimator P based on Q (a rho-estimator) and measure its risk by an Hellinger-type distance. When P does belong to the model, this risk is bounded by s...
• MULTICLASS CLASSIFICATION, INFORMATION, DIVERGENCE AND SURROGATE RISK AI翻译
  作者：Duchi, John; Khosravi, Khashayar; Ruan, Feng
  作者单位：Stanford University
  摘要：We provide a unifying view of statistical information measures, multiway Bayesian hypothesis testing, loss functions for multiclass classification problems and multidistribution f-divergences, elaborating equivalence results between all of these objects, and extending existing results for binary outcome spaces to more general ones. We consider a generalization of f-divergences to multiple distributions, and we provide a constructive equivalence between divergences, statistical information (in ...
• THINK GLOBALLY, FIT LOCALLY UNDER THE MANIFOLD SETUP: ASYMPTOTIC ANALYSIS OF LOCALLY LINEAR EMBEDDING AI翻译
  作者：Wu, Hau-Tieng; Wu, Nan
  作者单位：Duke University; Duke University; University of Toronto
  摘要：Since its introduction in 2000, Locally Linear Embedding (LLE) has been widely applied in data science. We provide an asymptotical analysis of LLE under the manifold setup. We show that for a general manifold, asymptotically we may not obtain the Laplace-Beltrami operator, and the result may depend on nonuniform sampling unless a correct regularization is chosen. We also derive the corresponding kernel function, which indicates that LLE is not a Markov process. A comparison with other commonly...