Related papers: Nonnegative approximations of nonnegative tensors

We study the problem of finding orthogonal low-rank approximations of symmetric tensors. In the case of matrices, the approximation is a truncated singular value decomposition which is then symmetric. Moreover, for rank-one approximations…

We study the posterior contraction rates of a Bayesian method with Gaussian process priors in nonparametric regression and its plug-in property for differential operators. For a general class of kernels, we establish convergence rates of…

An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate…

There is no easy extension of Kaplan-Meier and Nelson-Aalen estimators to the bivariate case, and estimating bivariate survival distributions nonparametrically is associated with various non-trivial problems. The Dabrowska estimator will…

We show that in finite-dimensional nonlinear approximations, the best $r$-term approximant of a function $f$ almost always exists over $\mathbb{C}$ but that the same is not true over $\mathbb{R}$, i.e., the infimum $\inf_{f_1,\dots,f_r \in…

Bernstein-von Mises theorems for nonparametric Bayes priors in the Gaussian white noise model are proved. It is demonstrated how such results justify Bayes methods as efficient frequentist inference procedures in a variety of concrete…

Statistical methods relating tensor predictors to scalar outcomes in a regression model generally vectorize the tensor predictor and estimate the coefficients of its entries employing some form of regularization, use summaries of the tensor…

In this paper, the Neyman-Pearson lemma for general sublinear expectations is studied. We weaken the assumptions for sublinear expectations in [1] and give a completely new method to study this problem. Applying Mazur-Orlicz Theorem and the…

Approximate Bayesian computation (ABC) is commonly used for parameter estimation and model comparison for intractable simulator-based models whose likelihood function cannot be evaluated. In this paper we instead investigate the feasibility…

A new form of the Cunningham correction factor is presented that requires no experimental fitting. It is expanded to provide a predictive heuristic for non-spherical particles, via definition of a "correction tensor''. Its accuracy is…

We consider the inverse problem of estimating an unknown function $u$ from noisy measurements $y$ of a known, possibly nonlinear, map $\mathcal{G}$ applied to $u$. We adopt a Bayesian approach to the problem and work in a setting where the…

Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…

Aggregating estimators using exponential weights depending on their risk appears optimal in expectation but not in probability. We use here a slight overpenalization to obtain oracle inequality in probability for such an explicit…

Unlike matrix completion, tensor completion does not have an algorithm that is known to achieve the information-theoretic sample complexity rate. This paper develops a new algorithm for the special case of completion for nonnegative…

We explore the problem of deriving a posteriori probabilities of being defective for the members of a population in the non-adaptive group testing framework. Both noiseless and noisy testing models are addressed. The technique, which relies…

A symmetric tensor, which has a symmetric nonnegative decomposition, is called a completely positive tensor. We consider the completely positive tensor decomposition problem. A semidefinite algorithm is presented for checking whether a…

In this paper, we consider a functional linear regression model, where both the covariate and the response variable are functional random variables. We address the problem of optimal nonparametric estimation of the conditional expectation…

A novel approximate Bayesian filter based on backward stochastic differential equations is introduced. It uses a nonlinear Feynman--Kac representation of the filtering problem and the approximation of an unnormalized filtering density using…

We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown function.…

Fitting a Candecomp/Parafac (CP) decomposition (also known as Canonical Polyadic decomposition) to a multi-way array or higher-order tensor, is equivalent to finding a best low-rank approximation to the multi-way array or higher-order…