Related papers: Nonlinear Function Estimation with Empirical Bayes…
We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…
We focus on nonlinear Function-on-Scalar regression, where the predictors are scalar variables, and the responses are functional data. Most existing studies approximate the hidden nonlinear relationships using linear combinations of basis…
Approximate Message Passing (AMP) algorithms are a class of iterative procedures for computationally-efficient estimation in high-dimensional inference and estimation tasks. Due to the presence of an 'Onsager' correction term in its…
Due to its strong interpretability, linear regression is widely used in social science, from which significance test provides the significance level of models or coefficients in the traditional statistical inference. However, linear…
The sparse Beyesian learning (also referred to as Bayesian compressed sensing) algorithm is one of the most popular approaches for sparse signal recovery, and has demonstrated superior performance in a series of experiments. Nevertheless,…
We propose an efficient family of algorithms to learn the parameters of a Bayesian network from incomplete data. In contrast to textbook approaches such as EM and the gradient method, our approach is non-iterative, yields closed form…
This paper proposes a new Bayesian machine learning model that can be applied to large datasets arising in macroeconomics. Our framework sums over many simple two-component location mixtures. The transition between components is determined…
Vector approximate message passing (VAMP) is an efficient approximate inference algorithm used for generalized linear models. Although VAMP exhibits excellent performance, particularly when measurement matrices are sampled from rotationally…
The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of…
The a posteriori error estimator using the least-squares functional can be used for adaptive mesh refinement and error control even if the numerical approximations are not obtained from the corresponding least-squares method. This suggests…
We propose to address the common problem of linear estimation in linear statistical models by using a model selection approach via penalization. Depending then on the framework in which the linear statistical model is considered namely the…
In computational practice, most attention is paid to rational approximations of functions and approximations by the sum of exponents. We consider a wide enough class of nonlinear approximations characterized by a set of two required…
While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
In nonparametric regression analysis, errors are possibly correlated in practice, and neglecting error correlation can undermine most bandwidth selection methods. When no prior knowledge or parametric form of the correlation structure is…
Approximate message passing (AMP) is a low-cost iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions. However, AMP only applies to independent identically distributed (IID)…
Across scientific domains, a fundamental challenge is to characterize and compute the mappings from underlying physical processes to observed signals and measurements. While nonlinear neural networks have achieved considerable success, they…
We consider the problem of estimating the expected value of information (the knowledge gradient) for Bayesian learning problems where the belief model is nonlinear in the parameters. Our goal is to maximize some metric, while simultaneously…
We propose a kernel mixture of polynomials prior for Bayesian nonparametric regression. The regression function is modeled by local averages of polynomials with kernel mixture weights. We obtain the minimax-optimal rate of contraction of…
In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of…