Related papers: Nonlinear Function Estimation with Empirical Bayes…
Vector approximate message passing (VAMP) is a computationally simple approach to the recovery of a signal $\mathbf{x}$ from noisy linear measurements $\mathbf{y}=\mathbf{Ax}+\mathbf{w}$. Like the AMP proposed by Donoho, Maleki, and…
In this paper, we propose a new test for the detection of a change in a non-linear (auto-)regressive time series as well as a corresponding estimator for the unknown time point of the change. To this end, we consider an at-most-one-change…
We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
Complex network reconstruction is a hot topic in many fields. Currently, the most popular data-driven reconstruction framework is based on lasso. However, it is found that, in the presence of noise, lasso loses efficiency for weighted…
A non linear regression approach which consists of a specific regression model incorporating a latent process, allowing various polynomial regression models to be activated preferentially and smoothly, is introduced in this paper. The model…
In Bayesian inverse problems, it is common to consider several hyperparameters that define the prior and the noise model that must be estimated from the data. In particular, we are interested in linear inverse problems with additive…
The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors.…
A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy and reduced model…
This paper investigates the nonparametric estimation of a circular regression function in an errors-in-variables framework. Two settings are studied, depending on whether the covariates are circular or linear. Adaptive estimators are…
Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and…
For the nonparametric regression models with covariates contaminated with normal measurement errors, this paper proposes an extrapolation algorithm to estimate the nonparametric regression functions. By applying the conditional expectation…
There is a fundamental limitation in the prediction performance that a machine learning model can achieve due to the inevitable uncertainty of the prediction target. In classification problems, this can be characterized by the Bayes error,…
The ability to obtain reliable point estimates of model parameters is of crucial importance in many fields of physics. This is often a difficult task given that the observed data can have a very high number of dimensions. In order to…
The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation…
This paper investigates nonlinear panel regression models with interactive fixed effects and introduces a general framework for parameter estimation under potentially non-convex objective functions. We propose a computationally feasible…
We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this…
This work explores multi-modal inference in a high-dimensional simplified model, analytically quantifying the performance gain of multi-modal inference over that of analyzing modalities in isolation. We present the Bayes-optimal performance…
Previous results pertaining to algebraic state and parameter estimation of linear systems based on a special construction of a forward-backward kernel representation of linear differential invariants are extended to handle large noise in…
Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…