Related papers: Nonlinear Function Estimation with Empirical Bayes…
In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…
Bayesian estimation approaches, which are capable of combining the information of experimental data from different likelihood functions to achieve high precisions, have been widely used in phase estimation via introducing a controllable…
This paper considers probabilistic estimation of a low-rank matrix from non-linear element-wise measurements of its elements. We derive the corresponding approximate message passing (AMP) algorithm and its state evolution. Relying on…
We consider the problem of reconstructing the signal and the hidden variables from observations coming from a multi-layer network with rotationally invariant weight matrices. The multi-layer structure models inference from deep generative…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
Nonlinear regression problem is one of the most popular and important statistical tasks. The first methods like least squares estimation go back to Gauss and Legendre. Recent models and developments in statistics and machine learning like…
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…
Function approximation from input and output data pairs constitutes a fundamental problem in supervised learning. Deep neural networks are currently the most popular method for learning to mimic the input-output relationship of a general…
In a recent article (Proc. Natl. Acad. Sci., 110(36), 14557-14562), El Karoui et al. study the distribution of robust regression estimators in the regime in which the number of parameters p is of the same order as the number of samples n.…
The goal of a recommendation system is to predict the interest of a user in a given item by exploiting the existing set of ratings as well as certain user/item features. A standard approach to modeling this problem is Inductive Matrix…
This paper proposes a Vector Autoregression augmented with nonlinear factors that are modeled nonparametrically using regression trees. There are four main advantages of our model. First, modeling potential nonlinearities nonparametrically…
Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian…
We consider the problem of predicting a real random variable from a functional explanatory variable. The problem is attacked by mean of nonparametric kernel approach which has been recently adapted to this functional context. We derive…
Recently, several promising approximate message passing (AMP) based algorithms have been developed for bilinear recovery with model $\boldsymbol{Y}=\sum_{k=1}^K b_k \boldsymbol{A}_k \boldsymbol{C} +\boldsymbol{W} $, where $\{b_k\}$ and…
The great advances of learning-based approaches in image processing and computer vision are largely based on deeply nested networks that compose linear transfer functions with suitable non-linearities. Interestingly, the most frequently…
This letter proposes a novel message-passing algorithm for signal recovery in compressed sensing. The proposed algorithm solves the disadvantages of approximate message-passing (AMP) and orthogonal/vector AMP, and realizes their advantages.…
We consider the problem of recovering linear image of unknown signal belonging to a given convex compact signal set from noisy observation of another linear image of the signal. We develop a simple generic efficiently computable nonlinear…
This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood…
Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…