Related papers: Regularized Maximum Likelihood Estimation for the …
Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP…
Estimating the ratio of two probability densities from finitely many observations of the densities is a central problem in machine learning and statistics with applications in two-sample testing, divergence estimation, generative modeling,…
Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…
In many supervised learning applications, the response consists of both continuous and binary outcomes. Studies have shown that jointly modeling such mixed-type responses can substantially improve predictive performance compared to separate…
Computational image reconstruction algorithms generally produce a single image without any measure of uncertainty or confidence. Regularized Maximum Likelihood (RML) and feed-forward deep learning approaches for inverse problems typically…
We study the non-parametric estimation of a multidimensional unknown density f in a tomography problem based on independent and identically distributed observations, whose common density is proportional to the Radon transform of f. We…
Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional…
We propose a new approach to non-parametric density estimation that is based on regularizing a Sobolev norm of the density. This method is statistically consistent, and makes the inductive bias of the model clear and interpretable. While…
Random feature approximation is arguably one of the most widely used techniques for kernel methods in large-scale learning algorithms. In this work, we analyze the generalization properties of random feature methods, extending previous…
Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
Datasets often have their intrinsic symmetries, and particular deep-learning models called equivariant or invariant models have been developed to exploit these symmetries. However, if some or all of these symmetries are only approximate,…
In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…
We investigate different methods for regularizing quantile regression when predicting either a subset of quantiles or the full inverse CDF. We show that minimizing an expected pinball loss over a continuous distribution of quantiles is a…
In this paper we introduce a method for nonparametric density estimation on geometric networks. We define fused density estimators as solutions to a total variation regularized maximum-likelihood density estimation problem. We provide…
Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a "forward problem" in which the unknown density is mapped to…
In the context of regressing a response $Y$ on a predictor $X$, we consider estimating the local modes of the distribution of $Y$ given $X=x$ when $X$ is prone to measurement error. We propose two nonparametric estimation methods, with one…
Sample reweighting is one of the most widely used methods for correcting the error of least squares learning algorithms in reproducing kernel Hilbert spaces (RKHS), that is caused by future data distributions that are different from the…
Quantile regression is often used when a comprehensive relationship between a response variable and one or more explanatory variables is desired. The traditional frequentists' approach to quantile regression has been well developed around…
Here we present new joint reconstruction and regularization techniques inspired by ideas in microlocal analysis and lambda tomography, for the simultaneous reconstruction of the attenuation coefficient and electron density from X-ray…