Related papers: Bona fide Riesz projections for density estimation

Let $\Omega \subset \mathbb{R}^n$ be a convex polytope ($n \leq 3$). The Ritz projection is the best approximation, in the $W^{1,2}_0$-norm, to a given function in a finite element space. When such finite element spaces are constructed on…

We present a Riesz integral representation theory in which functions, operators and measures take values in uniform commutative monoids (a commutative monoid with a uniformity making the binary operation of the monoid uniformly continuous).…

The ratio between two probability density functions is an important component of various tasks, including selection bias correction, novelty detection and classification. Recently, several estimators of this ratio have been proposed. Most…

Answering causal questions often involves estimating linear functionals of conditional expectations, such as the average treatment effect or the effect of a longitudinal modified treatment policy. By the Riesz representation theorem, these…

We propose a novel method to accurately reconstruct a set of images representing a single scene from few linear multi-view measurements. Each observed image is modeled as the sum of a background image and a foreground one. The background…

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…

Solutions to inverse problems that are ill-conditioned or ill-posed may have significant intrinsic uncertainty. Unfortunately, analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems. As a…

This paper develops a uniformly valid and asymptotically nonconservative test based on projection for a class of shape restrictions. The key insight we exploit is that these restrictions form convex cones, a simple and yet elegant structure…

The ratio of two probability density functions is a fundamental quantity that appears in many areas of statistics and machine learning, including causal inference, reinforcement learning, covariate shift, outlier detection, independence…

Quantized compressive sensing (QCS) deals with the problem of representing compressive signal measurements with finite precision representation, i.e., a mandatory process in any practical sensor design. To characterize the signal…

This paper is concerned with inference on the regression function of a high-dimensional linear model when outcomes are missing at random. We propose an estimator which combines a Lasso pilot estimate of the regression function with a bias…

To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…

While surface-based view synthesis algorithms are appealing due to their low computational requirements, they often struggle to reproduce thin structures. In contrast, more expensive methods that model the scene's geometry as a volumetric…

Let $(M, {g})$ be a compact, $d$-dimensional Riemannian manifold without boundary. Suppose further that $(M,g)$ is either two dimensional and has no conjugate points or $(M,g)$ has non-positive sectional curvature. The goal of this note is…

In this paper, we investigate the spectral projection of density matrices in quantum field theory. With appropriate regularization, the spectral projectors of density matrices are expected to be well-defined. These projectors can be…

Helmholtz stereopsis is one the versatile techniques for 3D geometry reconstruction from 2D images of objects with unknown and arbitrary reflectance surfaces. HS eliminates the need for surface reflectance, a challenging parameter to…

Random projection (RP) is a classical technique for reducing storage and computational costs. We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a…

Let $\mathcal{H}$ be a (separable) Hilbert space and $\{e_k\}_{k\geq 1}$ a fixed orthonormal basis of $\mathcal{H}$. Motivated by many papers on scaled projections, angles of subspaces and oblique projections, we define and study the notion…

Shape restrictions such as monotonicity on functions often arise naturally in statistical modeling. We consider a Bayesian approach to the problem of estimation of a monotone regression function and testing for monotonicity. We construct a…

Convex and penalized robust regression methods often suffer from a persistent bias induced by large outliers, limiting their effectiveness in adversarial or heavy-tailed settings. In this work, we study a smooth redescending non-convex…