相关论文: Supporting GENP with Random Multipliers

We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…

Conditional density estimation is complicated by multimodality, heteroscedasticity, and strong non-Gaussianity. Gaussian processes (GPs) provide a principled nonparametric framework with calibrated uncertainty, but standard GP regression is…

Sampling from the full posterior distribution of high-dimensional non-linear, non-Gaussian latent dynamical models presents significant computational challenges. While Particle Gibbs (also known as conditional sequential Monte Carlo) is…

Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…

The Gaussian process (GP) regression can be severely biased when the data are contaminated by outliers. This paper presents a new robust GP regression algorithm that iteratively trims the most extreme data points. While the new algorithm…

This paper introduces a new global optimization algorithm for solving the generalized linear multiplicative problem (GLMP). The algorithm starts by introducing $\bar{p}$ new variables and applying a logarithmic transformation to convert the…

We consider three Bayesian penalized regression models and show that the respective deterministic scan Gibbs samplers are geometrically ergodic regardless of the dimension of the regression problem. We prove geometric ergodicity of the…

Exact calculation and even multiplicative error estimation of matrix permanent are challenging for both classical and quantum computers. Regarding the permanents of random Gaussian matrices, the additive error estimation is closely linked…

We generalize a recent result of Haagerup; namely we show that a convolution with a standard Gaussian random matrix regularizes behaviour of Kadison--Fuglede determinant and Brown spectral distribution measure. In this way it is possible to…

We give both sufficient conditions and necessary conditions for the stochastic stability of non-uniformly expanding maps either with or without critical sets. We also show that the number of probability measures describing the statistical…

We consider a composite convex minimization problem associated with regularized empirical risk minimization, which often arises in machine learning. We propose two new stochastic gradient methods that are based on stochastic dual averaging…

We present a modified Gibbs sampler for general state spaces. We establish that this modification can lead to substantial gains in statistical efficiency while maintaining the overall quality of convergence. We illustrate our results in two…

Gaussian processes are a key component of many flexible statistical and machine learning models. However, they exhibit cubic computational complexity and high memory constraints due to the need of inverting and storing a full covariance…

A few recent works explored incorporating geometric priors to regularize the optimization of Gaussian splatting, further improving its performance. However, those early studies mainly focused on the use of low-order geometric priors (e.g.,…

We begin with isotropic Gaussian random fields, and show how the Bochner-Godement theorem gives a natural way to describe their covariance structure. We continue with a study of Mat\'ern processes on Euclidean space, spheres, manifolds and…

We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a non-asymptotic point of view. In particular, we define estimators with a…

We introduce a strategy to tackle some known obstructions of current approaches to the Fourier uniformity conjecture. Assuming GRH, we then show the conjecture holds for intervals of length at least $(\log X)^{\psi(X)}$, with $\psi(X)…

In this paper, a procedure is given for estimating the population mean in simple random sampling without replacement in the presence of auxiliary information. The mean squared error expressions of the proposed estimators have been derived…

Stein's unbiased risk estimate (SURE) gives an unbiased estimate of the $\ell_2$ risk of any estimator of the mean of a Gaussian random vector. We focus here on the case when the estimator minimizes a quadratic loss term plus a convex…

We study classically the problem of two relativistic particles with an invariant Duffing-like potential which reduces to the usual Duffing form in the nonrelativistic limit. We use a special relativistic generalization (RGEM) of the…