相关论文: A Dimension-Independent discriminant between distr…

This paper is focused on dimension-free PAC-Bayesian bounds, under weak polynomial moment assumptions, allowing for heavy tailed sample distributions. It covers the estimation of the mean of a vector or a matrix, with applications to least…

For high-dimensional inference problems, statisticians have a number of competing interests. On the one hand, procedures should provide accurate estimation, reliable structure learning, and valid uncertainty quantification. On the other…

When using complex Bayesian models to combine information, the checking for consistency of the information being combined is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models…

Standard maximum-likelihood estimators for binary-star and exoplanet eccentricities are biased high, in the sense that the estimated eccentricity tends to be larger than the true eccentricity. As with most non-trivial observables, a simple…

This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…

Heteroskedastic errors can lead to inaccurate statistical conclusions if they are not properly handled. We introduce a test for heteroskedasticity for the nonparametric regression model with multiple covariates. It is based on a suitable…

We consider the problem of estimating the division rate of a size-structured population in a nonparametric setting. The size of the system evolves according to a transport-fragmentation equation: each individual grows with a given transport…

Optimal transport and Wasserstein distances are flourishing in many scientific fields as a means for comparing and connecting random structures. Here we pioneer the use of an optimal transport distance between L\'{e}vy measures to solve a…

Consider a nonparametric regression model with one-sided errors and regression function in a general H\"older class. We estimate the regression function via minimization of the local integral of a polynomial approximation. We show uniform…

This paper explores hypothesis testing for the parametric forms of the mean and variance functions in regression models under diverging-dimension settings. To mitigate the curse of dimensionality, we introduce weighted residual empirical…

Deep neural networks often fail when deployed in real-world contexts due to distribution shift, a critical barrier to building safe and reliable systems. An emerging approach to address this problem relies on \emph{disagreement discrepancy}…

It has long been thought that high-dimensional data encountered in many practical machine learning tasks have low-dimensional structure, i.e., the manifold hypothesis holds. A natural question, thus, is to estimate the intrinsic dimension…

The study emphasizes the challenge of finding the optimal trade-off between bias and variance, especially as hyperparameter optimization increases in complexity. Through empirical analysis, three hyperparameter tuning algorithms…

Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…

The regression function is one of the key objects of binary classification, since it not only determines a Bayes optimal classifier, hence, defines an optimal decision boundary, but also encodes the conditional distribution of the output…

We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…

We introduce a novel and scalable Bayesian framework for multivariate-density-density regression (DDR), designed to model relationships between multivariate distributions. Our approach addresses the critical issue of distributions residing…

This paper presents a novel online learning method that aims at finding a separator hyperplane between data points labelled as either positive or negative. Since weights and biases of artificial neurons can directly be related to…

Given two distinct datasets, an important question is if they have arisen from the the same data generating function or alternatively how their data generating functions diverge from one another. In this paper, we introduce an approach for…

Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…