Related papers: Quantifying Heteroskedasticity via Bhattacharyya D…

In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order…

Recent advances in molecular simulations allow the evaluation of previously unattainable observables, such as rate constants for protein folding. However, these calculations are usually computationally expensive and even significant…

Persistent homology, the study of holes that appear in data as one thickens balls centered around its points over time, has theoretically guaranteed stability. That is, small data perturbations guarantee small changes in the lifetimes of…

We introduce a new one-parameter family of divergence measures, called bounded Bhattacharyya distance (BBD) measures, for quantifying the dissimilarity between probability distributions. These measures are bounded, symmetric and positive…

In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the…

Einmahl, de Haan and Zhou (2016, Journal of the Royal Statistical Society: Series B, 78(1), 31-51) recently introduced a stochastic model that allows for heteroscedasticity of extremes. The model is extended to the situation where the…

Prediction with the possibility of abstention (or selective prediction) is an important problem for error-critical machine learning applications. While well-studied in the classification setup, selective approaches to regression are much…

Combining measurements which have "theoretical uncertainties" is a delicate matter, due to an unclear statistical basis. We present an algorithm based on the notion that a theoretical uncertainty represents an estimate of bias.

Pairwise Euclidean distance calculation is a fundamental step in many machine learning and data analysis algorithms. In real-world applications, however, these distances are frequently distorted by heteroskedastic noise$\unicode{x2014}$a…

Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time…

Heterogeneous datasets emerge in various machine learning and optimization applications that feature different input sources, types or formats. Most models or methods do not natively tackle heterogeneity. Hence, such datasets are often…

We consider inference in linear regression models that is robust to heteroskedasticity and the presence of many control variables. When the number of control variables increases at the same rate as the sample size the usual…

Tests based on heteroskedasticity robust standard errors are an important technique in econometric practice. Choosing the right critical value, however, is not simple at all: conventional critical values based on asymptotics often lead to…

Confidence estimation can improve the reliability of melody estimation by indicating which predictions are likely incorrect. The existing classification-based approach provides confidence for predicted pitch classes but fails to capture the…

Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way…

Modern data are increasingly both high-dimensional and heteroscedastic. This paper considers the challenge of estimating underlying principal components from high-dimensional data with noise that is heteroscedastic across samples, i.e.,…

A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…

This paper introduces a new framework to quantify distance between finite sets with uncertainty present, where probability distributions determine the locations of individual elements. Combining this with a Bayesian change point detection…

Missingness and measurement frequency are two sides of the same coin. How frequent should we measure clinical variables and conduct laboratory tests? It depends on many factors such as the stability of patient conditions, diagnostic…

This paper addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time…