Related papers: Point forecasting and forecast evaluation with gen…
This paper addresses the scalar regression problem through a novel solution to exactly optimize the Huber loss in a general semi-supervised setting, which combines multi-view learning and manifold regularization. We propose a principled…
Score matching enables the estimation of the gradient of a data distribution, a key component in denoising diffusion models used to recover clean data from corrupted inputs. In prior work, a heuristic weighting function has been used for…
This article introduces Huber means on Riemannian manifolds, providing a robust alternative to the Frechet mean by integrating elements of both square and absolute loss functions. The Huber means are designed to be highly resistant to…
A common goal in statistics and machine learning is estimation of unknowns. Point estimates alone are of little value without an accompanying measure of uncertainty, but traditional uncertainty quantification methods, such as confidence…
This paper presents a number of new findings about the canonical change point estimation problem. The first part studies the estimation of a change point on the real line in a simple stump model using the robust Huber estimating function…
We present a method for comparing point forecasts in a region of interest, such as the tails or centre of a variable's range. This method cannot be hedged, in contrast to conditionally selecting events to evaluate and then using a scoring…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
We propose a unified framework for fair regression tasks formulated as risk minimization problems subject to a demographic parity constraint. Unlike many existing approaches that are limited to specific loss functions or rely on challenging…
This paper designs a statistical quantification towards the intermittent power uncertainty in power systems. A negative-exponential forecast uncertainty function is constructed to represent the relationship between the statistics of…
We derive the joint asymptotic distribution of empirical quantiles and expected shortfalls under general conditions on the distribution of the underlying observations. In particular, we do not assume that the distribution function is…
The predictability of errors in deterministic temperature forecasts is investigated. More precisely, the aim is to issue warnings whenever the differences between forecast and verification exceed a given threshold. The warnings are…
What does it mean to say that, for example, the probability for rain tomorrow is between 20% and 30%? The theory for the evaluation of precise probabilistic forecasts is well-developed and is grounded in the key concepts of proper scoring…
We consider unregularized robust M-estimators for linear models under Gaussian design and heavy-tailed noise, in the proportional asymptotics regime where the sample size n and the number of features p are both increasing such that $p/n \to…
In this paper, we study robust covariance estimation under the approximate factor model with observed factors. We propose a novel framework to first estimate the initial joint covariance matrix of the observed data and the factors, and then…
New estimators for the mean and the covariance function for partially observed functional data are proposed using a detour via the fundamental theorem of calculus. The new estimators allow for a consistent estimation of the mean and…
In this paper, we examine the distribution and convergence properties of the estimation error $W = X - \hat{X}(Y)$, where $\hat{X}(Y)$ is the Bayesian estimator of a random variable $X$ from a noisy observation $Y = X +\sigma Z$ where…
To address model uncertainty under flexible loss functions in prediction problems, we propose a model averaging method that accommodates various loss functions, including asymmetric linear and quadratic loss functions, as well as many other…
To provide a comprehensive summary of the tail distribution, the expected shortfall is defined as the average over the tail above (or below) a certain quantile of the distribution. The expected shortfall regression captures the…
Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy…
This paper concerns the mathematical analyses of the diffusion model in machine learning. The drift term of the backward sampling process is represented as a conditional expectation involving the data distribution and the forward diffusion.…