相关论文: MVG-CRPS: A Robust Loss Function for Multivariate …

Probabilistic forecasts in the form of probability distributions over future events have become popular in several fields of statistical science. The dissimilarity between a probability forecast and an outcome is measured by a loss function…

Predictions of the uncertainty associated with extreme events are a vital component of any prediction system for such events. Consequently, the prediction system ought to be probabilistic in nature, with the predictions taking the form of…

Normal mean-variance mixture distributions are widely applied to simplify a model's implementation and improve their computational efficiency under the Maximum Likelihood (ML) approach. Especially for distributions with normal mean-variance…

Averages of proper scoring rules are often used to rank probabilistic forecasts. In many cases, the individual terms in these averages are based on observations and forecasts from different distributions. We show that some of the most…

Probabilistic regression models trained with maximum likelihood estimation (MLE), can sometimes overestimate variance to an unacceptable degree. This is mostly problematic in the multivariate domain. While univariate models often optimize…

Gaussian process model for vector-valued function has been shown to be useful for multi-output prediction. The existing method for this model is to re-formulate the matrix-variate Gaussian distribution as a multivariate normal distribution.…

Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by…

Forecasts of multivariate probability distributions are required for a variety of applications. Scoring rules enable the evaluation of forecast accuracy, and comparison between forecasting methods. We propose a theoretical framework for…

Multivariate conformal prediction requires nonconformity scores that compress residual vectors into scalars while preserving certain implicit geometric structure of the residual distribution. We introduce a Multivariate Kernel Score (MKS)…

We assess the impact of a multi-scale loss formulation for training probabilistic machine-learned weather forecasting models. The multi-scale loss is tested in AIFS-CRPS, a machine-learned weather forecasting model developed at the European…

Despite the success of Gaussian process based Model Predictive Control (MPC) in robotic control, its applicability scope is greatly hindered by multimodal disturbances that are prevalent in real-world settings. Here we propose a novel…

In Bayesian inference, predictive distributions are typically in the form of samples generated via Markov chain Monte Carlo (MCMC) or related algorithms. In this paper, we conduct a systematic analysis of how to make and evaluate…

The multivariate generalized Gaussian distribution (MGGD), also known as the multivariate exponential power (MEP) distribution, is widely used in signal and image processing. However, estimating MGGD parameters, which is required in…

A generalization of the classic Gaussian random variable to the family of Multi- Gaussian (MG) random variables characterized by shape parameter M > 0, in addition to the mean and the standard deviation, is introduced. The probability…

Distributional regression aims at estimating the conditional distribution of a targetvariable given explanatory co-variates. It is a crucial tool for forecasting whena precise uncertainty quantification is required. A popular methodology…

The paper presents numerical experiments and some theoretical developments in prediction with expert advice (PEA). One experiment deals with predicting electricity consumption depending on temperature and uses real data. As the pattern of…

Verifying probabilistic forecasts for extreme events is a highly active research area because popular media and public opinions are naturally focused on extreme events, and biased conclusions are readily made. In this context, classical…

Multivariate time series (MTS) forecasting is an essential problem in many fields. Accurate forecasting results can effectively help decision-making. To date, many MTS forecasting methods have been proposed and widely applied. However,…

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…

Over the last three decades, ensemble forecasts have become an integral part of forecasting the weather. They provide users with more complete information than single forecasts as they permit to estimate the probability of weather events by…