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Dominant approaches for modelling Partial Differential Equations (PDEs) rely on deterministic predictions, yet many physical systems of interest are inherently chaotic and uncertain. While training probabilistic models from scratch is…

Machine Learning · Computer Science 2026-03-03 Cristiana Diaconu , Miles Cranmer , Richard E. Turner , Tanya Marwah , Payel Mukhopadhyay

The Distributional Random Forest (DRF) is a recently introduced Random Forest algorithm to estimate multivariate conditional distributions. Due to its general estimation procedure, it can be employed to estimate a wide range of targets such…

Statistics Theory · Mathematics 2023-12-20 Jeffrey Näf , Corinne Emmenegger , Peter Bühlmann , Nicolai Meinshausen

Conformal predictive systems are sets of predictive distributions with theoretical out-of-sample calibration guarantees. The calibration guarantees are typically that the set of predictions contains a forecast distribution whose prediction…

Methodology · Statistics 2025-11-03 Sam Allen , Enrico Pescara , Johanna Ziegel

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…

Machine Learning · Computer Science 2020-01-27 Vladimir V'yugin , Vladimir Trunov

Risk-sensitive reinforcement learning (RL) is crucial for maintaining reliable performance in high-stakes applications. While traditional RL methods aim to learn a point estimate of the random cumulative cost, distributional RL (DRL) seeks…

Machine Learning · Computer Science 2025-02-03 Minheng Xiao , Xian Yu , Lei Ying

Shapelet is a discriminative subsequence of time series. An advanced shapelet-based method is to embed shapelet into accurate and fast random forest. However, it shows several limitations. First, random shapelet forest requires a large…

Machine Learning · Computer Science 2019-04-23 Mohan Shi , Zhihai Wang , Jodong Yuan , Haiyang Liu

This paper considers the decision-dependent optimization problem, where the data distributions react in response to decisions affecting both the objective function and linear constraints. We propose a new method termed repeated projected…

Optimization and Control · Mathematics 2025-08-13 Zifan Wang , Changxin Liu , Thomas Parisini , Michael M. Zavlanos , Karl H. Johansson

The proliferation of intermittent distributed renewable energy sources (RES) in modern power systems has fundamentally compromised the reliability and accuracy of deterministic net load forecasting. Generative models, particularly diffusion…

Systems and Control · Electrical Eng. & Systems 2025-06-04 Yixiang Huang , Jianhua Pei , Luocheng Chen , Zhenchang Du , Jinfu Chen , Zirui Peng

Traditional neural network regression models provide only point estimates, failing to capture predictive uncertainty. Probabilistic neural networks (PNNs) address this limitation by producing output distributions, enabling the construction…

Machine Learning · Computer Science 2026-03-02 Farhad Pourkamali-Anaraki

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

Machine Learning · Computer Science 2025-10-07 Carlo Kneissl , Christopher Bülte , Philipp Scholl , Gitta Kutyniok

Models for human choice prediction in preference learning and psychophysics often consider only binary response data, requiring many samples to accurately learn preferences or perceptual detection thresholds. The response time (RT) to make…

Neurons and Cognition · Quantitative Biology 2023-06-13 Michael Shvartsman , Benjamin Letham , Stephen Keeley

To obtain a probabilistic model for a dependent variable based on some set of explanatory variables, a distributional approach is often adopted where the parameters of the distribution are linked to regressors. In many classical models this…

Methodology · Statistics 2020-01-14 Lisa Schlosser , Torsten Hothorn , Reto Stauffer , Achim Zeileis

Distributional Random Forest (DRF) is a flexible forest-based method to estimate the full conditional distribution of a multivariate output of interest given input variables. In this article, we introduce a variable importance algorithm for…

Machine Learning · Statistics 2024-02-15 Clément Bénard , Jeffrey Näf , Julie Josse

One of the key challenges that Reinforcement Learning (RL) faces is its limited capability to adapt to a change of data distribution caused by uncertainties. This challenge arises especially in RL systems using deep neural networks as…

Machine Learning · Computer Science 2025-06-17 Amornyos Horprasert , Esa Apriaskar , Xingyu Liu , Lanlan Su , Lyudmila S. Mihaylova

Performative prediction characterizes environments where predictive models alter the very data distributions they aim to forecast, triggering complex feedback loops. While prior research treats single-agent and multi-agent performativity as…

Machine Learning · Statistics 2026-02-04 Zhixian Zhang , Xiaotian Hou , Linjun Zhang

We propose a neural network approach to produce probabilistic weather forecasts from a deterministic numerical weather prediction. Our approach is applied to operational surface temperature outputs from the Global Deterministic Prediction…

Atmospheric and Oceanic Physics · Physics 2025-04-07 David Landry , Anastase Charantonis , Claire Monteleoni

Traditional regression and prediction tasks often only provide deterministic point estimates. To estimate the distribution or uncertainty of the response variable, traditional methods either assume that the posterior distribution of samples…

Machine Learning · Computer Science 2025-01-08 Daojun Liang , Haixia Zhang , Dongfeng Yuan

This paper investigates the joint optimization of condition-based maintenance and spare provisioning, incorporating insights obtained from sensor data. Prognostic models estimate components' remaining lifetime distributions (RLDs), which…

Optimization and Control · Mathematics 2025-07-14 Heraldo Rozas , Weijun Xie , Nagi Gebraeel , Stephen Robinson

Time series forecasting (TSF) is essential in various domains, and recent advancements in diffusion-based TSF models have shown considerable promise. However, these models typically adopt traditional diffusion patterns, treating TSF as a…

Machine Learning · Computer Science 2024-12-13 Jiaxin Gao , Qinglong Cao , Yuntian Chen

Ambiguity in medical image segmentation calls for models that capture full conditional distributions rather than a single point estimate. We present Prior-Guided Residual Diffusion (PGRD), a diffusion-based framework that learns voxel-wise…

Computer Vision and Pattern Recognition · Computer Science 2026-02-03 Fuyou Mao , Beining Wu , Yanfeng Jiang , Han Xue , Yan Tang , Hao Zhang