Machine Learning and Uncertainties in Climate Simulations
Date:
Invited Talk for the Machine Learning and Uncertainties in Climate Simulations, organized in Moulin Mer (France).
Title. Statistical Learning Framework for Distributional Regression using Continuous Ranked Probability Score
Abstract. Distributional regression fulfills a fundamental need of statistical analysis : being able to make forecasts and quantify their uncertainty.This approach overcomes the limits of classical regression which estimates only the conditional mean by estimation the whole conditional distribution. This methodology, called probabilistic forecast, is widely used in numerous fields such as meteorology and energy production, but its theoretical aspects have not been studied. By analogy with the classical theory of statistical learning, we define a framework where the predictor is a law of probability, called predictive law, and where the loss function is given by a strictly proper scoring rule. Bayes predictor is then the conditional law. In the case of the Continuous Ranked Probability Score, we study then the minimax rate of convergence andshow that, the k nearest neighbors algorithm for the distributional regression reaches the optimal rate of convergence in dimension d ≥ 2,while the kernel algorithm reaches the optimal rate of convergence inany dimension
Support of the presentation : here Associated article : Distributional regression and its evaluation with the CRPS: Bounds and convergence of the minimax risk, Pic et al. (2022) link