Benjamin Goehry’s research while affiliated with University of Paris-Saclay and other places

Random forests were introduced by Breiman in 2001. We study theoretical aspects of both original Breiman’s random forests and a simplified version, the centred random forests. Under the independent and identically distributed hypothesis, Scornet, Biau and Vert proved the consistency of Breiman’s random forest, while Biau studied the simplified version and obtained a rate of convergence in the sparse case. However, the i.i.d hypothesis is generally not satisfied for example when dealing with time series. We extend the previous results to the case where observations are weakly dependent, more precisely when the sequences are stationary β−mixing.

Cette thèse comporte deux objectifs. Un premier objectif concerne la prévision d’une charge totale dans le contexte des Smart Grids par des approches qui reposent sur la méthode de prévision ascendante. Le deuxième objectif repose quant à lui sur l’étude des forêts aléatoires dans le cadre d’observations dépendantes, plus précisément des séries temporelles. Nous étendons dans ce cadre les résultats de consistance des forêts aléatoires originelles de Breiman ainsi que des vitesses de convergence pour une forêt aléatoire simplifiée qui ont été tout deux jusqu’ici uniquement établis pour des observations indépendantes et identiquement distribuées. La dernière contribution sur les forêts aléatoires décrit une nouvelle méthodologie qui permet d’incorporer la structure dépendante des données dans la construction des forêts et permettre ainsi un gain en performance dans le cas des séries temporelles, avec une application à la prévision de la consommation d’un bâtiment.

The development of smart grid and new advanced metering infrastructures induces new opportunities and challenges for utilities. Exploiting smart meters information for forecasting stands as a key point for energy providers who have to deal with time varying portfolio of customers as well as grid managers who needs to improve accuracy of local forecasts to face with distributed renewable energy generation development. We propose a new machine learning approach to forecast the system load of a group of customers exploiting individual load measurements in real time and/or exogenous information like weather and survey data. Our approach consists in building experts using random forests trained on some subsets of customers then normalise their predictions and aggregate them with a convex expert aggregation algorithm to forecast the system load. We propose new aggregation methods and compare two strategies for building subsets of customers: 1) hierarchical clustering based on survey data and/or load features and 2) random clustering strategy. These approaches are evaluated on a real data set of residential Irish customers load at a half hourly resolution. We show that our approaches achieve a significant gain in short term load forecasting accuracy of around 25 percent of RMSE.