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Machine Learning Algorithms for Regression and Global Optimization of Risk Measures

Abstract : This thesis presents methods for estimation and optimization of stochastic black box functions. Motivated by the necessity to take risk-averse decisions in medecine, agriculture or finance, in this study we focus our interest on indicators able to quantify some characteristics of the output distribution such as the variance or the size of the tails. These indicators also known as measure of risk have received a lot of attention during the last decades. Based on the existing literature on risk measures, we chose to focus this work on quantiles, CVaR and expectiles. First, we will compare the following approaches to perform quantile regression on stochastic black box functions: the K-nearest neighbors, the random forests, the RKHS regression, the neural network regression and the Gaussian process regression. Then a new regression model is proposed in this study that is based on chained Gaussian processes inferred by variational techniques. Though our approach has been initially designed to do quantile regression, we showed that it can be easily applied to expectile regression. Then, this study will focus on optimisation of risk measures. We propose a generic approach inspired from the X -armed bandit which enables the creation of an optimiser and an upper bound on the simple regret that can be adapted to any risk measure. The importance and relevance of this approach is illustrated by the optimization of quantiles and CVaR. Finally, some optimisation algorithms for the conditional quantile and expectile are developed based on Gaussian processes combined with UCB and Thompson sampling strategies.
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Contributor : Léonard Torossian <>
Submitted on : Wednesday, June 9, 2021 - 11:19:52 PM
Last modification on : Wednesday, June 16, 2021 - 3:53:12 AM


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  • HAL Id : tel-03255973, version 1


Léonard Torossian. Machine Learning Algorithms for Regression and Global Optimization of Risk Measures. Statistics [math.ST]. MITT, 2019. English. ⟨tel-03255973⟩



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