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\title[A few topics in Reinforcement Learning]{From Field problems to Machine Learning}
\subtitle{An introduction to the Data Science workflow\\and a motivation to understand Machine Learning}
%\title{The Optimal Swapping Problem during Nuclear Refueling Operations}


\author{E. Rachelson}

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\date{}


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\begin{document}

\begin{frame}{A probabilistic approach to ML}
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Bayesian approach: find $y$ that maximizes $\mathbb{P}(Y=y|\textrm{data}, X=x)$
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This problem of Bayesian inference is hard to solve without additional hypothesis.
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\begin{frame}{A probabilistic approach to ML}
\only<1>{
\begin{block}{Gaussian Processes}
\begin{itemize}
\item Compute the most probable function that passes through the data points, given a priori information about how related two data points are (through a covariance kernel);
\item Also provide a measure of prediction uncertainty in each point;
\item Are computed offline and require an $N\times N$ matrix inversion for $N$ data points in the training set (computationnally costly);
\item Careful engineering of covariance kernels can help incorporate priori knowledge into Gaussian Processes;
\item Are suitable both for regression and classification.
\end{itemize}
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\only<2>{Note that Gaussian Processes are widely used in preliminary design phases, especially as surrogate models that replace physics computations.

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