Deviation bound for non-causal machine learning

Concentration inequalities have been widely used in machine learning theory. Model selection techniques, for instance, relies heavily on concentration inequality [Massart, 2007]. They have also been used for high dimensional procedures [Bickel et al., 2009, Alquier et al., 2020] or for studying different machine learning framework, such as time series prediction[Kuznetsov and Mohri, 2015], online machine learning[Sanchez-Perez, 2015] or classification problems [Freund et al., 2004]. Many concentration inequalities has been proposed for different framework and different hypothesis. An interested reader may read [Boucheron et al., 2013] for an overview on stationary concentration inequalities.