Baptiste Abélès

Baptiste Abélès, Eugenio Clerico, Gergely Neu

Traditional generalization results in statistical learning require a training data set made of independently drawn examples. Most of the recent efforts to relax this independence assumption have considered either purely temporal (mixing) dependencies, or graph-dependencies, where non-adjacent vertices correspond to independent random variables. Both approaches have their own limitations, the former requiring a temporal ordered structure, and the latter lacking a way to quantify the strength of inter-dependencies. In this work, we bridge these two lines of work by proposing a framework where dependencies decay with graph distance. We derive generalization bounds leveraging the online-to-PAC framework, by deriving a concentration result and introducing an online learning framework incorporating the graph structure. The resulting high-probability generalization guarantees depend on both the mixing rate and the graph's chromatic number.

Baptiste Abeles, Eugenio Clerico, Gergely Neu

We study the generalization error of statistical learning algorithms in a non-i.i.d. setting, where the training data is sampled from a stationary mixing process. We develop an analytic framework for this scenario based on a reduction to online learning with delayed feedback. In particular, we show that the existence of an online learning algorithm with bounded regret (against a fixed statistical learning algorithm in a specially constructed game of online learning with delayed feedback) implies low generalization error of said statistical learning method even if the data sequence is sampled from a mixing time series. The rates demonstrate a trade-off between the amount of delay in the online learning game and the degree of dependence between consecutive data points, with near-optimal rates recovered in a number of well-studied settings when the delay is tuned appropriately as a function of the mixing time of the process.