A1217
Title: Empirical PAC-Bayes bounds for Markov chains
Authors: Pierre Alquier - ESSEC Business School (Singapore) [presenting]
Vahe Karagulyan - ESSEC Business School (France)
Abstract: The core of generalization theory was developed for independent observations. Some PAC and PAC-Bayes bounds are available for data that exhibit a temporal dependence. However, there are constants in these bounds that depend on properties of the data-generating process: mixing coefficients, mixing time, spectral gap... Such constants are unknown in practice. A new PAC-Bayes bound for Markov chains is proven. This bound depends on a quantity called the pseudo-spectral gap. The main novelty is that an empirical bound on the pseudo-spectral gap can be provided when the state space is finite. Thus, the first fully empirical PAC-Bayes bound for Markov chains is obtained. This extends beyond the finite case, although this requires additional assumptions. On simulated experiments, the empirical version of the bound is essentially as tight as the non-empirical one.
