Minimax Online Prediction of Varying Bernoulli Process under Variational Approximation
Proceedings of The Eleventh Asian Conference on Machine Learning, PMLR 101:141-156, 2019.
We consider the online prediction of a varying Bernoulli process (sequence of varying Bernoulli probabilities) from a single binary sequence. A real-valued online prediction method has been proposed as a prior work that incorporates the smoothness of the prediction sequence into the concept of the regret. Also, a Bayesian prediction method for the varying Bernoulli processes has been developed based on the variational inference. However, the former is not applicable to loss functions other than the squared error function, and the latter has no guarantee on the regret as an online prediction method. We propose a new online prediction method of a varying Bernoulli process from a single binary sequence with a guarantee to minimize the maximum regret under variational approximation. Through numerical experiments, we compare the Bayesian prediction method with the proposed method by using the regret with/without approximation and the KL divergence from the true underlying process. We discuss the prediction accuracy and influences of the approximation of the proposed method.