Semi-Supervised Recursive Learning of Discriminative Mixture Models for Time-Series Classification

We pose pattern classification as a density estimation problem where we consider mixtures of generative models under partially labeled data setups. Unlike traditional approaches that estimate density everywhere in data space, we focus on the density along the decision boundary that can yield more discriminative models with superior classification performance. We extend our earlier work on the recursive estimation method for discriminative mixture models to semi-supervised learning setups where some of the data points lack class labels. Our model exploits the mixture structure in the functional gradient framework: it searches for the base mixture component model in a greedy fashion, maximizing the conditional class likelihoods for the labeled data and at the same time minimizing the uncertainty of class label prediction for unlabeled data points. The objective can be effectively imposed as individual mixture component learning on weighted data, hence our mixture learning typically becomes highly efficient for popular base generative models like Gaussians or hidden Markov models. Moreover, apart from the expectation-maximization algorithm, the proposed recursive estimation has several advantages including the lack of need for a pre-determined mixture order and robustness to the choice of initial parameters. We demonstrate the benefits of the proposed approach on a comprehensive set of evaluations consisting of diverse time-series classification problems in semi-supervised scenarios.