Bayesian regression selecting valuable subset from mixed bag training data

This paper addresses a problem in which we learn a regression model from sets of training data. Each of the sets has an only single label, and only one of the training data in the set reflects the label. This is particularly the case when the label is attached to a group of data, such as time-series data. The label is not attached to the point of the sequence but rather attached to particular time window of the sequence. As such, a small part of the time window likely reflects the label, whereas the other larger part of the time window likely does not reflect it. We design an algorithm for estimating which of the training data in each of the sets corresponds to the label, as well as for training the regression model on the basis of Bayesian modeling and posterior inference with variational Bayes. Our experimental results show that our approach perform better than baseline methods on an artificial dataset and on a real-world dataset.