Online learning using a Bayesian surprise metric

Dictionary.com defines learning as the process of acquiring knowledge. In psychology, learning is defined as the modification of behavior through training. In our work, we combine these definitions to define learning as the modification of a system model to incorporate the knowledge acquired by new observations. During learning, the system creates and modifies a model to improve its performance. As new samples are introduced, the system updates its model based on the new information provided by the samples. However, this update may not necessarily improve the model. We propose a Bayesian surprise metric to differentiate good data (beneficial) from outliers (detrimental), and thus help to selectively adapt the model parameters. The surprise metric is calculated based on the difference between the prior and the posterior distributions of the model when a new sample is introduced. The metric is useful not only to identify outlier data, but also to differentiate between the data carrying useful information for improving the model and those carrying no new information (redundant). Allowing only the relevant data to update the model would speed up the learning process and prevent the system from overfitting. The method is demonstrated in all three learning procedures: supervised, semi-supervised and unsupervised. The results show the benefit of surprise in both clustering and outlier detection.