Decision-Theoretic Approximations for Machine Learning

Decision theory focuses on the problem of making decisions under uncertainty. This uncertainty arises from the unknown aspects of the state of the world the decision maker is in or the unknown utility function of performing actions. The uncertainty can be modeled as a probability distribution capturing our belief about the world the decision maker is in. Upon making new observations, the decision maker becomes more confident about this model. In addition, if there is a prior belief on this uncertainty that may have obtained from similar experiments, the Bayesian methods may be employed. The loss incurred by the decision maker can also be utilized for the optimal action selection. Most machine learning algorithms developed though focus on one of these aspects for learning and prediction; either learning the probabilistic model or minimizing the loss. In probabilistic models, approximate inference, the process of obtaining the desired model from the observations when its is not tractable, does not consider the task loss. On the other end of the spectrum, the common practice in learning is to minimize the task loss without considering the uncertainty of prediction model. Therefore, we investigate the intersection of decision theory and machine learning considering both uncertainty in prediction model and the task loss.