Bayesian Active Learning for Classification and Preference Learning

Information theoretic active learning has been widely studied for probabilistic models. For simple regression an optimal myopic policy is easily tractable. However, for other tasks and with more complex models, such as classification with nonparametric models, the optimal solution is harder to compute. Current approaches make approximations to achieve tractability. We propose an approach that expresses information gain in terms of predictive entropies, and apply this method to the Gaussian Process Classifier (GPC). Our approach makes minimal approximations to the full information theoretic objective. Our experimental performance compares favourably to many popular active learning algorithms, and has equal or lower computational complexity. We compare well to decision theoretic approaches also, which are privy to more information and require much more computational time. Secondly, by developing further a reformulation of binary preference learning to a classification problem, we extend our algorithm to Gaussian Process preference learning.

Predictive neural coding of reward preference involves dissociable responses in human ventral midbrain and ventral striatum.

Food preferences are acquired through experience and can exert strong influence on choice behavior. In order to choose which food to consume, it is necessary to maintain a predictive representation of the subjective value of the associated food stimulus. Here, we explore the neural mechanisms by which such predictive representations are learned through classical conditioning. Human subjects were scanned using fMRI while learning associations between arbitrary visual stimuli and subsequent delivery of one of five different food flavors. Using a temporal difference algorithm to model learning, we found predictive responses in the ventral midbrain and a part of ventral striatum (ventral putamen) that were related directly to subjects' actual behavioral preferences. These brain structures demonstrated divergent response profiles, with the ventral midbrain showing a linear response profile with preference, and the ventral striatum a bivalent response. These results provide insight into the neural mechanisms underlying human preference behavior.

On the relation of slow feature analysis and Laplacian eigenmaps

The past decade has seen a rise of interest in Laplacian eigenmaps (LEMs) for nonlinear dimensionality reduction. LEMs have been used in spectral clustering, in semisupervised learning, and for providing efficient state representations for reinforcement learning. Here, we show that LEMs are closely related to slow feature analysis (SFA), a biologically inspired, unsupervised learning algorithm originally designed for learning invariant visual representations. We show that SFA can be interpreted as a function approximation of LEMs, where the topological neighborhoods required for LEMs are implicitly defined by the temporal structure of the data. Based on this relation, we propose a generalization of SFA to arbitrary neighborhood relations and demonstrate its applicability for spectral clustering. Finally, we review previous work with the goal of providing a unifying view on SFA and LEMs. © 2011 Massachusetts Institute of Technology.