Online Learning of Non-stationary Sequences

We consider an online learning scenario in which the learner can make predictions on the basis of a fixed set of experts. The performance of each expert may change over time in a manner unknown to the learner. We formulate a class of universal learning algorithms for this problem by expressing them as simple Bayesian algorithms operating on models analogous to Hidden Markov Models (HMMs). We derive a new performance bound for such algorithms which is considerably simpler than existing bounds. The bound provides the basis for learning the rate at which the identity of the optimal expert switches over time. We find an analytic expression for the a priori resolution at which we need to learn the rate parameter. We extend our scalar switching-rate result to models of the switching-rate that are governed by a matrix of parameters, i.e. arbitrary homogeneous HMMs. We apply and examine our algorithm in the context of the problem of energy management in wireless networks. We analyze the new results in the framework of Information Theory.

On Convergence Properties of the EM Algorithm for Gaussian Mixtures

"Expectation-Maximization'' (EM) algorithm and gradient-based approaches for maximum likelihood learning of finite Gaussian mixtures. We show that the EM step in parameter space is obtained from the gradient via a projection matrix $P$, and we provide an explicit expression for the matrix. We then analyze the convergence of EM in terms of special properties of $P$ and provide new results analyzing the effect that $P$ has on the likelihood surface. Based on these mathematical results, we present a comparative discussion of the advantages and disadvantages of EM and other algorithms for the learning of Gaussian mixture models.

Modeling Invariances in Inferotemporal Cell Tuning

In macaque inferotemporal cortex (IT), neurons have been found to respond selectively to complex shapes while showing broad tuning ("invariance") with respect to stimulus transformations such as translation and scale changes and a limited tuning to rotation in depth. Training monkeys with novel, paperclip-like objects, Logothetis et al. could investigate whether these invariance properties are due to experience with exhaustively many transformed instances of an object or if there are mechanisms that allow the cells to show response invariance also to previously unseen instances of that object. They found object-selective cells in anterior IT which exhibited limited invariance to various transformations after training with single object views. While previous models accounted for the tuning of the cells for rotations in depth and for their selectivity to a specific object relative to a population of distractor objects, the model described here attempts to explain in a biologically plausible way the additional properties of translation and size invariance. Using the same stimuli as in the experiment, we find that model IT neurons exhibit invariance properties which closely parallel those of real neurons. Simulations show that the model is capable of unsupervised learning of view-tuned neurons. The model also allows to make experimentally testable predictions regarding novel stimulus transformations and combinations of stimuli.