Many domains are naturally organized in an abstraction hierarchy or taxonomy, where the instances in “nearby” classes in the taxonomy are similar. In this pa- per, we provide a general probabilistic framework for clustering data into a set of classes organized as a taxonomy, where each class is associated with a prob- abilistic model from which the data was generated. The clustering algorithm simultaneously optimizes three things: the assignment of data instances to clus- ters, the models associated with the clusters, and the structure of the abstraction hierarchy. A unique feature of our approach is that it utilizes global optimization algorithms for both of the last two steps, reducing the sensitivity to noise and the propensity to local maxima that are characteristic of algorithms such as hierarchi- cal agglomerative clustering that only take local steps. We provide a theoretical analysis for our algorithm, showing that it converges to a local maximum of the joint likelihood of model and data. We present experimental results on synthetic data, and on real data in the domains of gene expression and text.

Many approaches to reinforcement learning combine neural net(cid:173) works or other parametric function approximators with a form of temporal-difference learning to estimate the value function of a Markov Decision Process. A significant disadvantage of those pro(cid:173) cedures is that the resulting learning algorithms are frequently un(cid:173) stable. In this work, we present a new, kernel-based approach to reinforcement learning which overcomes this difficulty and provably converges to a unique solution. By contrast to existing algorithms, our method can also be shown to be consistent in the sense that its costs converge to the optimal costs asymptotically. Our focus is on learning in an average-cost framework and on a practical ap(cid:173) plication to the optimal portfolio choice problem.

We present methods for learning and tracking human motion in video. We estimate a statistical model of typical activities from a large set of 3D periodic human motion data by segmenting these data automatically into "cycles". Then the mean and the princi(cid:173) pal components of the cycles are computed using a new algorithm that accounts for missing information and enforces smooth tran(cid:173) sitions between cycles. The learned temporal model provides a prior probability distribution over human motions that can be used in a Bayesian framework for tracking human subjects in complex monocular video sequences and recovering their 3D motion.

We consider the training of neural networks in cases where the nonlinear relationship of interest gradually changes over time. One possibility to deal with this problem is by regularization where a variation penalty is added to the usual mean squared error criterion. To learn the regularized network weights we suggest the Iterative Extended Kalman Filter (IEKF) as a learning rule, which may be derived from a Bayesian perspective on the regularization problem. A primary application of our algorithm is in financial derivatives pricing, where neural networks may be used to model the dependency of the derivatives' price on one or several underlying assets. After giving a brief introduction to the problem of derivatives pricing we present experiments with German stock index options data showing that a regularized neural network trained with the IEKF outperforms several benchmark models and alternative learning procedures. In particular, the performance may be greatly improved using a newly designed neural network architecture that accounts for no-arbitrage pricing restrictions.

We apply the idea of averaging ensembles of estimators to probability density estimation. In particular, we use Gaussian mixture models which are important components in many neural-network applications. We investigate the performance of averaging using three data sets. For comparison, we employ two traditional regularization approaches, i.e., a maximum penalized likelihood approach and a Bayesian approach. In the maximum penalized likelihood approach we use penalty functions derived from conjugate Bayesian priors such that an expectation maximization (EM) algorithm can be used for training. In all experiments, the maximum penalized likelihood approach and averaging improved performance considerably if compared to a maximum likelihood approach. In two of the experiments, the maximum penalized likelihood approach outperformed averaging. In one experiment averaging was clearly superior. Our conclusion is that maximum penalized likelihood gives good results if the penalty term in the cost function is appropriate for the particular problem. If this is not the case, averaging is superior since it shows greater robustness by not relying on any particular prior assumption. The Bayesian approach worked very well on a low-dimensional toy problem but failed to give good performance in higher dimensional problems.

We compare the performance of multilayer perceptrons and density estimating neural networks in the task of forecasting the return and the volatility of the DAX index. We claim that for nontrivial target distributions, density estimating networks should lead to improved predictions. The reason is that the latter are capable of embodying more complex probability models for the target noise. We discuss appropriate distribution assumptions for the important cases of outliers and non constant variances, and give interpretations of the new estimates in regression theory.