Hierarchical learning machines are non-regular and non-identifiable statistical models, whose true parameter sets are analytic sets with singularities. Using algebraic analysis, we rigorously prove that the stochastic complexity of a non-identifiable learning machine is asymptotically equal to '1 log n - (ml - 1) log log n

This is one of the theoretical results most frequently cited to justify the use of sigmoidal neural networks in applications. By this statement one refers to the fact that sigmoidal neural networks have been shown to be able to approximate any continuous function arbitrarily well. Numerous results in the literature have established variants of this universal approximation property by considering distinct function classes to be approximated by network architectures using different types of neural activation functions with respect to various approximation criteria, see for instance [1, 2, 3, 5, 6, 11, 12, 14, 15].

A very simple model of two reciprocally connected attractor neural networks isstudied analytically in situations similar to those encountered in delay match-to-sample tasks with intervening stimuli and in tasks of memory guided attention. The model qualitatively reproduces many of the experimental data on these types of tasks and provides a framework for the understanding of the experimental observations in the context of the attractor neural network scenario.

The problem of developing good policies for partially observable Markov decision problems (POMDPs) remains one of the most challenging areas ofresearch in stochastic planning. One line of research in this area involves the use of reinforcement learning with belief states, probability distributionsover the underlying model states. This is a promising methodfor small problems, but its application is limited by the intractability ofcomputing or representing a full belief state for large problems. Recent work shows that, in many settings, we can maintain an approximate belief state, which is fairly close to the true belief state. In particular, great success has been shown with approximate belief states that marginalize out correlations between state variables. In this paper, we investigate two methods of full belief state reinforcement learning and one novel method for reinforcement learning using factored approximate belief states. We compare the performance of these algorithms on several well-known problem from the literature. Our results demonstrate the importance ofapproximate belief state representations for large problems.

This paper examines the role of biological constraints in the human auditory localizationprocess. A psychophysical and neural system modeling approach was undertaken in which performance comparisons between competing models and a human subject explore the relevant biologically plausible"realism constraints". The directional acoustical cues, upon which sound localization is based, were derived from the human subject's head-related transfer functions (HRTFs). Sound stimuli were generated by convolving bandpass noise with the HRTFs and were presented toboth the subject and the model. The input stimuli to the model was processed using the Auditory Image Model of cochlear processing.

This increase in synaptic strength must be countered by a mechanism for weakening the synapse [4]. The biological correlate, long-term depression (LTD) has also been observed in the laboratory; that is, synapses are observed to weaken when low presynaptic activity coincides with high postsynaptic activity [5]-[6].

Stochastic meta-descent (SMD) is a new technique for online adaptation oflocal learning rates in arbitrary twice-differentiable systems. Like matrix momentum it uses full second-order information while retaining O(n) computational complexity by exploiting the efficient computation of Hessian-vector products. Here we apply SMD to independent component analysis, and employ the resulting algorithmfor the blind separation of time-varying mixtures. By matching individual learning rates to the rate of change in each source signal's mixture coefficients, our technique is capable of simultaneously trackingsources that move at very different, a priori unknown speeds. 1 Introduction Independent component analysis (ICA) methods are typically run in batch mode in order to keep the stochasticity of the empirical gradient low. Often this is combined with a global learning rate annealing scheme that negotiates the tradeoff between fast convergence and good asymptotic performance.

Visualization of input data and feature selection are intimately related. A good feature selection algorithm can identify meaningful coordinate projections for low dimensional data visualization. Conversely, a good visualization technique can suggest meaningfulfeatures to include in a model. Input variable selection is the most important step in the model selection process. Given a target variable, a set of input variables can be selected as explanatory variables by some prior knowledge.

There are many hierarchical clustering algorithms available, but these lack a firm statistical basis. Here we set up a hierarchical probabilistic mixture model, where data is generated in a hierarchical tree-structured manner. Markov chain Monte Carlo (MCMC) methods are demonstrated which can be used to sample from the posterior distribution over trees containing variable numbers of hidden units.

We present a variational Bayesian method for model selection over families of kernels classifiers like Support Vector machines or Gaussian processes.The algorithm needs no user interaction and is able to adapt a large number of kernel parameters to given data without having to sacrifice training cases for validation. This opens the possibility touse sophisticated families of kernels in situations where the small "standard kernel" classes are clearly inappropriate. We relate the method to other work done on Gaussian processes and clarify the relation between Support Vector machines and certain Gaussian process models. 1 Introduction Bayesian techniques have been widely and successfully used in the neural networks and statistics community and are appealing because of their conceptual simplicity, generality and consistency with which they solve learning problems. In this paper we present a new method for applying the Bayesian methodology to Support Vector machines. We will briefly review Gaussian Process and Support Vector classification in this section and clarify their relationship by pointing out the common roots. Although we focus on classification here, it is straightforward to apply the methods to regression problems as well. In section 2 we introduce our algorithm and show relations to existing methods. Finally, we present experimental results in section 3 and close with a discussion in section 4. Let X be a measure space (e.g.