We propose a novel approach for building finite memory predictive models similarin spirit to variable memory length Markov models (VLMMs). The models are constructed by first transforming the n-block structure of the training sequence into a spatial structure of points in a unit hypercube, such that the longer is the common suffix shared by any two n-blocks, the closer lie their point representations. Such a transformation embodies a Markov assumption - n-blocks with long common suffixes are likely to produce similar continuations. Finding a set of prediction contexts is formulated as a resource allocation problem solved by vector quantizing the spatial n-block representation. We compare our model with both the classical and variable memory length Markov models on three data sets with different memory and stochastic components. Our models have a superior performance, yet, their construction is fully automatic, which is shown to be problematic in the case of VLMMs.

For many problems, the correct behavior of a model depends not only on its input-output mapping but also on properties of its Jacobian matrix, the matrix of partial derivatives of the model's outputs with respect to its inputs.

The algorithm builds on the basic principles of decomposition proposed by Osuna et.

The problem that we address in this paper is how a mobile robot can plan in order to arrive at its goal with minimum uncertainty. Traditional motion planning algorithms oftenassume that a mobile robot can track its position reliably, however, in real world situations, reliable localization may not always be feasible. Partially Observable Markov Decision Processes (POMDPs) provide one way to maximize the certainty of reaching the goal state, but at the cost of computational intractability for large state spaces. The method we propose explicitly models the uncertainty of the robot's position as a state variable, and generates trajectories through the augmented pose-uncertainty space. By minimizing the positional uncertainty at the goal, the robot reduces the likelihood it becomes lost. We demonstrate experimentally that coastal navigation reduces the uncertainty at the goal, especially with degraded localization.

We develop a hierarchical generative model to study cue combination. Themodel maps a global shape parameter to local cuespecific parameters,which in tum generate an intensity image. Inferring shape from images is achieved by inverting this model. Inference produces a probability distribution at each level; using distributions rather than a single value of underlying variables at each stage preserves information about the validity of each local cue for the given image. This allows the model, unlike standard combination models, to adaptively weight each cue based on general cuereliability and specific image context.

We find that a necessary requirement for effective associative memorylearning is that the efficacies of the incoming synapses should be uncorrelated. This requirement is difficult to achieve in a robust manner by Hebbian synaptic learning, since it depends on network level information. Effective learning can yet be obtained by a neuronal process that maintains a zero sum of the incoming synapticefficacies. This normalization drastically improves the memory capacity of associative networks, from an essentially bounded capacity to one that linearly scales with the network's size. It also enables the effective storage of patterns with heterogeneous coding levels in a single network.

We describe a class of probabilistic models that we call credibility networks. Using parse trees as internal representations of images, credibility networks are able to perform segmentation and recognition simultaneously,removing the need for ad hoc segmentation heuristics. Promising results in the problem of segmenting handwritten digitswere obtained.

I consider a topographic projection between two neuronal layers with different densitiesof neurons. Given the number of output neurons connected toeach input neuron (divergence or fan-out) and the number of input neurons synapsing on each output neuron (convergence or fan-in) I determine the widths of axonal and dendritic arbors which minimize the total volume ofaxons and dendrites. My analytical results can be summarized qualitativelyin the following rule: neurons of the sparser layer should have arbors wider than those of the denser layer. This agrees with the anatomical data from retinal and cerebellar neurons whose morphology andconnectivity are known. The rule may be used to infer connectivity ofneurons from their morphology.

The project pursued in this paper is to develop from first information-geometric principles a general method for learning the similarity between text documents.

I describe a silicon network consisting of a group of excitatory neurons anda global inhibitory neuron. The output of the inhibitory neuron is normalized with respect to the input strengths.