Often a learning problem has natural quantitative measure of generalization. If a loss function is defined the natural measure is the generalization error, i.e., the expected loss on a random sample independent of the training set. Generalizability is a key topic of learning theory and much progress has been reported. Analytic results for a broad class of machines can be found in the litterature [8, 12, 9, 10] describing the asymptotic generalization ability of supervised algorithms that are continuously parameterized. Asymptotic bounds on generalization for general machines havebeen advocated by Vapnik [11]. Generalization results valid for finite training sets can only be obtained for specific learning machines, see e.g.

We have developed a VLSI silicon neuron and a corresponding mathematical modelthat is a two state-variable system. We describe the circuit implementation and compare the behaviors observed in the silicon neuron and the mathematical model. We also perform bifurcation analysis ofthe mathematical model by varying the externally applied current and show that the behaviors exhibited by the silicon neuron under corresponding conditionsare in good agreement to those predicted by the bifurcation analysis.

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We study a population decoding paradigm in which the maximum likelihood inferenceis based on an unfaithful decoding model (UMLI). This is usually the case for neural population decoding because the encoding process of the brain is not exactly known, or because a simplified decoding modelis preferred for saving computational cost. We consider an unfaithful decoding model which neglects the pairwise correlation between neuronal activities, and prove that UMLI is asymptotically efficient whenthe neuronal correlation is uniform or of limited-range. The performance of UMLI is compared with that of the maximum likelihood inference based on a faithful model and that of the center of mass decoding method.It turns out that UMLI has advantages of decreasing the computational complexity remarkablely and maintaining a high-level decoding accuracy at the same time. The effect of correlation on the decoding accuracy is also discussed.

Ever since Pearl's probability propagation algorithm in graphs with cycles was shown to produce excellent results for error-correcting decoding a few years ago, we have been curious about whether local probability propagation could be used successfully for machine learning.One of the simplest adaptive models is the factor analyzer, which is a two-layer network that models bottom layer sensory inputs as a linear combination of top layer factors plus independent Gaussiansensor noise. We show that local probability propagation in the factor analyzer network usually takes just a few iterations to perform accurate inference, even in networks with 320 sensors and 80 factors. We derive an expression for the algorithm's fixed point and show that this fixed point matches the exact solution ina variety of networks, even when the fixed point is unstable.

This learning function is based on recent experimental findings .

The Facial Action Coding System (FACS) (9) is an objective method for quantifying facial movement in terms of component actions. This system is widely used in behavioral investigations of emotion, cognitive processes, and social interaction. The coding ispresently performed by highly trained human experts. This paper explores and compares techniques for automatically recognizing facialactions in sequences of images. These methods include unsupervised learning techniques for finding basis images such as principal component analysis, independent component analysis and local feature analysis, and supervised learning techniques such as Fisher's linear discriminants.

In this paper, we propose that information maximization can provide aunified framework for understanding saccadic eye movements. Inthis framework, the mutual information among the cortical representations of the retinal image, the priors constructed from our long term visual experience, and a dynamic short-term internal representation constructed from recent saccades provides a map for guiding eye navigation. By directing the eyes to locations ofmaximum complexity in neuronal ensemble responses at each step, the automatic saccadic eye movement system greedily collects information about the external world, while modifying the neural representations in the process. This framework attempts to connect several psychological phenomena, such as pop-out and inhibition of return, to long term visual experience and short term working memory. It also provides an interesting perspective on contextual computation and formation of neural representation in the visual system. 1 Introduction When we look at a painting or a visual scene, our eyes move around rapidly and constantly to look at different parts of the scene.

Spatial information comes in two forms: direct spatial information (for example, retinal position) and indirect temporal contiguity information, since objects encountered sequentially are in general spatially close.

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.