A Theory of How the Brain Might Work

I wish to propose a quite speculative new version of the grandmother cell theory to explain how the brain, or parts of it, may work. In particular, I discuss how the visual system may learn to recognize 3D objects. The model would apply directly to the cortical cells involved in visual face recognition. I will also outline the relation of our theory to existing models of the cerebellum and of motor control. Specific biophysical mechanisms can be readily suggested as part of a basic type of neural circuitry that can learn to approximate multidimensional input-output mappings from sets of examples and that is expected to be replicated in different regions of the brain and across modalities. The main points of the theory are: -the brain uses modules for multivariate function approximation as basic components of several of its information processing subsystems. -these modules are realized as HyperBF networks (Poggio and Girosi, 1990a,b). -HyperBF networks can be implemented in terms of biologically plausible mechanisms and circuitry. The theory predicts a specific type of population coding that represents an extension of schemes such as look-up tables. I will conclude with some speculations about the trade-off between memory and computation and the evolution of intelligence.

On the Dirichlet Prior and Bayesian Regularization

A common objective in learning a model from data is to recover its network structure, while the model parameters are of minor interest. For example, we may wish to recover regulatory networks from high-throughput data sources. In this paper we examine how Bayesian regularization using a Dirichlet prior over the model parameters affects the learned model structure in a domain with discrete variables. Surprisingly, a weak prior in the sense of smaller equivalent sample size leads to a strong regularization of the model structure (sparse graph) given a sufficiently large data set. In particular, the empty graph is obtained in the limit of a vanishing strength of prior belief. This is diametrically opposite to what one may expect in this limit, namely the complete graph from an (unregularized) maximum likelihood estimate. Since the prior affects the parameters as expected, the prior strength balances a "trade-off" between regularizing the parameters or the structure of the model. We demonstrate the benefits of optimizing this trade-off in the sense of predictive accuracy.

(Semi-)Predictive Discretization During Model Selection

In this paper, we present an approach to discretizing multivariate continuous data while learning the structure of a graphical model. We derive the joint scoring function from the principle of predictive accuracy, which inherently ensures the optimal trade-off between goodness of fit and model complexity (including the number of discretization levels). Using the so-called finest grid implied by the data, our scoring function depends only on the number of data points in the various discretization levels. Not only can it be computed efficiently, but it is also independent of the metric used in the continuous space. Our experiments with gene expression data show that discretization plays a crucial role regarding the resulting network structure.

Direction Estimation of Pedestrian from Images

The capability of estimating the walking direction of people would be useful in many applications such as those involving autonomous cars and robots. We introduce an approach for estimating the walking direction of people from images, based on learning the correct classification of a still image by using SVMs. We find that the performance of the system can be improved by classifying each image of a walking sequence and combining the outputs of the classifier. Experiments were performed to evaluate our system and estimate the trade-off between number of images in walking sequences and performance.