A central theme of computational vision research has been the re(cid:173) alization that reliable estimation of local scene properties requires propagating measurements across the image. Many authors have therefore suggested solving vision problems using architectures of locally connected units updating their activity in parallel. Unfor(cid:173) tunately, the convergence of traditional relaxation methods on such architectures has proven to be excruciatingly slow and in general they do not guarantee that the stable point will be a global mini(cid:173) mum. In this paper we show that an architecture in which Bayesian Be(cid:173) liefs about image properties are propagated between neighboring units yields convergence times which are several orders of magni(cid:173) tude faster than traditional methods and avoids local minima. In particular our architecture is non-iterative in the sense of Marr [5]: at every time step, the local estimates at a given location are op(cid:173) timal given the information which has already been propagated to that location.

In this paper we propose a method for learning Bayesian belief networks from data. The method uses artificial neural networks as probability estimators, thus avoiding the need for making prior assumptions on the nature of the probability distributions govern(cid:173) ing the relationships among the participating variables. This new method has the potential for being applied to domains containing both discrete and continuous variables arbitrarily distributed. We compare the learning performance of this new method with the performance of the method proposed by Cooper and Herskovits in [7]. The experimental results show that, although the learning scheme based on the use of ANN estimators is slower, the learning accuracy of the two methods is comparable.

Real-valued random hidden variables can be useful for modelling latent structure that explains correlations among observed vari(cid:173) ables. I propose a simple unit that adds zero-mean Gaussian noise to its input before passing it through a sigmoidal squashing func(cid:173) tion. Such units can produce a variety of useful behaviors, ranging from deterministic to binary stochastic to continuous stochastic. I show how "slice sampling" can be used for inference and learning in top-down networks of these units and demonstrate learning on two simple problems.

Exact inference in densely connected Bayesian networks is computation(cid:173) ally intractable, and so there is considerable interest in developing effec(cid:173) tive approximation schemes. One approach which has been adopted is to bound the log likelihood using a mean-field approximating distribution. While this leads to a tractable algorithm, the mean field distribution is as(cid:173) sumed to be factorial and hence unimodal. In this paper we demonstrate the feasibility of using a richer class of approximating distributions based on mixtures of mean field distributions. We derive an efficient algorithm for updating the mixture parameters and apply it to the problem of learn(cid:173) ing in sigmoid belief networks.

This paper reports about an application of Bayes' inferred neu(cid:173) ral network classifiers in the field of automatic sleep staging. The reason for using Bayesian learning for this task is two-fold. First, Bayesian inference is known to embody regularization automati(cid:173) cally. Second, a side effect of Bayesian learning leads to larger variance of network outputs in regions without training data. This results in well known moderation effects, which can be used to detect outliers.

Image intensity variations can result from several different object surface effects, including shading from 3-dimensional relief of the object, or paint on the surface itself. An essential problem in vision, which people solve naturally, is to attribute the proper physical cause, e.g. We ad(cid:173) dressed this problem with an approach combining psychophysical and Bayesian computational methods. We assessed human performance on a set of test images, and found that people made fairly consistent judgements of surface properties. Our computational model assigned simple prior probabilities to different relief or paint explanations for an image, and solved for the most probable interpretation in a Bayesian framework.

Until recently, artificial intelligence researchers have frowned upon the application of probability propagation in Bayesian belief net(cid:173) works that have cycles. The probability propagation algorithm is only exact in networks that are cycle-free. However, it has recently been discovered that the two best error-correcting decoding algo(cid:173) rithms are actually performing probability propagation in belief networks with cycles. Our increasingly wired world demands efficient methods for communicating bits of information over physical channels that introduce errors. Examples of real-world channels include twisted-pair telephone wires, shielded cable-TV wire, fiber-optic cable, deep-space radio, terrestrial radio, and indoor radio.

I consider the problem of learning concepts from small numbers of pos(cid:173) itive examples, a feat which humans perform routinely but which com(cid:173) puters are rarely capable of. Bridging machine learning and cognitive science perspectives, I present both theoretical analysis and an empirical study with human subjects for the simple task oflearning concepts corre(cid:173) sponding to axis-aligned rectangles in a multidimensional feature space. Existing learning models, when applied to this task, cannot explain how subjects generalize from only a few examples of the concept. I propose a principled Bayesian model based on the assumption that the examples are a random sample from the concept to be learned. The model gives precise fits to human behavior on this simple task and provides qualitati ve insights into more complex, realistic cases of concept learning.

We explore in this study the statistical properties of this normalization in the presence of noise. Using simulations, we show that divisive normalization is a close approximation to a maximum likelihood estimator, which, in the context of population coding, is the same as an ideal observer. We also demonstrate ana(cid:173) lytically that this is a general property of a large class of nonlinear recurrent networks with line attractors. Our work suggests that divisive normalization plays a critical role in noise filtering, and that every cortical layer may be an ideal observer of the activity in the preceding layer. Information processing in the cortex is often formalized as a sequence of a linear stages followed by a nonlinearity.

Many belief networks have been proposed that are composed of binary units. However, for tasks such as object and speech recog(cid:173) nition which produce real-valued data, binary network models are usually inadequate. Independent component analysis (ICA) learns a model from real data, but the descriptive power of this model is severly limited. We begin by describing the independent factor analysis (IFA) technique, which overcomes some of the limitations of ICA. We then create a multilayer network by cascading single(cid:173) layer IFA models.