In this paper, the technique of stacking, previously only used for supervised learning, is applied to unsupervised learning. Specifi(cid:173) cally, it is used for non-parametric multivariate density estimation, to combine finite mixture model and kernel density estimators. Ex(cid:173) perimental results on both simulated data and real world data sets clearly demonstrate that stacked density estimation outperforms other strategies such as choosing the single best model based on cross-validation, combining with uniform weights, and even the sin(cid:173) gle best model chosen by "cheating" by looking at the data used for independent testing.

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.

We derive a learning algorithm for inferring an overcomplete basis by viewing it as probabilistic model of the observed data. Over(cid:173) complete bases allow for better approximation of the underlying statistical density. Using a Laplacian prior on the basis coefficients removes redundancy and leads to representations that are sparse and are a nonlinear function of the data. This can be viewed as a generalization of the technique of independent component anal(cid:173) ysis and provides a method for blind source separation of fewer mixtures than sources. We demonstrate the utility of overcom(cid:173) plete representations on natural speech and show that compared to the traditional Fourier basis the inferred representations poten(cid:173) tially have much greater coding efficiency.

We present a computationally efficient algorithm for function ap(cid:173) proximation with piecewise linear sigmoidal nodes. A one hidden layer network is constructed one node at a time using the method of fitting the residual. The task of fitting individual nodes is accom(cid:173) plished using a new algorithm that searchs for the best fit by solving a sequence of Quadratic Programming problems. Unique characteristics of this algorithm include: finite step convergence, a simple stop(cid:173) ping criterion, a deterministic methodology for seeking "good" local minima, good scaling properties and a robust numerical implemen(cid:173) tation.

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.

The technique of principal component analysis (PCA) has recently been expressed as the maximum likelihood solution for a generative latent variable model. In this paper we use this probabilistic reformulation as the basis for a Bayesian treatment of PCA. Our key result is that ef(cid:173) fective dimensionality of the latent space (equivalent to the number of retained principal components) can be determined automatically as part of the Bayesian inference procedure. An important application of this framework is to mixtures of probabilistic PCA models, in which each component can determine its own effective complexity.

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.

Inference is a key component in learning probabilistic models from par(cid:173) tially observable data. When learning temporal models, each of the many inference phases requires a traversal over an entire long data se(cid:173) quence; furthermore, the data structures manipulated are exponentially large, making this process computationally expensive. In [2], we describe an approximate inference algorithm for monitoring stochastic processes, and prove bounds on its approximation error. In this paper, we apply this algorithm as an approximate forward propagation step in an EM algorithm for learning temporal Bayesian networks. We provide a related approxi(cid:173) mation for the backward step, and prove error bounds for the combined algorithm.

We compare the ability of three exemplar-based memory models, each using three different face stimulus representations, to account for the probability a human subject responded "old" in an old/new facial mem(cid:173) ory experiment. The models are 1) the Generalized Context Model, 2) SimSample, a probabilistic sampling model, and 3) MMOM, a novel model related to kernel density estimation that explicitly encodes stim(cid:173) ulus distinctiveness. The representations are 1) positions of stimuli in MDS "face space," 2) projections of test faces onto the "eigenfaces" of the study set, and 3) a representation based on response to a grid of Gabor filter jets. Of the 9 model/representation combinations, only the distinc(cid:173) tiveness model in MDS space predicts the observed "morph familiarity inversion" effect, in which the subjects' false alarm rate for morphs be(cid:173) tween similar faces is higher than their hit rate for many of the studied faces. This evidence is consistent with the hypothesis that human mem(cid:173) ory for faces is a kernel density estimation task, with the caveat that dis(cid:173) tinctive faces require larger kernels than do typical faces.