Logistic regression analysis of high-dimensional data, such as natural language text, poses computational and statistical challenges. Maximum likelihood estimation often fails in these applications. We present a simple Bayesian logistic regression approach that uses a Laplace prior to avoid overfitting and produces sparse predictive models for text data. We apply this approach to a range of document classification problems and show that it produces compact predictive models at least as effective as those produced by support vector machine classifiers or ridge logistic regression combined with feature selection. We describe our model fitting algorithm, our open source implementations (BBR and BMR), and experimental results.

Many neurons in the brain, such as place cells in the rodent hippocampus, have localized receptive fields, i.e., they respond to a small neighborhood of stimulus space. What is the functional significance of such representations and how can they arise? Here, we propose that localized receptive fields emerge in similarity-preserving networks of rectifying neurons that learn low-dimensional manifolds populated by sensory inputs. Numerical simulations of such networks on standard datasets yield manifold-tiling localized receptive fields. More generally, we show analytically that, for data lying on symmetric manifolds, optimal solutions of objectives, from which similarity-preserving networks are derived, have localized receptive fields. Therefore, nonnegative similarity-preserving mapping (NSM) implemented by neural networks can model representations of continuous manifolds in the brain.

Supervised learning approaches to text classification are in practice often required to work with small and unsystematically collected training sets. The alternative to supervised learning is usually viewed to be building classifiers by hand, using a domain expert's understanding of which features of the text are related to the class of interest. This is expensive, requires a degree of sophistication about linguistics and classification, and makes it difficult to use combinations of weak predictors. We propose instead combining domain knowledge with training examples in a Bayesian framework. Domain knowledge is used to specify a prior distribution for the parameters of a logistic regression model, and labeled training data is used to produce a posterior distribution, whose mode we take as the final classifier. We show on three text categorization data sets that this approach can rescue what would otherwise be disastrously bad training situations, producing much more effective classifiers.

Abstract-A key step in insect olfaction is the transformation of a dense representation of odors in a small population of neurons -projection neurons (PNs) of the antennal lobe -into a sparse representation in a much larger population of neuronsKenyon cells (KCs) of the mushroom body. What computational purpose does this transformation serve? We propose that the PN-KC network implements an online clustering algorithm which we derive from the k-means cost function. The vector of PN-KC synaptic weights converging onto a given KC represents the corresponding cluster centroid. KC activities represent attribution indices, i.e. the degree to which a given odor presentation is attributed to each cluster. Remarkably, such clustering view of the PN-KC circuit naturally accounts for several of its salient features. First, attribution indices are nonnegative thus rationalizing rectification in KCs. Second, the constraint on the total sum of attribution indices for each presentation is enforced by a Lagrange multiplier identified with the activity of a single inhibitory interneuron reciprocally connected with KCs. Third, the soft-clustering version of our algorithm reproduces observed sparsity and overcompleteness of the KC representation which may optimize supervised classification downstream.