We design a new learning algorithm for the Set Covering Machine from a PAC-Bayes perspective and propose a PAC-Bayes risk bound which is minimized for classifiers achieving a non trivial margin-sparsity tradeoff.

Long-distance language modeling is important not only in speech recognition and machine translation, but also in high-dimensional discrete sequence modeling in general. However, the problem of context length has almost been neglected so far and a naïve bag-of-words history has been employed in natural language processing. In contrast, in this paper we view topic shifts within a text as a latent stochastic process to give an explicit probabilistic generative model that has partial exchangeability. We propose an online inference algorithm using particle filters to recognize topic shifts to employ the most appropriate length of context automatically. Experiments on the BNC corpus showed consistent improvement over previous methods involving no chronological order.

We considered a gamma distribution of interspike intervals as a statistical model for neuronal spike generation. The model parameters consist of a time-dependent firing rate and a shape parameter that characterizes spiking irregularities of individual neurons. Because the environment changes with time, observed data are generated from the time-dependent firing rate, which is an unknown function. A statistical model with an unknown function is called a semiparametric model, which is one of the unsolved problem in statistics and is generally very difficult to solve. We used a novel method of estimating functions in information geometry to estimate the shape parameter without estimating the unknown function. We analytically obtained an optimal estimating function for the shape parameter independent of the functional form of the firing rate. This estimation is efficient without Fisher information loss and better than maximum likelihood estimation.

We describe a novel method for learning templates for recognition and localization of objects drawn from categories. A generative model represents the configuration of multiple object parts with respect to an object coordinate system; these parts in turn generate image features. The complexity of the model in the number of features is low, meaning our model is much more efficient to train than comparative methods. Moreover, a variational approximation is introduced that allows learning to be orders of magnitude faster than previous approaches while incorporating many more features.

There have been many graph-based approaches for semi-supervised classification. One problem is that of hyperparameter learning: performance depends greatly on the hyperparameters of the similarity graph, transformation of the graph Laplacian and the noise model. We present a Bayesian framework for learning hyperparameters for graph-based semisupervised classification. Given some labeled data, which can contain inaccurate labels, we pose the semi-supervised classification as an inference problem over the unknown labels. Expectation Propagation is used for approximate inference and the mean of the posterior is used for classification. The hyperparameters are learned using EM for evidence maximization. We also show that the posterior mean can be written in terms of the kernel matrix, providing a Bayesian classifier to classify new points. Tests on synthetic and real datasets show cases where there are significant improvements in performance over the existing approaches.

We present a competitive analysis of some nonparametric Bayesian algorithms in a worst-case online learning setting, where no probabilistic assumptions about the generation of the data are made. We consider models which use a Gaussian process prior (over the space of all functions) and provide bounds on the regret (under the log loss) for commonly used nonparametric Bayesian algorithms -- including Gaussian regression and logistic regression -- which show how these algorithms can perform favorably under rather general conditions. These bounds explicitly handle the infinite dimensionality of these nonparametric classes in a natural way. We also make formal connections to the minimax and minimum description length (MDL) framework. Here, we show precisely how Bayesian Gaussian regression is a minimax strategy.

Nested sampling is a new Monte Carlo method by Skilling [1] intended for general Bayesian computation. Nested sampling provides a robust alternative to annealing-based methods for computing normalizing constants. It can also generate estimates of other quantities such as posterior expectations. The key technical requirement is an ability to draw samples uniformly from the prior subject to a constraint on the likelihood. We provide a demonstration with the Potts model, an undirected graphical model.

We study the problem of maximum entropy density estimation in the presence of known sample selection bias. We propose three bias correction approaches. The first one takes advantage of unbiased sufficient statistics which can be obtained from biased samples. The second one estimates the biased distribution and then factors the bias out. The third one approximates the second by only using samples from the sampling distribution. We provide guarantees for the first two approaches and evaluate the performance of all three approaches in synthetic experiments and on real data from species habitat modeling, where maxent has been successfully applied and where sample selection bias is a significant problem.

We present a Bayesian framework for explaining how people reason about and predict the actions of an intentional agent, based on observing its behavior. Action-understanding is cast as a problem of inverting a probabilistic generative model, which assumes that agents tend to act rationally in order to achieve their goals given the constraints of their environment. Working in a simple sprite-world domain, we show how this model can be used to infer the goal of an agent and predict how the agent will act in novel situations or when environmental constraints change. The model provides a qualitative account of several kinds of inferences that preverbal infants have been shown to perform, and also fits quantitative predictions that adult observers make in a new experiment.

Theories of visual attention commonly posit that early parallel processes extract conspicuous features such as color contrast and motion from the visual field. These features are then combined into a saliency map, and attention is directed to the most salient regions first. Top-down attentional control is achieved by modulating the contribution of different feature types to the saliency map. A key source of data concerning attentional control comes from behavioral studies in which the effect of recent experience is examined as individuals repeatedly perform a perceptual discrimination task (e.g., "what shape is the odd-colored object?"). The robust finding is that repetition of features of recent trials (e.g., target color) facilitates performance. We view this facilitation as an adaptation to the statistical structure of the environment. We propose a probabilistic model of the environment that is updated after each trial. Under the assumption that attentional control operates so as to make performance more efficient for more likely environmental states, we obtain parsimonious explanations for data from four different experiments. Further, our model provides a rational explanation for why the influence of past experience on attentional control is short lived.