Given an $n$-vertex weighted tree with structural diameter $S$ and a subset of $m$ vertices, we present a technique to compute a corresponding $m \times m$ Gram matrix of the pseudoinverse of the graph Laplacian in $O(n+ m^2 + m S)$ time. We discuss the application of this technique to fast label prediction on a generic graph. We approximate the graph with a spanning tree and then we predict with the kernel perceptron. We address the approximation of the graph with either a minimum spanning tree or a shortest path tree. The fast computation of the pseudoinverse enables us to address prediction problems on large graphs. To this end we present experiments on two web-spam classification tasks, one of which includes a graph with 400,000 nodes and more than 10,000,000 edges. The results indicate that the accuracy of our technique is competitive with previous methods using the full graph information.

Discriminative tasks, including object categorization and detection, are central components of high-level computer vision. Sometimes, however, we are interested inmore refined aspects of the object in an image, such as pose or particular regions. In this paper we develop a method (LOOPS) for learning a shape and image feature model that can be trained on a particular object class, and used to outline instances of the class in novel images. Furthermore, while the training data consists of uncorresponded outlines, the resulting LOOPS model contains a set of landmark points that appear consistently across instances, and can be accurately localized in an image. Our model achieves state-of-the-art results in precisely outlining objectsthat exhibit large deformations and articulations in cluttered natural images. These localizations can then be used to address a range of tasks, including descriptive classification, search, and clustering.

Adaptation of visually guided reaching movements in novel visuomotor environments (e.g.wearing prism goggles) comprises not only motor adaptation but also substantial sensory adaptation, corresponding to shifts in the perceived spatial location of visual and proprioceptive cues. Previous computational modelsof the sensory component of visuomotor adaptation have assumed that it is driven purely by the discrepancy introduced between visual andproprioceptive estimates of hand position and is independent of any motor component of adaptation. We instead propose a unified model in which sensory and motor adaptation are jointly driven by optimal Bayesian estimation of the sensory and motor contributions to perceived errors. Our model is able to account for patterns of performance errors during visuomotor adaptationas well as the subsequent perceptual aftereffects. This unified model also makes the surprising prediction that force field adaptation willelicit similar perceptual shifts, even though there is never any discrepancy between visual and proprioceptive observations. We confirm this prediction with an experiment.

We consider the problem of binary classification where the classifier may abstain instead of classifying each observation. The Bayes decision rule for this setup, known as Chow's rule, is defined by two thresholds on posterior probabilities. From simple desiderata, namely the consistency and the sparsity of the classifier, we derive the double hinge loss function that focuses on estimating conditional probabilities only in the vicinity of the threshold points of the optimal decision rule. We show that, for suitable kernel machines, our approach is universally consistent. We cast the problem of minimizing the double hinge loss as a quadratic program akin to the standard SVM optimization problem and propose an active set method to solve it efficiently. We finally provide preliminary experimental results illustrating the interest of our constructive approach to devising loss functions.

We propose an efficient sequential Monte Carlo inference scheme for the recently proposed coalescent clustering model (Teh et al, 2008). Our algorithm has a quadratic runtime while those in (Teh et al, 2008) is cubic. In experiments, we were surprised to find that in addition to being more efficient, it is also a better sequential Monte Carlo sampler than the best in (Teh et al, 2008), when measured in terms of variance of estimated likelihood and effective sample size.

In this paper we propose a new incremental spike sorting model that automatically eliminates refractory period violations, accounts for action potential waveform drift, and can handle appearance" and "disappearance" of neurons. Our approach is to augment a known time-varying Dirichlet process that ties together a sequence of infinite Gaussian mixture models, one per action potential waveform observation, with an interspike-interval-dependent likelihood that prohibits refractory period violations. We demonstrate this model by showing results from sorting two publicly available neural data recordings for which the a partial ground truth labeling is known."

Many nonlinear dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector autoregressive (VAR) process. In this paper, we present a nonparametric approach to the learning of an unknown number of persistent, smooth dynamical modes by utilizing a hierarchical Dirichlet process prior. We develop a sampling algorithm that combines a truncated approximation to the Dirichlet process with an efficient joint sampling of the mode and state sequences. The utility and flexibility of our model are demonstrated on synthetic data, sequences of dancing honey bees, and the IBOVESPA stock index.

With the increased availability of data for complex domains, it is desirable to learn Bayesian network structures that are sufficiently expressive for generalization while also allowing for tractable inference. While the method of thin junction trees can, in principle, be used for this purpose, its fully greedy nature makes it prone to overfitting, particularly when data is scarce. In this work we present a novel method for learning Bayesian networks of bounded treewidth that employs global structure modifications and that is polynomial in the size of the graph and the treewidth bound. At the heart of our method is a triangulated graph that we dynamically update in a way that facilitates the addition of chain structures that increase the bound on the model's treewidth by at most one. We demonstrate the effectiveness of our ``treewidth-friendly'' method on several real-life datasets. Importantly, we also show that by using global operators, we are able to achieve better generalization even when learning Bayesian networks of unbounded treewidth.

We apply robust Bayesian decision theory to improve both generative and discriminative learners under bias in class proportions in labeled training data, when the true class proportions are unknown. For the generative case, we derive an entropy-based weighting that maximizes expected log likelihood under the worst-case true class proportions. For the discriminative case, we derive a multinomial logistic model that minimizes worst-case conditional log loss. We apply our theory to the modeling of species geographic distributions from presence data, an extreme case of label bias since there is no absence data. On a benchmark dataset, we find that entropy-based weighting offers an improvement over constant estimates of class proportions, consistently reducing log loss on unbiased test data.

Is accurate classification possible in the absence of hand-labeled data?