We formulate the problem of graph inference where part of the graph is known as a supervised learning problem, and propose an algorithm to solve it. The method involves the learning of a mapping of the vertices to a Euclidean space where the graph is easy to infer, and can be formulated as an optimization problem in a reproducing kernel Hilbert space. We report encouraging results on the problem of metabolic network reconstruction from genomic data.

We propose the hierarchical Dirichlet process (HDP), a nonparametric Bayesian model for clustering problems involving multiple groups of data. Each group of data is modeled with a mixture, with the number of components being open-ended and inferred automatically by the model. Further, components can be shared across groups, allowing dependencies across groups to be modeled effectively as well as conferring generalization to new groups. Such grouped clustering problems occur often in practice, e.g. in the problem of topic discovery in document corpora. We report experimental results on three text corpora showing the effective and superior performance of the HDP over previous models.

Go is an ancient oriental game whose complexity has defeated attempts to automate it. We suggest using probability in a Bayesian sense to model the uncertainty arising from the vast complexity of the game tree. We present a simple conditional Markov random field model for predicting the pointwise territory outcome of a game. The topology of the model reflects the spatial structure of the Go board. We describe a version of the Swendsen-Wang process for sampling from the model during learning and apply loopy belief propagation for rapid inference and prediction. The model is trained on several hundred records of professional games. Our experimental results indicate that the model successfully learns to predict territory despite its simplicity.

We establish learning rates to the Bayes risk for support vector machines (SVMs) with hinge loss. In particular, for SVMs with Gaussian RBF kernels we propose a geometric condition for distributions which can be used to determine approximation properties of these kernels. Finally, we compare our methods with a recent paper of G. Blanchard et al..

We show that anomaly detection can be interpreted as a binary classification problem. Using this interpretation we propose a support vector machine (SVM) for anomaly detection. We then present some theoretical results which include consistency and learning rates. Finally, we experimentally compare our SVM with the standard one-class SVM.

We present a novel approach to collaborative prediction, using low-norm instead of low-rank factorizations. The approach is inspired by, and has strong connections to, large-margin linear discrimination. We show how to learn low-norm factorizations by solving a semi-definite program, and discuss generalization error bounds for them.

Semantic taxonomies such as WordNet provide a rich source of knowledge for natural language processing applications, but are expensive to build, maintain, and extend. Motivated by the problem of automatically constructing and extending such taxonomies, in this paper we present a new algorithm for automatically learning hypernym (isa) relations from text. Our method generalizes earlier work that had relied on using small numbers of handcrafted regular expression patterns to identify hypernym pairs. Using "dependency path" features extracted from parse trees, we introduce a general-purpose formalization and generalization of these patterns. Given a training set of text containing known hypernym pairs, our algorithm automatically extracts useful dependency paths and applies them to new corpora to identify novel pairs. On our evaluation task (determining whether two nouns in a news article participate in a hypernym relationship), our automatically extracted database of hypernyms attains both higher precision and higher recall than WordNet.

We devise and experiment with a dynamical kernel-based system for tracking hand movements from neural activity. The state of the system corresponds to the hand location, velocity, and acceleration, while the system's input are the instantaneous spike rates. The system's state dynamics is defined as a combination of a linear mapping from the previous estimated state and a kernel-based mapping tailored for modeling neural activities. In contrast to generative models, the activity-to-state mapping is learned using discriminative methods by minimizing a noise-robust loss function. We use this approach to predict hand trajectories on the basis of neural activity in motor cortex of behaving monkeys and find that the proposed approach is more accurate than both a static approach based on support vector regression and the Kalman filter.

Decision trees are surprisingly adaptive in three important respects: They automatically (1) adapt to favorable conditions near the Bayes decision boundary; (2) focus on data distributed on lower dimensional manifolds; (3) reject irrelevant features. In this paper we examine a decision tree based on dyadic splits that adapts to each of these conditions to achieve minimax optimal rates of convergence. The proposed classifier is the first known to achieve these optimal rates while being practical and implementable.

We present a novel method for learning with Gaussian process regression in a hierarchical Bayesian framework. In a first step, kernel matrices on a fixed set of input points are learned from data using a simple and efficient EM algorithm. This step is nonparametric, in that it does not require a parametric form of covariance function. In a second step, kernel functions are fitted to approximate the learned covariance matrix using a generalized Nystr om method, which results in a complex, data driven kernel. We evaluate our approach as a recommendation engine for art images, where the proposed hierarchical Bayesian method leads to excellent prediction performance.