March 2010

Structured prediction tasks pose a fundamental trade-off between the need for model complexity to increase predictive power and the limited computational resources for inference in the exponentially-sized output spaces such models require. We formulate and develop structured prediction cascades: a sequence of increasingly complex models that progressively filter the space of possible outputs. We represent an exponentially large set of filtered outputs using max marginals and propose a novel convex loss function that balances filtering error with filtering […]

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Latent variable models represent hidden structure in observational data.To account for the distribution of the observational data changing over time, space or some other covariate, we need generalizations of latent variable models that explicitly capture this dependency on the covariate. A variety of such generalizations has been proposed for latent variable models based on the Dirichlet process. We address dependency on covariates in binary latent feature models, by introducing a dependent Indian buffet process. The model generates, for […]

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Supervised learning from multiple labeling sources is an increasingly important problem in machine learning and data mining. This paper develops a probabilistic approach to this problem when annotators may be unreliable (labels are noisy), but also their expertise varies depending on the data they observe (annotators may have knowledge about different parts of the input space). That is, an annotator may not be consistently accurate (or inaccurate) across the task domain. The presented approach produces classification and annotator […]

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Projection Reconstruction Nuclear Magnetic Resonance (PR-NMR) is a new technique to generate multi-dimensional NMR spectra, which have discrete features that are relatively sparsely distributed in space. A small number of projections from lower dimensional NMR spectra are used to reconstruct the multi-dimensional NMR spectra. We propose an efficient algorithm which employs a blocked Gibbs sampler to accurately reconstruct NMR spectra. This statistical method generates samples in Bayesian scheme. Our proposed algorithm is tested on a set of six […]

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Levy processes play an important role in the stochastic process theory. However, since samples are non-i.i.d., statistical learning results based on the i.i.d. scenarios cannot be utilized to study the risk bounds for Levy processes. In this paper, we present risk bounds for non-i.i.d. samples drawn from Levy processes in the PAC-learning framework. In particular, by using a concentration inequality for infinitely divisible distributions, we first prove that the function of risk error is Lipschitz continuous with a […]

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Many real world applications employ multi-variate performance measures and each example can belong to multiple classes. The currently most popular approaches train an SVM for each class, followed by ad hoc thresholding. Probabilistic models using Bayesian decision theory are also commonly adopted. In this paper, we propose a Bayesian online multi-label classification framework (BOMC) which learns a probabilistic linear classifier. The likelihood is modeled by a graphical model similar to TrueSkill$^text{TM}$, and inference is based on Gaussian density […]

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Multi-task learning seeks to improve the generalization performance of a learning task with the help of other related learning tasks. Among the multi-task learning methods proposed thus far, Bonilla et al.’s method provides a novel multi-task extension of Gaussian process (GP) by using a task covariance matrix to model the relationships between tasks. However, learning the task covariance matrix directly has both computational and representational drawbacks. In this paper, we propose a Bayesian extension by modeling the task […]

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We propose a fully Bayesian approach for generalized kernel models (GKMs), which are extensions of generalized linear models in the feature space induced by a reproducing kernel. We place a mixture of a point-mass distribution and Silverman’s g-prior on the regression vector of GKMs. This mixture prior allows a fraction of the regression vector to be zero. Thus, it serves for sparse modeling and Bayesian computation. For inference, we exploit data augmentation methodology to develop a Markov chain […]

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We are concerned with a multivariate response regression problem where the interest is in considering correlations both across response variates and across response samples. In this paper we develop a new Bayesian nonparametric model for such a setting based on Dirichlet process priors. Building on an additive kernel model, we allow each sample to have its own regression matrix. Although this overcomplete representation could in principle suffer from severe overfitting problems, we are able to provide effective control […]

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We propose a novel group regularization which we call exclusive lasso. Unlike the group lasso regularizer that assumes co-varying variables in groups, the proposed exclusive lasso regularizer models the scenario when variables in the same group compete with each other. Analysis is presented to illustrate the properties of the proposed regularizer. We present a framework of kernel-based multi-task feature selection algorithm based on the proposed exclusive lasso regularizer. An efficient algorithm is derived to solve the related optimization […]

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