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21
Bayesian decoding of brain images
, 2008
"... This paper introduces a multivariate Bayesian (MVB) scheme to decode or recognise brain states from neuroimages. It resolves the illposed manytoone mapping, from voxel values or data features to a target variable, using a parametric empirical or hierarchical Bayesian model. This model is inverted ..."
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Cited by 31 (2 self)
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This paper introduces a multivariate Bayesian (MVB) scheme to decode or recognise brain states from neuroimages. It resolves the illposed manytoone mapping, from voxel values or data features to a target variable, using a parametric empirical or hierarchical Bayesian model. This model is inverted using standard variational techniques, in this case expectation maximisation, to furnish the model evidence and the conditional density of the model’s parameters. This allows one to compare different models or hypotheses about the mapping from functional or structural anatomy to perceptual and behavioural consequences (or their deficits). We frame this approach in terms of decoding measured brain states to predict or classify outcomes using the rhetoric established in pattern classification of neuroimaging data. However, the aim of MVB is not to predict (because the outcomes are known) but to enable inference on different models of structure– function mappings; such as distributed and sparse representations. This allows
Bayesian Online Learning for Multilabel and Multivariate Performance Measures
"... Many real world applications employ multivariate 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 ..."
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Cited by 8 (1 self)
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Many real world applications employ multivariate 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 aBayesian online multilabel classification framework (BOMC) which learns a probabilistic linear classifier. The likelihood is modeled by a graphical model similar to TrueSkillTM, and inference is based on Gaussian density filtering with expectation propagation. Using samples from the posterior, we label the testing data by maximizing the expected F1score. Our experiments on Reuters1v2 dataset show BOMC compares favorably to the stateoftheart online learners in macroaveraged F1score and training time. 1
Outlier robust Gaussian process classification
 In Structural, Syntactic, and Statistical Pattern Recognition
, 2008
"... Abstract. Gaussian process classifiers (GPCs) are a fully statistical model for kernel classification. We present a form of GPC which is robust to labeling errors in the data set. This model allows label noise not only near the class boundaries, but also far from the class boundaries which can resul ..."
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Cited by 3 (0 self)
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Abstract. Gaussian process classifiers (GPCs) are a fully statistical model for kernel classification. We present a form of GPC which is robust to labeling errors in the data set. This model allows label noise not only near the class boundaries, but also far from the class boundaries which can result from mistakes in labelling or gross errors in measuring the input features. We derive an outlier robust algorithm for training this model which alternates iterations based on the EP approximation and hyperparameter updates until convergence. We show the usefulness of the proposed algorithm with model selection method through simulation results. 1
Learning Preferences with Hidden Common Cause Relations
"... Abstract. Gaussian processes have successfully been used to learn preferences among entities as they provide nonparametric Bayesian approaches for model selection and probabilistic inference. For many entities encountered in realworld applications, however, there are complex relations between them. ..."
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Abstract. Gaussian processes have successfully been used to learn preferences among entities as they provide nonparametric Bayesian approaches for model selection and probabilistic inference. For many entities encountered in realworld applications, however, there are complex relations between them. In this paper, we present a preference model which incorporates information on relations among entities. Specifically, we propose a probabilistic relational kernel model for preference learning based on Silva et al.’s mixed graph Gaussian processes: a new prior distribution, enhanced with relational graph kernels, is proposed to capture the correlations between preferences. Empirical analysis on the LETOR datasets demonstrates that relational information can improve the performance of preference learning. 1
Message passing algorithms for Dirichlet diffusion trees
 In Proceedings of the 28th Annual International Conference on Machine Learning
, 2011
"... We demonstrate efficient approximate inference for the Dirichlet Diffusion Tree (Neal, 2003), a Bayesian nonparametric prior over tree structures. Although DDTs provide a powerful and elegant approach for modeling hierarchies they haven’t seen much use to date. One problem is the computational co ..."
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We demonstrate efficient approximate inference for the Dirichlet Diffusion Tree (Neal, 2003), a Bayesian nonparametric prior over tree structures. Although DDTs provide a powerful and elegant approach for modeling hierarchies they haven’t seen much use to date. One problem is the computational cost of MCMC inference. We provide the first deterministic approximate inference methods for DDT models and show excellent performance compared to the MCMC alternative. We present message passing algorithms to approximate the Bayesian model evidence for a specific tree. This is used to drive sequential tree building and greedy search to find optimal tree structures, corresponding to hierarchical clusterings of the data. We demonstrate appropriate observation models for continuous and binary data. The empirical performance of our method is very close to the computationally expensive MCMC alternative on a density estimation problem, and significantly outperforms kernel density estimators. 1
Preference Learning with Extreme Examples ∗
"... In this paper, we consider a general problem of semisupervised preference learning, in which we assume that we have the information of the extreme cases and some ordered constraints, our goal is to learn the unknown preferences of the other places. Taking the potential housing place selection probl ..."
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In this paper, we consider a general problem of semisupervised preference learning, in which we assume that we have the information of the extreme cases and some ordered constraints, our goal is to learn the unknown preferences of the other places. Taking the potential housing place selection problem as an example, we have many candidate places together with their associated information (e.g., position, environment), and we know some extreme examples (i.e. several places are perfect for building a house, and several places are the worst that cannot build a house there), and we know some partially ordered constraints (i.e. for two places, which place is better), then how can we judge the preference of one potential place whose preference is unknown beforehand? We propose a Bayesian framework based on Gaussian process to tackle this problem, from which we not only solve for the unknown preferences, but also the hyperparameters contained in our model. 1
MCMC for variationally sparse Gaussian processes, arXiv:1506.04000, 2015. M. Filippone Bayesian inference for Gaussian processes
"... Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to approximate the posterior when the likelihood is not Gaussian a ..."
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Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to approximate the posterior when the likelihood is not Gaussian and how to estimate covariance function parameter posteriors. This paper simultaneously addresses these, using a variational approximation to the posterior which is sparse in support of the function but otherwise freeform. The result is a Hybrid MonteCarlo sampling scheme which allows for a nonGaussian approximation over the function values and covariance parameters simultaneously, with efficient computations based on inducingpoint sparse GPs. Code to replicate each experiment in this paper is available at github.com/sparseMCMC. 1
Relational Gaussian Processes for Learning Preference Relations
"... Preference learning has received increasing attention in both machine learning and information retrieval. The goal of preference learning is to automatically learn a model to rank entities (e.g., documents, webpages, ..."
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Preference learning has received increasing attention in both machine learning and information retrieval. The goal of preference learning is to automatically learn a model to rank entities (e.g., documents, webpages,