1 SUMMARY Kernel models for classification and regression have emerged as widely applied tools in statistics and machine learning. We discuss a Bayesian framework and theory for kernel methods, providing a new rationalisation of kernel regression based on non-parametric Bayesian models. Functional analytic results ensure that such a non-parametric prior specification induces a class of function...

Abstract. The area under the curve (AUC) measures such as the area under the receiver operating characteristics curve (AUROC) and the area under the precision-recall curve (AUPR) are known to be more appropriate than the error rate, especially, for imbalanced data sets. There are several algorithms to optimize AUC measures instead of minimizing the error rate. However, this idea has not been fu...

Kernel models for classification and regression have emerged as widely applied tools in statistics and machine learning. We discuss a Bayesian framework and theory for kernel methods, providing a new rationalization of kernel regression based on nonparametric Bayesian models. Functional analytic results ensure that such a nonparametric prior specification induces a class of functions that span ...

Graph signals arise from physical networks, such as power and communication systems, or a result of convenient representation data with complex structure, social networks. We consider the problem general graph signal recovery noisy, corrupted, incomplete measurements under structural parametric constraints, smoothness in frequency domain. In this paper, we formulate non-Bayesian estimation weig...

Bayesian network models provide an attractive framework for multimodal sensor fusion. They combine an intuitive graphical representation with efficient algorithms for inference and learning. However, the unsupervised nature of standard parameter learning algorithms for Bayesian networks can lead to poor performance in classification tasks. We have developed a supervised learning framework for B...

We propose a Bayesian framework for assessing the relative strengths of data-driven ambiguity sets in distributionally robust optimization (DRO) when the underlying distribution is defined by a finite-dimensional parameter. The key idea is to measure the relative size between a candidate ambiguity set and a specific asymptotically optimal set. As the amount of data grows large, this asymptotica...