In this report we show some consequences of the work done by Pontil et al. in 1]. In particular we show that in the same hypotheses of the theorem proved in their paper, the optimal approximating hyperplane f R found by SVM regression classiies the data. This means that y i f R (x i) > 0 for points which live externally to the margin between the two classes or points which live internally to th...

We investigate the convergence properties of heuristic matrix relevance updates in Learning Vector Quantization. Under mild assumptions on the training process, stationarity conditions can be worked out which characterize the outcome of training in terms of the relevance matrix. It is shown that the original training schemes single out one specific direction in feature space which depends on th...

Harris Drucker [email protected] AT&T Research and Monmouth University, West Long Branch, NJ 07764, USA Behzad Shahrary [email protected] David C. Gibbon [email protected] AT&T Research, 200 Laurel Ave., Middletown, NJ, 07748, USA. Correspondence should be addressed to: Dr. Harris Drucker Monmouth University West Long Branch, NJ 07764 phone: 732-571-3698 email: [email protected] ...

We adopt the Relevance Vector Machine (RVM) framework to handle cases of tablestructured data such as image blocks and image descriptors. This is achieved by coupling the regularization coefficients of rows and columns of features. We present two variants of this new gridRVM framework, based on the way in which the regularization coefficients of the rows and columns are combined. Appropriate va...

In recent years, learning ranking function for information retrieval has drawn the attentions of the researchers from information retrieval and machine learning community. In existing approaches of learning to rank, the sparse prediction model only can be learned by support vector learning approach. However, the number of support vectors grows steeply with the size of the training data set. In ...

Recently, sparse kernel methods such as the Relevance Vector Machine (RVM) have become very popular for solving regression problems. The sparsity and performance of these methods depend on selecting an appropriate kernel function, which is typically achieved using a cross-validation procedure. In this paper we propose a modification to the incremental RVM learning method, that also learns the l...

Function approximation methods, such as neural networks, radial basis functions, and support vector machines, have been used in reinforcement learning to deal with large state spaces. However, they can become unstable with changes in the samples state distributions and require many samples for good estimations of value functions. Recently, Bayesian approaches to reinforcement learning have show...

We investigate the effect of several adaptive metrics in the context of figure-ground segregation, using Generalized LVQ to train a classifier for image regions. Extending the Euclidean metrics towards local matrices of relevance-factors does not only lead to a higher classification accuracy and increased robustness on heterogeneous/noisy data, but also figureground segregation using this adapt...