We apply Stochastic Meta-Descent (SMD), a stochastic gradient optimization method with gain vector adaptation, to the training of Conditional Random Fields (CRFs). On several large data sets, the resulting optimizer converges to the same quality of solution over an order of magnitude faster than limited-memory BFGS, the leading method reported to date. We report results for both exact and inexact inference techniques. 1.

We develop gain adaptation methods that improve convergence of the kernel Hebbian algorithm (KHA) for iterative kernel PCA (Kim et al., 2005). KHA has a scalar gain parameter which is either held constant or decreased according to a predetermined annealing schedule, leading to slow convergence. We accelerate it by incorporating the reciprocal of the current estimated eigenvalues as part of a gain vector. An additional normalization term then allows us to eliminate a tuning parameter in the annealing schedule. Finally we derive and apply stochastic meta-descent (SMD) gain vector adaptation (Schraudolph, 1999, 2002) in reproducing kernel Hilbert space to further speed up convergence. Experimental results on kernel PCA and spectral clustering of USPS digits, motion capture and image denoising, and image super-resolution tasks confirm that our methods converge substantially faster than conventional KHA. To demonstrate scalability, we perform kernel PCA on the entire MNIST data set.

Abstract. In many applicative contexts in which textual documents are labelled with thematic categories, a distinction is made between the primary categories of a document, which represent the topics that are central to it, and and its secondary categories, which represent topics that the document only touches upon. We contend that this distinction, so far neglected in text categorization research, is important and deserves to be explicitly tackled. The contribution of this paper is three-fold. First, we propose an evaluation measure for this preferential text categorization task, whereby different kinds of misclassifications involving either primary or secondary categories have a different impact on effectiveness. Second, we establish several baseline results for this task on a well-known benchmark for patent classification in which the distinction between primary and secondary categories is present; these results are obtained by reformulating the preferential text categorization task in terms of well established classification problems, such as single and/or multi-label multiclass classification; state-of-the-art learning technology such as SVMs and kernel-based methods are used. Third, we improve on these results by using a recently proposed class of algorithms explicitly devised for learning from training data expressed in

We introduce two methods to improve convergence of the Kernel Hebbian Algorithm (KHA) for iterative kernel PCA. KHA has a scalar gain parameter which is either held constant or decreased as 1/t, leading to slow convergence. Our KHA/et algorithm accelerates KHA by incorporating the reciprocal of the current estimated eigenvalues as a gain vector. We then derive and apply Stochastic Meta-Descent (SMD) to KHA/et; this further speeds convergence by performing gain adaptation in RKHS. Experimental results for kernel PCA and spectral clustering of USPS digits as well as motion capture and image de-noising problems confirm that our methods converge substantially faster than conventional KHA. 1

Recent approaches to independent component analysis have used kernel independence measures to obtain very good performance in ICA, particularly in areas where classical methods experience difficulty (for instance, sources with near-zero kurtosis). In this chapter, we compare two efficient extensions of these methods for large-scale problems: random subsampling of entries in the Gram matrices used in defining the independence measures, and incomplete Cholesky decomposition of these matrices. We derive closed-form, efficiently computable approximations for the gradients of these measures, and compare their performance on ICA using both artificial and music data. We show that kernel ICA can scale up to larger problems than yet attempted, and that incomplete Cholesky decomposition performs better than random sampling.