Stability-based model selection

Model selection is linked to model assessment, which is the problem of comparing different models, or model parameters, for a specific learning task. For supervised learning, the standard practical technique is crossvalidation, which is not applicable for semi-supervised and unsupervised settings. In this paper, a new model assessment scheme is introduced which is based on a notion of stability. The stability measure yields an upper bound to cross-validation in the supervised case, but extends to semi-supervised and unsupervised problems. In the experimental part, the performance of the stability measure is studied for model order selection in comparison to standard techniques in this area.

The need for open source software in machine learning

Open source tools have recently reached a level of maturity which makes them suitable for building large-scale real-world systems. At the same time, the field of machine learning has developed a large body of powerful learning algorithms for diverse applications. However, the true potential of these methods is not used, since existing implementations are not openly shared, resulting in software with low usability, and weak interoperability. We argue that this situation can be significantly improved by increasing incentives for researchers to publish their software under an open source model. Additionally, we outline the problems authors are faced with when trying to publish algorithmic implementations of machine learning methods. We believe that a resource of peer reviewed software accompanied by short articles would be highly valuable to both the machine learning and the general scientific community

Accurate Error Bounds for the Eigenvalues of the Kernel Matrix

The eigenvalues of the kernel matrix play an important role in a number of kernel methods, in particular, in kernel principal component analysis. It is well known that the eigenvalues of the kernel matrix converge as the number of samples tends to infinity. We derive probabilistic finite sample size bounds on the approximation error of individual eigenvalues which have the important property that the bounds scale with the eigenvalue under consideration, reflecting the actual behavior of the approximation errors as predicted by asymptotic results and observed in numerical simulations. Such scalin

J.M.: The noisy euclidean traveling salesman problem and learning

We consider noisy Euclidean traveling salesman problems in the plane, which are random combinatorial problems with underlying structure. Gibbs sampling is used to compute average trajectories, which estimate the underlying structure common to all instances. This procedure requires identifying the exact relationship between permutations and tours. In a learning setting, the average trajectory is used as a model to construct solutions to new instances sampled from the same source. Experimental results show that the average trajectory can in fact estimate the underlying structure and that overfitting effects occur if the trajectory adapts too closely to a single instance.

Denoising and Dimension . . .

We show that the relevant information about a classification problem in feature space is contained up to negligible error in a finite number of leading kernel PCA components if the kernel matches the underlying learning problem. Thus, kernels not only transform data sets such that good generalization can be achieved even by linear discriminant functions, but this transformation is also performed in a manner which makes economic use of feature space dimensions. In the best case, kernels provide efficient implicit representations of the data to perform classification. Practically, we propose an algorithm which enables us to recover the subspace and dimensionality relevant for good classification. Our algorithm can therefore be applied (1) to analyze the interplay of data set and kernel in a geometric fashion, (2) to help in model selection, and to (3) de-noise in feature space in order to yield better classification results