Mikio L. Braun

ICML Conference 2015 Conference Paper

Hidden Markov Anomaly Detection

• Nico Görnitz
• Mikio L. Braun
• Marius Kloft

We introduce a new anomaly detection methodology for data with latent dependency structure. As a particular instantiation, we derive a hidden Markov anomaly detector that extends the regular one-class support vector machine. We optimize the approach, which is non-convex, via a DC (difference of convex functions) algorithm, and show that the parameter v can be conveniently used to control the number of outliers in the model. The empirical evaluation on artificial and real data from the domains of computational biology and computational sustainability shows that the approach can achieve significantly higher anomaly detection performance than the regular one-class SVM.

ICML Conference 2012 Conference Paper

Canonical Trends: Detecting Trend Setters in Web Data

• Felix Bießmann
• Jens-Michalis Papaioannou
• Mikio L. Braun
• Andreas Harth

JMLR Journal 2011 Journal Article

Kernel Analysis of Deep Networks

• Grégoire Montavon
• Mikio L. Braun
• Klaus-Robert Müller

When training deep networks it is common knowledge that an efficient and well generalizing representation of the problem is formed. In this paper we aim to elucidate what makes the emerging representation successful. We analyze the layer-wise evolution of the representation in a deep network by building a sequence of deeper and deeper kernels that subsume the mapping performed by more and more layers of the deep network and measuring how these increasingly complex kernels fit the learning problem. We observe that deep networks create increasingly better representations of the learning problem and that the structure of the deep network controls how fast the representation of the task is formed layer after layer. [abs] [ pdf ][ bib ] &copy JMLR 2011. ( edit, beta )

JMLR Journal 2008 Journal Article

On Relevant Dimensions in Kernel Feature Spaces

• Mikio L. Braun
• Joachim M. Buhmann
• Klaus-Robert Müller

We show that the relevant information of a supervised learning problem is contained up to negligible error in a finite number of leading kernel PCA components if the kernel matches the underlying learning problem in the sense that it can asymptotically represent the function to be learned and is sufficiently smooth. Thus, kernels do not only transform data sets such that good generalization can be achieved using only linear discriminant functions, but this transformation is also performed in a manner which makes economical use of feature space dimensions. In the best case, kernels provide efficient implicit representations of the data for supervised learning problems. Practically, we propose an algorithm which enables us to recover the number of leading kernel PCA components 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 aid in model selection, and (3) to denoise in feature space in order to yield better classification results. [abs] [ pdf ][ bib ] &copy JMLR 2008. ( edit, beta )

ICML Conference 2007 Conference Paper

Kernelizing PLS, degrees of freedom, and efficient model selection

• Nicole Krämer 0002
• Mikio L. Braun

JMLR Journal 2007 Journal Article

The Need for Open Source Software in Machine Learning

• Sören Sonnenburg
• Mikio L. Braun
• Cheng Soon Ong
• Samy Bengio
• Leon Bottou
• Geoffrey Holmes
• Yann LeCun
• Klaus-Robert Müller

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. [abs] [ pdf ][ bib ] &copy JMLR 2007. ( edit, beta )

JMLR Journal 2006 Journal Article

Accurate Error Bounds for the Eigenvalues of the Kernel Matrix

• Mikio L. Braun

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 scaling bounds have so far only been known for tail sums of eigenvalues. Asymptotically, the bounds presented here have a slower than stochastic rate, but the number of sample points necessary to make this disadvantage noticeable is often unrealistically large. Therefore, under practical conditions, and for all but the largest few eigenvalues, the bounds presented here form a significant improvement over existing non-scaling bounds. [abs] [ pdf ][ bib ] &copy JMLR 2006. ( edit, beta )