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Dörthe Malzahn

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5 papers

1 author row

JMLR Journal 2003 Journal Article

An Approximate Analytical Approach to Resampling Averages (Kernel Machines Section)

Dörthe Malzahn
Manfred Opper

Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica "trick" of statistical physics and the TAP approach for approximate Bayesian inference. We demonstrate our approach on regression with Gaussian processes. A comparison with averages obtained by Monte-Carlo sampling shows that our method achieves good accuracy. [abs] [ pdf ][ ps.gz ][ ps ]

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NeurIPS Conference 2003 Conference Paper

Approximate Analytical Bootstrap Averages for Support Vector Classifiers

Dörthe Malzahn
Manfred Opper

We compute approximate analytical bootstrap averages for support vec- tor classiﬁcation using a combination of the replica method of statistical physics and the TAP approach for approximate inference. We test our method on a few datasets and compare it with exact averages obtained by extensive Monte-Carlo sampling.

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NeurIPS Conference 2002 Conference Paper

A Statistical Mechanics Approach to Approximate Analytical Bootstrap Averages

Dörthe Malzahn
Manfred Opper

We apply the replica method of Statistical Physics combined with a vari- ational method to the approximate analytical computation of bootstrap averages for estimating the generalization error. We demonstrate our ap- proach on regression with Gaussian processes and compare our results with averages obtained by Monte-Carlo sampling.

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NeurIPS Conference 2001 Conference Paper

A Variational Approach to Learning Curves

Dörthe Malzahn
Manfred Opper

We combine the replica approach from statistical physics with a varia- tional approach to analyze learning curves analytically. We apply the method to Gaussian process regression. As a main result we derive ap- proximative relations between empirical error measures, the generaliza- tion error and the posterior variance.

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NeurIPS Conference 2000 Conference Paper

Learning Curves for Gaussian Processes Regression: A Framework for Good Approximations

Dörthe Malzahn
Manfred Opper

Based on a statistical mechanics approach, we develop a method for approximately computing average case learning curves for Gaus(cid: 173) sian process regression models. The approximation works well in the large sample size limit and for arbitrary dimensionality of the input space. We explain how the approximation can be systemati(cid: 173) cally improved and argue that similar techniques can be applied to general likelihood models.

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