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Journals and Conferences
Based on a statistical mechanics approach, we develop a method for approximately computing average case learning curves for Gaussian 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 systematically improved and argue that similar… (More)
We combine the replica approach from statistical physics with a variational approach to analyze learning curves analytically. We apply the method to Gaussian process regression. As a main result we derive approximative relations between empirical error measures, the generalization error and the posterior variance.
Processes: A Statistical Mechanics Study Dörthe Malzahn, Manfred Opper (1) Informatics and Mathematical Modelling, Technical University of Denmark, Richard-Petersens-Plads Building 321, DK-2800 Lyngby, Denmark (2) School of Engineering and Applied Science / NCRG, Aston University, Birmingham B4 7ET, United Kingdom (Dated: May 27, 2002) Abstract We employ… (More)
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… (More)
We compute approximate analytical bootstrap averages for support vector 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.
Using a variational technique, we generalize the statistical physics approach of learning from random examples to make it applicable to real data. We demonstrate the validity and relevance of our method by computing approximate estimators for generalization errors that are based on training data alone.
We apply the replica method of Statistical Physics combined with a variational method to the approximate analytical computation of bootstrap averages for estimating the generalization error. We demonstrate our approach on regression with Gaussian processes and compare our results with averages obtained by Monte-Carlo sampling.
Studies in 15 industries revealed characteristic empirical relationships between workplace environmental conditions and outside weather conditions. These relationships, expressed in the form of predictive models for Wet Bulb Globe Temperature, can be used to estimate WBGT from weather forecasts, weather reports, or current meterorological measurements.