Extraction of the Most Sensitive Directions via Gaussian Process Modeling
Burnaev E., Erofeev P., Prikhodko P.
Poster for the conference "Uncertainties in Computer Models 2012" (Sheffield)
For many industrial problems it is necessary to reconstruct unknown dependency based on it’s values on the given sample. On of the most effective methods for solving this problem is an approximation based on gaussian processes. It’s known that one of the most popular ways to model covariation of gaussian process is exponential covariance function based on weighted Euclidean distance. However this a priory assumption about covariance structure of the data source means that directions of most significant variation of considered dependency are expected to lie along original coordinate axes. This assumption may not be satisfied in practice. We propose effective way to model covariance structure of the data for a more general case. Effective algorithm of hyperparameters tuning is described. On a number of examples it’s demonstrated that proposed method also allows to solve the problem of effective dimension reduction. Finally we propose statistical test that allows to estimate reduced dimensionality of data. All statements are justified by providing experimental results on a number of test problems.