A New Accurate Approximation for the Gaussian Process Classification Problem

Gaussian processes is a very promising novel technology that has been applied for both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the classification case. The reason is that we encounter intractable integrals. In this paper we propose a new approximate solution for the Gaussian process classification problem. The approximating formula is based on certain transformations of the variables and manipulations that lead to orthant multivariate Gaussian integrals. An approximation is then applied that leads to a very simple formula. In spite of its simplicity, the formula gives better results in terms of classification accuracy and speed compared to some of the well-known competing methods.