Laplace Approximation Inference for Multivariate Gaussian Process Classification Model With Multiclass
Wanhyun Cho, Sanggyun Kim, Soonyoung Park · ITC-CSCC :International Technical Conference on Circuits Systems, Computers and Communications · 2015
We provide a comprehensive algorithm for Laplace approximate inference in multivariate Gaussian process classification model with multiclass. First, we have derived the posterior distribution of the latent function representing each class of observation based on the training data by using the Bayesian theorem and Laplace approximation, and compute its mode and the covariance matrix. Further, we calculate the marginal distribution of the class indicator vector for observations. Second, we have also derived the predictive distribution of the latent function corresponding to the new input vector by using the existing training data as well as the new input vector. Next, we generate the n random samples from the predictive distribution of latent function corresponding to input vector. Further, we calculate the estimate of the classification probability by using the formula of the link function on the basis of generated random samples. Finally, we will classify the input vector to the class which its classification probability is maximized.