This article discusses the Gaussian Process Latent Variable Model, which is detailed in Section 15.5 of the book ‘Machine Learning: A Probabilistic Perspective’ by Kevin P. Murphy. The article explains the log-likelihood objective function and how it can be used to calculate the partial derivatives of the log-likelihood with respect to the latent variables. The author explains how equations 6 and 7 can be used to derive equation 4, and questions the validity of equation 5.
