The topic of this seminar is the application of the iterated posterior linearisation technique to classification using Gaussian process. The seminar will first cover the iterated posterior linearisation technique in nonlinear Bayesian inference using Gaussian distributions. This technique was originally introduced to improve non-linear Gaussian filters, such as the extended Kalman filter (EKF) or unscented Kalman filter (UKF), to deal with significant nonlinearities. To date, this Bayesian inference technique has been extended to be able to deal with Bayesian smoothing, belief propagation, simultaneous localisation and mapping, and machine learning classification using Gaussian processes. The second part of this seminar will focus on the application of the iterated posterior linearisation technique to Gaussian process classification, and its comparison with expectation propagation (EP) and Laplace methods. The contents of this seminar will be mainly based on the papers: [1] Á. F. García-Fernández, F. Tronarp and S. Särkkä, "Gaussian Process Classification Using Posterior Linearization," in IEEE Signal Processing Letters, vol. 26, no. 5, pp. 735-739, May 2019. [2] F. Tronarp, A. F. García-Fernández, S. Särkkä, "Iterative filtering and smoothing In non-Linear and non-Gaussian systems using conditional moments,” IEEE Signal Processing Letters, vol. 25, no. 3, pp. 408-412, March 2018. [3] Á. F. García-Fernández, L. Svensson, M. R. Morelande and S. Särkkä, "Posterior Linearization Filter: Principles and Implementation Using Sigma Points," in IEEE Transactions on Signal Processing, vol. 63, no. 20, pp. 5561-5573, Oct.15, 2015.
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