Two Parameter Inference Methods in Likelihood-Free Models: Approximate Bayesian Computation and Contrastive Divergence.

다국어 초록 (Multilingual Abstract)

This dissertation is a summary of my three major projects in my PhD program.A version of Chapter 2 has been accepted by Statistica Sinica [Bai Jiang, Tung-Yu Wu, Charles Zheng, and Wing Hung Wong. Learning summary statistic for Approximate Bayesian Computation via deep neural network. arXiv preprint arXiv:1510.02175. 2015]. I was the first author, responsible for all major areas of concept formation, methodology, mathematical proof, experiments, data analysis, as well as the majority of manuscript composition. Wu T-Y contributed to conducting simulation experiments, and Zheng C contributed to manuscript composition and proofreading the mathematical texts in the proof. Wong WH was the supervisory author on this project and was involved throughout the project.A version of Chapter 3 has been submitted to one of the top journals in Statistics and is now available in arXiv, a repository of electronic preprints, [Tung-Yu Wu, Bai Jiang, Yifan Jin, Wing Hung Wong. Convergence of Contrastive Divergence algorithm in exponential family. arXiv preprint arXiv:1603.05729. 2016]. Wu T-Y and I were co-first authors contributing equally to this project. Wu T-Y was involved in the early stages of concept formation and conducted preliminary experiments. I was responsible for mathematical proof, experiments, data analysis and manuscript composition. Jin Y was involved in the early stages of concept formation and contributed to mathematical proof. Wong WH was the supervisory author on this project and was involved throughout the project.A version of Chapter 4 has been submitted to one of the top journals in Statistics and is now available in arXiv [Bai Jiang, Tung-Yu Wu, Wing Hung Wong. Convergence of Contrastive Divergence with annealed learning rate in exponential family.arXiv preprint arXiv:1603.06220. 2016]. I was the first author, responsible for all major areas of concept formation, mathematical proof, experiments, data analysis and manuscript composition. Wu T-Y was involved in the early stage of concept formation. Wong WH was the supervisory author on this project and was involved throughout the project.