This thesis is mainly concerned with state-space methods for a class of deep Gaussian process (DGP) regression problems. As an example, one can think of a family of DGPs as solutions to stochastic differential equations (SDEs), and view their regression problems as filtering and smoothing problems. Additionally, this thesis also presents a few applications from (D)GPs, such as system identification of SDEs and spectro-temporal signal analysis.

Supervisor: Prof. Simo Särkkä.

Pre-examiners: Prof. Kody J. H. Law from The University of Manchester and Prof. David Duvenaud from University of Toronto.

Opponent: Prof. Manfred Opper from University of Birmingham.

The public defence of the thesis will be streamed online on December 10, 2021 at noon (Helsinki time) via Zoom link https://aalto.zoom.us/j/67529212279. It is free and open to the public, you are welcome to attend.

More details regarding the thesis itself can be found in its title pages.

The dissertation is in ./dissertation.pdf. Feel free to download and read~~

Note that you may also find an "official" version in aaltodoc published by Aalto University, the content of which has no difference with ./dissertation.pdf. However, the aaltodoc-version has many readability issues, please use ./dissertation.pdf instead.

1. ./dissertation.pdf. The PDF of the thesis.
2. ./errata.md. Errata of the thesis.
3. ./cover. This folder contains a Python script that generates the cover image.
4. ./lectio_praecursoria. This folder contains the presentation at the public defence of the thesis.
5. ./scripts. This folder contains Python scripts that are used to generate some of the figures in the thesis.
6. ./thesis_latex. This folder contains the LaTeX source of the thesis. Compiling the tex files here will generate a PDF the same as with ./dissertation.pdf.

1. https://github.com/zgbkdlm/ssdgp contains implementation of state-space deep Gaussian processes.
2. https://github.com/zgbkdlm/tme and https://github.com/zgbkdlm/tmefs contain implementation of Taylor moment expansion method and its filter and smoother applications.

Bibtex:

@phdthesis{Zhao2021Thesis,
	title = {State-space deep Gaussian processes with applications},
	author = {Zheng Zhao},
	school = {Aalto University},
	year = {2021},
}

Plain text:

Zheng Zhao. State-space deep Gaussian processes with applications. PhD thesis, Aalto University, 2021.

Unless otherwise stated, all rights belong to the author Zheng Zhao. This repository consists of files covered by different licenses, please check their licenses before you use them.

You are free to download, display, and print ./dissertation.pdf for your own personal use. Commercial use of it is prohibited.

I would like to thank Adrien (Monte) Corenflos, Christos Merkatas, Dennis Yeung, and Sakira Hassan for their time and efforts for reviewing and checking the languange of the thesis.

Zheng Zhao, [email protected]