Contents of the publications and author's contributions

The titles of the nine publications of this thesis and their relationships are shown in Figure 1.2.

Figure 1.2: Publications of the thesis. Journal articles have two frames and conference papers just one. Relationships are shown as edges that are undirected since there is no clear causality.

Publication I introduces a framework for creating graphical models from simple building blocks. It is based on variational Bayesian learning, and unlike other such frameworks, it can model nonlinearities and nonstationary variance. Once the user defines the model structure, the algorithms for learning and inference are automatically derived. The present author developed a part of the framework, carried out a small part in the implementation, made two of the three experiments and wrote a large part of the paper.

Well-founded handling of missing values is one of the advantages of Bayesian modelling. Publication II studies the reconstruction of missing values in nonlinear factor analysis. The present author made the implementation, ran the experiments, and wrote most of the paper under the guidance of Dr. Harri Valpola.

Values in the data are often either observed, or missing, but some cases fall in between: Sometimes it is known that a measurement is inaccurate, or perhaps there is only a lower bound. Publication III studies handling and reconstruction of such partially observed values in the variational Bayesian framework. It also brings up a situation where the cost function of the variational Bayesian learning can diverge to negative infinity. It can be solved using partially observed values or by adding virtual noise in the data.

Publication IV applies a state-of-the-art method from machine learning to the problem of nonlinear model-predictive control. Three different control schemes are studied, one is based directly on the learned neural network, the second one is the traditional nonlinear model-predictive control, and the third one is based on Bayesian inference. The present author designed the novel control scheme and wrote a large part of the paper.

The control application brought up a setting to which none of the tested inference algorithms for nonlinear state-space models suited well. Publication V introduces a novel algorithm that both converges reliably and is still fast. The present author designed the algorithm and wrote a large part of the paper.

The last four publications involve relations. Publication VI gives the first extension of graphical models to both nonlinear and relational direction at the same time. The relations in the data define a structure for a graphical model where unknown variables can then be inferred using variational Bayesian methods. The novel method is applied to the analysis of the board game Go.

Hidden Markov models (HMMs) are very popular for analysing sequential data. Logical hidden Markov models (LOHMMs) extend traditional hidden Markov models to deal with sequences of structured symbols in the form of logical atoms, rather than characters. Publication VII formally introduces LOHMMs and presents efficient solutions to the three central inference problems for LOHMMs: evaluation, most likely hidden state sequence and parameter estimation. The idea came from Prof. Luc De Raedt whereas Dr. Kristian Kersting and the present author jointly formalised and implemented the LOHMMs. The present author's contribution in experimentation and writing were minor.

In Publication VIII, LOHMMs are applied to the domain of bioinformatics. The task was to extract structural signatures of folds for classes of proteins according to the classification scheme SCOP. The results indicate that LOHMMs possess several advantages over other methods. The present author took part in the design, implementation, experimentation, and writing.

The increase of descriptive power of LOHMMs over HMMs comes at the expense of a more complex model selection problem, since different abstraction levels need to be explored. Publication IX presents a novel algorithm for choosing the model structure. The effectiveness of the algorithm is confirmed both theoretically and by experimentation with real-world unix command sequence data. The work was done jointly by Dr. K. Kersting and the present author.