Introduction

Statistical machine learning aims at discovering relevant concepts and representation of data collected in various fields of life. Learned models can be used to analyse and summarise the data, to reconstruct missing information and predict future data, to make decisions, plan and control. There has been huge research activity covering various tasks in various applications leading to a diverse collection of methods.

Let us consider an example of intensive care unit which is a hospital bed equipped for medical care and observation to people in a critical or unstable condition. Hanson and Marshall (2001) note that the intensive care environment is particularly suited to the implementation of artificial intelligence tools because of the wealth of available data and the inherent opportunities for increased efficiency in inpatient care. There are about 250 variables online, daily laboratory data, and relational background data including care history, nutrition, infections, relatives, and demographic data. In principle, there are machine learning methods that could be used to learn from previous patients and applied to new patients. In practice, it is very difficult to take the wealth of information into account because of the diversity of data and applicable methods. Similar situation applies in other application areas from robotics to economical modelling.

Graphical models (Bishop, 2006; Cowell et al., 1999; Pearl, 1988; Neapolitan, 2004; Jensen et al., 1990) are an important subclass of statistical machine learning methods that have clear semantics and a sound theoretical foundation. A graphical model is a graph whose nodes represent random variables and edges define the dependency structure between them. Bayesian inference solves the probability distribution over unknown variables given the data. Many methods in machine learning that are not originally graphical models, can be reinterpreted or transformed into the framework. This allows one to combine different methods in a principled manner, as well as to reuse ideas and software between sometimes surprisingly different applications.

Latent variable models aim at explaining the observed data by supplementing it with unknown factors or a hidden state. The idea is that even if the regularities in the data itself are difficult to find, the dependencies between latent variables and observations are simpler, given that a proper representation is found. Model parameters and latent variables can be solved at the same time in the framework of graphical models.

Basic tasks in graphical models, such as inference and learning, have been solved for decades, but relaxing the strict assumptions such as linearity of the dependencies or that the data comes in uniform samples, is a challenging and an active field of research. This thesis studies and introduces several extensions to the well-known existing graphical models.

This thesis consists of an introductory part, whose structure is shown in Figure 1.1, and nine publications described in Section 1.3.

Figure 1.1: Dependency structure of the chapters of the thesis.