Perhaps the most important suggestion for future work is to bring lessons learned from the special cases of nonlinear state-space models and logical hidden Markov models back to the more general frameworks. Both have good algorithms for learning and inference that could be generalised.7.1 The method for nonlinear state-space models includes properties such as posterior dependencies and control, that have not been implemented in the otherwise more flexible Bayes Blocks framework.
The visualisation of the learning process could help understanding the methods better, as well as help to find better initialisations, model structures, or means to avoid local minima. This is especially important for new users who do not know the methods well. Also general usability in most methods needs improvement so that potential users become users at all.
The number of node types in the Bayes Blocks framework could be increased. Feasible blocks not presented here include discrete variables, the error function nonlinearity (see Frey and Hinton, 1999), the absolute value, the maximum function (adapt Harva and Kabán, 2005), and MLP networks. The posterior dependencies of Gaussian variables could be handled relatively easily if the clique size of the join tree (see Figure 3.1) stays reasonable. If the clique size is too large, it is possible to use dummy random variables that have posterior correlations with other variables but no other role in modelling. The framework could also allow parallel processing. The assumption that vectorised nodes have the same length and they all have the same parents restrict their use in relational models, whereas scalar nodes have a lot of overhead and are thus inefficient when used to emulate more flexible vector nodes.
In some applications, the components of the data have coordinates, like the pixels of an image in computer vision. A latent variable could refer to the coordinates, as is done for instance by Winn and Joijic (2005). In another example, changing the pitch of a voice moves it vertically in the spectrogram. It would be quite reasonable to model the place of an object or a pitch of a voice with latent variables, but MLP networks would not be well suited to model the mapping to observations. It would be important to be able to model these rather different kinds of nonlinear mappings compared to the ones used in this thesis.
All the learning methods in this thesis aim at unsupervised learning where all the data is modelled with equal interest. When it is known beforehand how the model is going to be used, one could concentrate the learning efforts to the task at hand. This related to attention in cognitive modelling, and discriminative learning (see Taskar et al., 2002, for an example) in machine learning. Even better, Lasserre et al. (2006) introduce a principled hybrid of generative and discriminative models.
More applications are needed to show the full potential of the studied methods. Nonlinear state-space models could easily be used as feature extraction in speech recognition. An interesting application for relational models would be to study library data including title, contents, lending history, classification, and keywords for the material. The found model could be then applied to find structure in web pages. The application to the game of Go could also be continued. An experimental comparison of Bayes Blocks and BUGS software libraries would reveal strengths and weaknesses of different posterior approximations.
In control or decision making, sometimes the best decision is to first gather more information to be able to make better decisions later. This is known as probing or exploration, depending on whether information is gathered about the state of the world or the model of the world. It would be interesting to continue work by Bar-Shalom (1981) studying probing in control and by Thrun (1992) studying exploration in control.
There are many ways to combine neural (nonlinear) and logical (relational) methods. In the models presented here, the logical part defines the structure where the neural part then operates. It would be possible to let the neural part decide which logical structures to study. Such a system would be able to use computational resources more efficiently. For instance in the game of Go, a neural pattern recognition system could decide with which settings a search for local move sequences should be performed.