Formerly, we have divided our models into two categories: static and dynamic. In static modeling, each observation or data sample is independent of the others. In dynamic models, the dependencies between consecutive observations are modeled. The generalization of both is that the relations are described in the data itself, that is, each observation might have a different structure.

Many models have been developed for relational discrete data, and for data with nonlinear dependencies between continuous values. In (Raiko, 2005), we combine two of these methods, relational Markov networks and hierarchical nonlinear factor analysis (HNFA), resulting in using nonlinear models in a structure determined by the relations in the data. The method developed in (Raiko, 2005) is applied in that paper to the board game Go.

Figure: Visualizations of the statistical estimates of the ownership (left) and importance (right) of different areas on the board during a game of (13x13) Go.

Many real-world sequences such as protein secondary structures or shell logs exhibit rich internal structures. Logical hidden Markov models (Kersting et al., 2006) have been proposed as one solution. They deal with logical sequences, i.e., sequences over an alphabet of logical atoms. This comes at the expense of a more complex model selection problem. Indeed, different abstraction levels have to be explored. In (Kersting and Raiko, 2005), we have proposed a novel method for selecting logical hidden Markov models. Convergence and experimental results are provided showing the effectiveness of the developed method.

References

T. Raiko, "Nonlinear relational Markov networks with an application to the game of Go". In Proc. of the Int. Conf. on Artificial Neural Networks (ICANN 2005), Warsaw, Poland, September 2005, pp. 989-996. Pdf (204k).

K. Kersting, L. De Raedt, and T. Raiko. Logical Hidden Markov Models. In the Journal of Artificial Intelligence Research (JAIR), volume 25, pages 425-456, April, 2006. Publisher electronic edition.

K. Kersting and T. Raiko, "'Say EM' for selecting probabilistic models for logical sequences". In Proc. of the 21st Conf. on Uncertainty in Artificial Intelligence (UAI 2005), Edinburgh, Scotland, 2005, pp. 300-307. Pdf (205k).