Living beings, robotic and software artefacts can all be seen as agents acting and perceiving within an environment. When observed under that perspective, a new concept is accessible: information in the sense of Shannon. It has long been known that information and control are interrelated concepts. However it is only recently that this perspective has been better understood and used in order to study cognition. In this thesis, we build upon such an information-theoretic perspective and add some biologically motivated assumptions. They introduce various constraints on the capture, the processing, or the storage of information by an agent. Using such constraints it is possible to understand some limits on the control abilities of agents, and to derive algorithms that optimize these abilities. More specifically this thesis uses the recently introduced concept of empowerment, i.e. the ability to act upon the environment and perceive back the changes through the sensors. Maximizing this quantity leads to a wide range of cognitively interesting properties. This work studies some of these properties. One of them, the ability to capture information that is relevant for the perception-action loop of the agent, is deeply investigated and algorithms for exploiting this ability are presented. The second part of the thesis deals with the use of the information-theoretic framework when multiple agents are interacting with each other. Empowerment maximization in this context leads to two phenomena: the generation of complex structures, and the emergence of synchronised and potentially cooperative interactions. In this thesis, the first phenomenon is empirically investigated through various spatial scenarios in order to understand the kind of structures that are generated and under which conditions they appear. Connections are made between the second phenomenon and the concept of the multiple-access channel. Using recent developments of this information-theoretic model, it is possible to precisely study the kind of interactions that can occur, and the situations that lead to synchronised or cooperative behaviour. The general aim of this work is to give a comprehensive picture of the information-theoretic framework for studying the perception-action loop, bringing both single and multi-agents aspects together. The concepts presented in this thesis allows one to study some fundamental aspects of cognition, to engineer self-motivated robotic systems, or to drive self-organization in multi-agents systems.

Bayesian methods are often criticized on the grounds of subjectivity. Furthermore, misspecified priors can have a deleterious effect on Bayesian inference. Noting that model selection is effectively a test of many hypotheses, Dr. Valen E. Johnson sought to eliminate the need of prior specification by computing Bayes' factors from frequentist test statistics. In his pioneering work that was published in the year 2005, Dr. Johnson proposed using so-called local priors for computing Bayes? factors from test statistics. Dr. Johnson and Dr. Jianhua Hu used Bayes' factors for model selection in a linear model setting. In an independent work, Dr. Johnson and another colleage, David Rossell, investigated two families of non-local priors for testing the regression parameter in a linear model setting. These non-local priors enable greater separation between the theories of null and alternative hypotheses. In this dissertation, I extend model selection based on Bayes' factors and use nonlocal priors to define Bayes' factors based on test statistics. With these priors, I have been able to reduce the problem of prior specification to setting to just one scaling parameter. That scaling parameter can be easily set, for example, on the basis of frequentist operating characteristics of the corresponding Bayes' factors. Furthermore, the loss of information by basing a Bayes' factors on a test statistic is minimal. Along with Dr. Johnson and Dr. Hu, I used the Bayes' factors based on the likelihood ratio statistic to develop a method for clustering gene expression data. This method has performed well in both simulated examples and real datasets. An outline of that work is also included in this dissertation. Further, I extend the clustering model to a subclass of the decomposable graphical model class, which is more appropriate for genotype data sets, such as single-nucleotide polymorphism (SNP) data. Efficient FORTRAN programming has enabled me to apply the methodology to hundreds of nodes. For problems that produce computationally harder probability landscapes, I propose a modification of the Markov chain Monte Carlo algorithm to extract information regarding the important network structures in the data. This modified algorithm performs well in inferring complex network structures. I use this method to develop a prediction model for disease based on SNP data. My method performs well in cross-validation studies.