# Thomas Fabricius Master of Science, Ph.D. student. Tel: (+45) 45 25 38 94. E-mail: tf@eivind.imm.dtu.dk

I am currently working on my Ph.D. Bayesian Signal Detection and Processing with Application in Wireless Communication which is a continuation of my Master Thesis Bayesian Model Selection by Markov Chain Monte Carlo Methods. Model selection impl ies modelling, for that reason am I very interested in Machine Learning which deal with the problem of infering parameters. I am at most devoted to the Bayesian learning paradigm of probabilistic learning. Solving Bayesian model problems quickly gets out o f the closed form solution scope, for that reason is nummerical methods and approximations the only solutions. The sampling approach is the one which has taken most of my time, but recently the variational approximations has taken some of my time and I have proposed, in my master thesis, a variational approximation to the Artificial Neural Network (ANN).

The model selection problem have I tried to solve by "path-sampling", unfortunately models can often implement different intepretations of data. As an example, which I have examined in my master thesis, regression outputs can be implemeted as func tions over inputs with additive Gaussian noise. One intpretation could then be to implement all the signal as noise, which would be the most plausible explanation when the effective number of data examples are less than the number of parameters in the mod el. Another intepretation of data is, the one we expect exists, to implement data as the functions over the inputs added by noise with some level. These different ways of intepreting data have a large tendency to bias the Model Selection towards the start ing model i.e. the model intepretaion that is valid in the initial samples.

All the theoretical aspect is very well applied to communication theory. In communication theory we often make an entropy decoding with a binary alphabet as output, eventually we also perform some redundancy encoding. The problem is then to infer the send symbols after transmission over a noisy channel. This implies solving Bayesian integrals (or rather sums over the possible states). This is in genral a complex task. For that reason is it necessary to use approximations to get it run realtime, we call the sollutions for nonoptimal decoders. The approximations are borrowed from statistical physics of disordered spin-systems, where the naive mean-field and Thouhless-Anderson-Palmer (TAP) approximations are very well applyable. This field also gives some nice ways to analyse the nonoptimal decoders, which in general are good at low signal to noise ratios and at weak dependencies between the decoded bits. Often the system of bits behave differently in different regimes of the estimated or postulated signal to noise ratio or what would be identical in physics, the temperature. Physicists talk about the magnetic or ferromagnetic or even spin-glass phase of the system, where we go from one global sollution to many equal probable solutions. The work on nonoptimal decoders is conducted together with Nokia Digital Signal Processing Group, where we look at more specific detector systems.
Curriculum Vitae