The main focus of the Inferential Sciences grouup is the development and application of Bayesian probabilistic methods to a wide variety of problems. During the period of the report, there has been continued development of Bayesian methods as applied to non-linear modelling. This has led to the development of density networks for protein structure determination (Mackay 1996d) and models with multiple hyperparameters to model non-stationary data (MacKay & Takeuchi 1996). Ensemble learning using free energy minimization has been investigated and the Evidence framework derived from it (MacKay 1995g; MacKay 1995b). Free energy minimization has also been used as the basis for an efficient decoding algorithm for linear error-correcting codes (MacKay 1995d). Using Bayesian networks and the belief propagation algorithm, good error-correcting codes based on sparse matrices have been devloped (MacKay & Neal 1995). These codes have achieved better performance than almost any other known codes. Extensions of these codes to non-binary alphabets using Galois field theory have also been researched.
Research into priors on infinite networks and the inference of electronic band structure has led to the development of Gaussian processes as efficient and robust regression tools (Gibbs & MacKay, in preparation (a)). Approximate techniques have been developed to adapt Gaussian processes to problems with large data sets. A framework for classification using Gaussian processes has also been developed using variational free energy techniques (Gibbs & Mackay, in preparation (b)).
The group has engaged in several collaborations with the University of Cambridge Metallurgy Department, using neural networks and Gaussian processes to model the impact toughness, cracking susceptibility and microstructure of welds (Ichikawa et al., in preparation; Bhadeshia et al. 1995). Work has also been done with the University of Cambridge Chemistry Department on the modelling of quantum pseudo-potentials to estimate the vibrationally averaged properties of weakly bound molecules.