Bayesian online algorithms for learning in discrete Hidden Markov Models

We propose and analyze two different Bayesian online algorithms for learning in discrete Hidden Markov Models and compare their performance with the already known Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalization we draw learning curves in simplified situations for these algorithms and compare their performances.

Helicopter vibration sensor selection using data visualisation

The main objective of the project is to enhance the already effective health-monitoring system (HUMS) for helicopters by analysing structural vibrations to recognise different flight conditions directly from sensor information. The goal of this paper is to develop a new method to select those sensors and frequency bands that are best for detecting changes in flight conditions. We projected frequency information to a 2-dimensional space in order to visualise flight-condition transitions using the Generative Topographic Mapping (GTM) and a variant which supports simultaneous feature selection. We created an objective measure of the separation between different flight conditions in the visualisation space by calculating the Kullback-Leibler (KL) divergence between Gaussian mixture models (GMMs) fitted to each class: the higher the KL-divergence, the better the interclass separation. To find the optimal combination of sensors, they were considered in pairs, triples and groups of four sensors. The sensor triples provided the best result in terms of KL-divergence. We also found that the use of a variational training algorithm for the GMMs gave more reliable results.

Fully probabilistic control for stochastic nonlinear control systems with input dependent noise

Robust controllers for nonlinear stochastic systems with functional uncertainties can be consistently designed using probabilistic control methods. In this paper a generalised probabilistic controller design for the minimisation of the Kullback-Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented emphasising how the uncertainty can be systematically incorporated in the absence of reliable systems models. To achieve this objective all probabilistic models of the system are estimated from process data using mixture density networks (MDNs) where all the parameters of the estimated pdfs are taken to be state and control input dependent. Based on this dependency of the density parameters on the input values, explicit formulations to the construction of optimal generalised probabilistic controllers are obtained through the techniques of dynamic programming and adaptive critic methods. Using the proposed generalised probabilistic controller, the conditional joint pdfs can be made to follow the ideal ones. A simulation example is used to demonstrate the implementation of the algorithm and encouraging results are obtained.

Fully probabilistic control design in an adaptive critic framework

Optimal stochastic controller pushes the closed-loop behavior as close as possible to the desired one. The fully probabilistic design (FPD) uses probabilistic description of the desired closed loop and minimizes Kullback-Leibler divergence of the closed-loop description to the desired one. Practical exploitation of the fully probabilistic design control theory continues to be hindered by the computational complexities involved in numerically solving the associated stochastic dynamic programming problem. In particular very hard multivariate integration and an approximate interpolation of the involved multivariate functions. This paper proposes a new fully probabilistic contro algorithm that uses the adaptive critic methods to circumvent the need for explicitly evaluating the optimal value function, thereby dramatically reducing computational requirements. This is a main contribution of this short paper.

Online learning in discrete hidden Markov models

We present and analyze three different online algorithms for learning in discrete Hidden Markov Models (HMMs) and compare their performance with the Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of the generalization error we draw learning curves in simplified situations and compare the results. The performance for learning drifting concepts of one of the presented algorithms is analyzed and compared with the Baldi-Chauvin algorithm in the same situations. A brief discussion about learning and symmetry breaking based on our results is also presented. © 2006 American Institute of Physics.