Learning Transparent models from Data Driven algorithms to Enhance streaming data analysis

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The aim of this project is to enable Bayesian filters to work in conjunction with the algorithms used to train neural networks, in both a supervised and unsupervised fashion to model dynamic and measurement models, thus allowing them the exploit prior knowledge of the system and analyse the behaviour of the system under these circumstances, and use this to analyse incoming streams of data and predict future data, whilst remaining fully transparent. This will be achieved by developing a method of using supervised learning in state space models, using a fully transparent statistical model with a firm mathematical basis and foundation. In linear/ Gaussian environments, this requires the estimation of the process and measurement matrix, and the noise covariance matrices. In non linear settings, it requires use of neural networks to model dynamic and measurement models in the supervised case where there is access to a hidden state 'x' as well as the measurement in 'z'. Then, this will be extended by developing a method of using unsupervised learning in state space models, where there is access to only the sequence of measurements. Iterated posterior linearization filters (IPLF) will be utilised to deal with neural network non linearities.