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

这个项目的目的是使贝叶斯过滤器能够与用于训练神经网络的算法一起工作，以监督和非监督的方式对动态和测量模型进行建模，从而使它们能够利用系统的先验知识，分析系统在这些情况下的行为，并利用这一点来分析传入的数据流和预测未来的数据，同时保持完全透明。这将通过开发一种在状态空间模型中使用监督学习的方法来实现，该方法使用具有坚实的数学基础和基础的完全透明的统计模型。在线性/高斯环境中，这需要估计过程和测量矩阵以及噪声协方差矩阵。在非线性设置中，它需要使用神经网络来对有监督情况下的动态和测量模型进行建模，在这种情况下，可以访问隐藏状态‘x’以及‘z’中的测量。然后，将通过开发一种在状态空间模型中使用无监督学习的方法来扩展这一点，在状态空间模型中，只能访问测量序列。迭代后验线性化滤波器(IPLF)将被用来处理神经网络的非线性。

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.