Bayesian robust state-space mixture model

MatLab object for grouping sequences of real-valued, noisy data according to their underlying dynami

The BRSSMM class implements algorithms for simulating and estimating the parameters of a finite mixture of state-space models. Mixture models are typically used in cluster analysis, i.e. grouping data into a finite number of classes, or mixture components. The state-space representation is often used for modelling stochastic dynamical systems where some of the the variables are not directly observable. The purpose of the BRSSMM class is to group sequences of data according to their underlying dynamics. This model in particular is designed for problems where the dynamics are linear, or near-linear, and the data contain outliers and/or missing values.

A BRSSMM object models each component as a stochastic, linear dynamical system with class-specific parameters. The parameters affect how the states evolve, and how they relate to the data. Parameters are equipped with a conjugate prior distribution as per the Bayesian paradigm. The model also contains hidden variables representing missing values in the data, as well as the quality of the data. The posterior distributions over the parameters, states and hidden variables are estimated by an approximate variational inference algorithm.

This submission includes a test function that generates a set of synthetic data and learns a model from these data. The test function also plots the data clustered according to the model, and the variational lower bound on the marginal log-likelihood of the data after each iteration.

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INSTRUCTIONS:

After downloading this submission, extract the compressed file inside your MatLab working directory and run the test function (brssmmtest.m) for a demonstration.