Filtering of High-Dimensional Data for Sequential Classification

In many science and engineering problems, we observe high-dimensional data acquired sequentially. At each time instant, these data correspond to one of a predefined number of classes. The sequence of classes follows a certain pattern, with the transition probabilities of the classes being unknown. Our hypothesized generative model of the observed data involves two latent processes. The first is a root process representing the sequence of classes, while the second is a low-dimensional process generated as a Markovian process, depending on the current class and the previous value of the low-dimensional process. The observed high-dimensional process is generated from the low-dimensional state process. Our objective is to infer the posterior distributions of the classes as they evolve over time based on the observed data and the adopted model. To achieve this, we propose a method for estimating the latent processes. We demonstrate the effectiveness of our approach on synthesized data.