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Gaussian Latent Dirichlet Allocation for Discrete Human State Discovery

In this article we propose and validate an unsupervised probabilistic model, Gaussian Latent Dirichlet Allocation (GLDA), for the problem of discrete state discovery from repeated, multivariate psychophysiological samples collected from multiple, inherently distinct, individuals. Psychology and medical research heavily involves measuring potentially related but individually inconclusive variables from a cohort of participants to derive diagnosis, necessitating clustering analysis. Traditional probabilistic clustering models such as Gaussian Mixture Model (GMM) assume a global mixture of component distributions, which may not be realistic for observations from different patients. The GLDA model borrows the individual-specific mixture structure from a popular topic model Latent Dirichlet Allocation (LDA) in Natural Language Processing and merges it with the Gaussian component distributions of GMM to suit continuous type data. We implemented GLDA using STAN (a probabilistic modeling language) and applied it on two datasets, one containing Ecological Momentary Assessments (EMA) and the other heart measures from electrocardiogram and impedance cardiograph. We found that in both datasets the GLDA-learned class weights achieved significantly higher correlations with clinically assessed depression, anxiety, and stress scores than those produced by the baseline GMM. Our findings demonstrate the advantage of GLDA over conventional finite mixture models for human state discovery from repeated multivariate data, likely due to better characterization of potential underlying between-participant differences. Future work is required to validate the utility of this model on a broader range of applications.