  Traditional approaches in mental health research apply General Linear Models
(GLM) to describe the longitudinal dynamics of observed psycho-behavioral
measurements (questionnaire summary scores). Similarly, GLMs are also applied
to characterize relationships between neurobiological measurements (regional
fMRI signals) and perceptual stimuli or other regional signals. While these
methods are useful for exploring linear correlations among the isolated signals
of those constructs (i.e., summary scores or fMRI signals), these classical
frameworks fall short in providing insights into the comprehensive system-level
dynamics underlying observable changes. Hidden Markov Models (HMM) are a
statistical model that enable us to describe the sequential relations among
multiple observable constructs, and when applied through the lens of Finite
State Automata (FSA), can provide a more integrated and intuitive framework for
modeling and understanding the underlying controller (the prescription for how
to respond to inputs) that fundamentally defines any system, as opposed to
linearly correlating output signals produced by the controller. We present a
simple and intuitive HMM processing pipeline vcHMM (See Preliminary Data) that
highlights FSA theory and is applicable for both behavioral analysis of
questionnaire data and fMRI data. HMMs offer theoretic promise as they are
computationally equivalent to the FSA, the control processor of a Turing
Machine (TM) The dynamic programming Viterbi algorithm is used to leverage the
HMM model. It efficiently identifies the most likely sequence of hidden states.
The vcHMM pipeline leverages this grammar to understand how behavior and neural
activity relate to depression.
