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CoMPASS Framework

CoMPASS (Cognitive Mapping of Planned Actions with State Spaces) is a hierarchical probabilistic framework that integrates local movement dynamics with goal-directed cognitive states to decode latent behavioral states from complex spatial navigation data.

Two-Level Hierarchy

Level 1: Fine-Grained Motor States

Goal: Identify moment-to-moment behavioral states based on instantaneous movement kinematics.

Modeling Strategy:

  • Features/Data Streams:
    • Step size (instantaneous displacement between frames)
    • Turn angle (change in heading direction)
  • Apply a custom Hidden Markov Model (HMM) with specialized emission distributions designed for locomotor data:
    • Step lengths → Gamma distribution (models positive, right-skewed displacement data)
    • Turn angles → von Mises distribution (circular/directional model) OR Gamma distribution of absolute angles (magnitude model)
  • Robust parameter initialization using median, IQR, and MAD statistics to handle tracking noise
  • EM optimization with multiple algorithms (BFGS, L-BFGS-B, Nelder-Mead, Powell) tested across repetitions
  • Behavioral constraints enforced: State 1 must have lower step + higher turn than State 2

Output:

  • Hidden States decoded:
    • State 1: Low step length + High turn angle → Active Surveillance
    • State 2: High step length + Low turn angle → Automated Ambulation
  • Per-frame latent state sequence (Viterbi decoding)
  • Posterior state probabilities for uncertainty quantification

Rationale: The Gamma distribution is appropriate for step lengths because they are strictly positive and often right-skewed. The von Mises distribution is the circular analogue of the Gaussian distribution, making it ideal for directional data like turn angles.

Level 2: Goal-Directed Cognitive States

Goal: Identify internal goal states that guide behavior in pursuit of the reward zone, overlaying the motor states with cognitive intent.

Modeling Strategy:

  • Use the Level 1 state sequence as input
  • Combine with reward-contextual features:
    • Angular deviation - Sternum-based angular deviation from the reward path
    • Value-based distance - Distance to target weighted by value function
    • KDE-based proximity - Kernel density estimate quantifying spatial proximity to target zone
  • Bayesian Gaussian Mixture Model (BGMM) for robust initialization
  • GMM-HMM (Gaussian Mixture Model - Hidden Markov Model) to capture temporal dependencies and transitions between goal states
  • Leave-One-Session-Out (LOSO) cross-validation with phase-aligned training
  • Early stopping based on log-likelihood trends (optional patience tuning)
  • Model selection using AIC

Output:

  • Level 2 States decoded (per session):
    • Reward Oriented - Goal-directed behavior toward target
    • Non-Reward Oriented - Exploratory or non-goal-directed behavior

Final Hierarchical States:

The framework combines Level 1 motor states with Level 2 cognitive states to produce 4 interpretable behavioral modes:

  1. Active Surveillance, Reward Oriented - Cautious, high-turning exploration while oriented toward reward
  2. Active Surveillance, Non-Reward Oriented - Cautious, high-turning exploration without reward orientation
  3. Automated Ambulation, Reward Oriented - Fast, directed movement toward reward
  4. Automated Ambulation, Non-Reward Oriented - Fast, directed movement in non-rewarded directions

These composite states capture both the motor dynamics (how the animal moves) and the cognitive intent (what the animal is pursuing), providing a rich behavioral segmentation for downstream analysis.