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Expert-Guided POMDP Learning for Data-Efficient Modeling in Healthcare

Marco Locatelli, Arjen Hommersom, Roberto Clemens Cerioli, Daniela Besozzi, Fabio Stella

TL;DR

The paper tackles learning POMDP parameters from limited healthcare data by introducing Fuzzy-MAP EM, which injects expert knowledge through fuzzy pseudo-counts into the M-step to perform MAP estimation. The method leverages Takagi-Sugeno fuzzy models to encode domain rules, producing $N_T^{\text{fuzzy}}$ and $N_O^{\text{fuzzy}}$ that regularize parameter updates via hyperparameters $\lambda_T,\lambda_O$; the augmented counts define $\tilde{N}_T$, $\tilde{N}_O$, and related sufficient statistics for updates. Empirical results on synthetic data show improved transition accuracy and observation fit under low-data and high-noise regimes, outperforming standard EM. A Myasthenia Gravis case study demonstrates the practical utility by recovering a clinically coherent two-state POMDP and capturing the drug effect of Ravulizumab, highlighting potential for data-efficient decision support in rare diseases. Overall, the work offers a novel integration of expert fuzzy reasoning with probabilistic learning to enhance robustness and applicability in healthcare contexts where data are scarce and noisy.

Abstract

Learning the parameters of Partially Observable Markov Decision Processes (POMDPs) from limited data is a significant challenge. We introduce the Fuzzy MAP EM algorithm, a novel approach that incorporates expert knowledge into the parameter estimation process by enriching the Expectation Maximization (EM) framework with fuzzy pseudo-counts derived from an expert-defined fuzzy model. This integration naturally reformulates the problem as a Maximum A Posteriori (MAP) estimation, effectively guiding learning in environments with limited data. In synthetic medical simulations, our method consistently outperforms the standard EM algorithm under both low-data and high-noise conditions. Furthermore, a case study on Myasthenia Gravis illustrates the ability of the Fuzzy MAP EM algorithm to recover a clinically coherent POMDP, demonstrating its potential as a practical tool for data-efficient modeling in healthcare.

Expert-Guided POMDP Learning for Data-Efficient Modeling in Healthcare

TL;DR

The paper tackles learning POMDP parameters from limited healthcare data by introducing Fuzzy-MAP EM, which injects expert knowledge through fuzzy pseudo-counts into the M-step to perform MAP estimation. The method leverages Takagi-Sugeno fuzzy models to encode domain rules, producing and that regularize parameter updates via hyperparameters ; the augmented counts define , , and related sufficient statistics for updates. Empirical results on synthetic data show improved transition accuracy and observation fit under low-data and high-noise regimes, outperforming standard EM. A Myasthenia Gravis case study demonstrates the practical utility by recovering a clinically coherent two-state POMDP and capturing the drug effect of Ravulizumab, highlighting potential for data-efficient decision support in rare diseases. Overall, the work offers a novel integration of expert fuzzy reasoning with probabilistic learning to enhance robustness and applicability in healthcare contexts where data are scarce and noisy.

Abstract

Learning the parameters of Partially Observable Markov Decision Processes (POMDPs) from limited data is a significant challenge. We introduce the Fuzzy MAP EM algorithm, a novel approach that incorporates expert knowledge into the parameter estimation process by enriching the Expectation Maximization (EM) framework with fuzzy pseudo-counts derived from an expert-defined fuzzy model. This integration naturally reformulates the problem as a Maximum A Posteriori (MAP) estimation, effectively guiding learning in environments with limited data. In synthetic medical simulations, our method consistently outperforms the standard EM algorithm under both low-data and high-noise conditions. Furthermore, a case study on Myasthenia Gravis illustrates the ability of the Fuzzy MAP EM algorithm to recover a clinically coherent POMDP, demonstrating its potential as a practical tool for data-efficient modeling in healthcare.

Paper Structure

This paper contains 21 sections, 5 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Partially Observable Markov Decision Processes
  4. Expectation-Maximization for POMDPs
  5. E-Step (Expectation).
  6. M-Step (Maximization).
  7. Takagi-Sugeno Fuzzy Models
  8. A Fuzzy-MAP Expectation-Maximization Algorithm
  9. Fuzzy Pseudo-Counts
  10. Fuzzy Pseudo-Counts Augmented M-step
  11. Numerical Experiments on Synthetic Data
  12. Low-Data Regime
  13. High-Noise Regime
  14. Therapeutic Protocols of Myasthenia Gravis
  15. Fuzzy Model of Adaptive Immune System Alterations in MG
  16. ...and 6 more sections

Figures (4)

  • Figure 1: Ground-truth observation distributions for each state.
  • Figure 2: Interaction map of the MG fuzzy model. Plain black (dotted red) lines represent positive (negative) regulations. Coloured boxes correspond to biological drugs.
  • Figure 3: Learned observation probability density distributions for IgG, Complement and Symptoms variables, separated by latent state. State 1 (blue) represents the "Mild MG" condition, and State 2 (orange) represents the "Severe MG" condition.
  • Figure A.4: Detailed specification of the fuzzy model for Myasthenia Gravis (MG)

Theorems & Definitions (2)

  • definition 1
  • definition 2