Nonlinear Fusion of Depression Self-Questionnaires Using Probabilistic Cutoff Optimization

Reliable interpretation of depression state across multiple self-report questionnaires is critical for consistent clinical decision-making. However, conventional approaches typically apply linear correlation to independently scored instruments, neglecting the nonlinear relationships and measurement uncertainties inherent in psychological assessments. This study introduces a nonlinear correlationbased fusion framework for jointly interpreting CES-D and PHQ-9 scores, enabling a unified, probabilistically coherent representation of depressive states. A nonlinear trendline is first fitted to capture the intrinsic nonlinear correlation between the two questionnaires. Using the Covariance Projection Filter (CPF), individual scores are then projected onto this manifold by accounting for subject-specific uncertainty, yielding maximum-probability fused estimates. Initial cutoff boundaries derived from these projections are subsequently refined through cross-entropy-based optimization, which aligns boundary positions with a probabilistic severity landscape while ensuring smooth transitions between clinical states. Experiments using real-world data and psychiatrist-labeled diagnoses demonstrate that the proposed framework produces more stable, interpretable results. The approach provides a principled foundation for integrating multi-instrument mental-health assessments and supports the development of more reliable digital screening systems.