EvoMorph: Counterfactual Explanations for Continuous Time-Series Extrinsic Regression Applied to Photoplethysmography

TL;DR

EvoMorph tackles the need for trustworthy explanations in TSER on wearable PPG signals by generating multiple physiology-consistent counterfactuals. It casts counterfactual generation as a multi-objective optimization problem solved by NSGA-III, using a morphology-aware descriptor set $\oldsymbol{\phi}(x)$ and coherent edit operators to produce diverse, plausible trajectories that move predictions toward a user-specified interval $\hat{\mathcal{Y}}=[y-\delta, y+\delta]$. The framework introduces a decomposition of objectives into $ ext{O}_{ ext{morph}}$, $ ext{O}_{ ext{maxgrad}}$, and $ ext{O}_{ ext{out}}$, enabling stable, on-distribution counterfactuals while preserving waveform morphology. A case study demonstrates that CFE dispersion approximates epistemic uncertainty similarly to bootstrap ensembles and correlates with data density, supporting uncertainty-aware model auditing. Across three PPG datasets, EvoMorph yields diverse, physiologically plausible CFEs that augment interpretability and provide practical insights into model reliability for clinical time-series analysis.

Abstract

Wearable devices enable continuous, population-scale monitoring of physiological signals, such as photoplethysmography (PPG), creating new opportunities for data-driven clinical assessment. Time-series extrinsic regression (TSER) models increasingly leverage PPG signals to estimate clinically relevant outcomes, including heart rate, respiratory rate, and oxygen saturation. For clinical reasoning and trust, however, single point estimates alone are insufficient: clinicians must also understand whether predictions are stable under physiologically plausible variations and to what extent realistic, attainable changes in physiological signals would meaningfully alter a model's prediction. Counterfactual explanations (CFE) address these "what-if" questions, yet existing time series CFE generation methods are largely restricted to classification, overlook waveform morphology, and often produce physiologically implausible signals, limiting their applicability to continuous biomedical time series. To address these limitations, we introduce EvoMorph, a multi-objective evolutionary framework for generating physiologically plausible and diverse CFE for TSER applications. EvoMorph optimizes morphology-aware objectives defined on interpretable signal descriptors and applies transformations to preserve the waveform structure. We evaluated EvoMorph on three PPG datasets (heart rate, respiratory rate, and oxygen saturation) against a nearest-unlike-neighbor baseline. In addition, in a case study, we evaluated EvoMorph as a tool for uncertainty quantification by relating counterfactual sensitivity to bootstrap-ensemble uncertainty and data-density measures. Overall, EvoMorph enables the generation of physiologically-aware counterfactuals for continuous biomedical signals and supports uncertainty-aware interpretability, advancing trustworthy model analysis for clinical time-series applications.

Figures (5)

• Figure 1: Waveform visualization (zoomed to samples 350-1200 within 4000-sample window) of a held-out BIDMCHR test instance (black), its NUN (gray dashed), and the full set of 251 diverse EvoMorph CFE (blue) generated for that test instance.
• Figure 2: Epistemic uncertainty and data density across target-value bins. Left: Mean confidence interval width as a function of the target-value bin center, comparing bootstrap-ensemble uncertainty computed from predictions on the test set with prediction dispersion over the set of EvoMorph CFE generated for each test instance. Right: Mean KDE NLL (inverse proxy for data density) and mean CFE-induced prediction variance across target bins, illustrating the correspondence between low data support and increased epistemic uncertainty.
• Figure 3: Diversity–smoothness–proximity trade-offs of EvoMorph counterfactuals across three PPG TSER tasks. Each point represents EvoMorph CFE; the x-axis reports per test instance number of diverse CFE generated, and the y-axis reports the maximum-gradient metric (a proxy for local waveform sharpness/spike-like artifacts). Point color encodes DTW-based proximity to the held-out test instance (darker = closer).
• Figure 4: Qualitative comparison of the held-out test instance (blue) from BIDMCSpO2 (oxygen saturation dataset), its NUN (green), and EvoMorph counterfactual for a representative oxygen saturation signal (yellow). Top to bottom: (1) Time-domain waveforms; (2) Power spectral density plot; (3) Magnitude spectrum (FFT); and (4) Time–frequency spectrogram. The counterfactual exhibits physiologically coherent temporal and spectral characteristics while shifting toward the target prediction, and remains broadly consistent with patterns observed in the natural signals (test instance and NUN).
• Figure 5: Aggregated evolution of NSGA-III objectives and algorithmic diagnostics across all test instances. Left column: median trajectories for the three optimization objectives, Morphology, Maximum Gradient, and Output Distance losses, over 50 generations. Right column: NSGA-III performance metrics, including population diversity, hypervolume, and convergence.