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Adaptive Shrinkage Estimation for Personalized Deep Kernel Regression in Modeling Brain Trajectories
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Proposes personalized deep kernel Gaussian process regression (pers-DKGP) that adaptively blends a population deep-kernel model and a subject-specific fine-tuned model via a learned XGBoost shrinkage weight to forecast brain biomarker trajectories.
Problem
Forecasting longitudinal brain biomarker trajectories (regional volumes, SPARE-AD/SPARE-BA) from sparse, irregular, high-dimensional imaging and clinical data, with personalization as new subject observations arrive.
Approach
Combines a population deep kernel GP (p-DKGP) with a subject-specific GP (ss-DKGP) that reuses the frozen population feature extractor, and learns a per-prediction shrinkage weight alpha (via XGBoost trained on oracle alphas) from both models' means, variances, and observation time.
Key results
- On Hippocampus R, adaptive shrinkage achieves Mean AE 0.243 vs 0.257 for the best constant alpha (0.5) in the ablation.
- On external studies, pers-DKGP reports Mean AE 0.197 on AIBL, 0.259 on OASIS, and 0.139 on PreventAD, outperforming LMM and GAM.
- Learned shrinkage alpha decreases as the number of observations increases, with XGBoost achieving R^2 above 0.67 across the seven ROI volumes.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace the best constant α with adaptive shrinkage (ablation) | Deep Kernel Regression · Hippocampus R | Mean AE: 0.257 (±0.007) -> 0.243 (±0.003) | Helped |
| replace the best constant α with adaptive shrinkage (ablation) | Deep Kernel Regression · Lateral Ventricle R | Mean AE: 0.143 (±0.006) -> 0.131 (±0.002) | Helped |
| replace the best constant α with adaptive shrinkage (ablation) | Deep Kernel Regression · Thalamus Proper R | Mean AE: 0.241 (±0.007) -> 0.219 (±0.003) | Helped |
| replace the best constant α with adaptive shrinkage (ablation) | Deep Kernel Regression · Hippocampus R | Mean Cov.: 0.808 -> 0.795 | Hurt |
| replace the best constant α with adaptive shrinkage (ablation) | Deep Kernel Regression · Lateral Ventricle R | Mean Cov.: 0.853 -> 0.855 | Helped |
| replace the best constant α with adaptive shrinkage (ablation) | Deep Kernel Regression · Thalamus Proper R | Mean Cov.: 0.934 -> 0.849 | Hurt |
| replace constant shrinkage with adaptive shrinkage | pers-DKGP · AIBL | Mean AE | Helped |
| replace constant shrinkage with adaptive shrinkage | pers-DKGP · OASIS | Mean AE | Helped |
| replace constant shrinkage with adaptive shrinkage | pers-DKGP · PreventAD | Mean AE | Helped |
| use subject-specific adaptive shrinkage with 2 observations instead of the population model with 1 observation | SPARE-AD prediction · SPARE-AD | Mean AE: 0.227 -> 0.233 | Hurt |
| increase history from 2 to 5 observations with adaptive shrinkage | SPARE-AD prediction · SPARE-AD | Mean AE: 0.233 -> 0.148 | Helped |
| choose α by optimizing on only the subject's observed trajectory rather than learning adaptive shrinkage across subjects (ablation) | Deep Kernel Regression posterior correction · Seven ROI Volume biomarkers | Predictive performance | Hurt |
Surprising findings
- Per-subject optimized shrinkage alpha (deterministic approach) performs worst, suggesting overfitting to limited single-subject data.
- Transformer and LSTM models failed to converge on sparse temporal data and were omitted from comparisons.
Limitations
- Independence assumption between p-DKGP and ss-DKGP errors biases the combined variance; errors are mildly correlated (0.136 to 0.394).
- Only univariate biomarker trajectories are modeled; extension to multivariate trajectories is future work.
- Transformer and LSTM baselines were excluded due to convergence issues on sparse data.
Experimental setup
Datasets: ADNI BLSA OASIS AIBL PreventAD iSTAGING
Benchmarks: ADNI BLSA OASIS AIBL PreventAD
Metrics: mean absolute error absolute error 95% CI prediction interval coverage interval width
Baselines: Linear Mixed Model Generalized Additive Model Deep Regression Deep Mixed Effects p-DKGP
Builds on: deep kernel learning linear mixed effects models deep mixed effects generalized additive models SHAP
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