Neural Conjugate Aggregation: Identifiable Unsupervised Multi-Sensor Regression under Heterogeneous Sensor Bias
This work addresses unsupervised data fusion with heterogeneous sensor bias, a problem in sensor networks and scientific monitoring where ground-truth labels are absent.
The authors propose Neural Conjugate Aggregation Model (NCAM) for unsupervised multi-sensor regression under heterogeneous bias, achieving improved predictive accuracy and well-calibrated uncertainty over baselines like mean aggregation and Kalman filtering on synthetic and air-quality datasets.
We study regression-based data fusion under uncertainty, where multiple noisy and biased measurement sources are available but ground-truth labels are absent during training. This setting arises in sensor networks, simulation ensembles, and scientific monitoring systems where supervision is costly or infeasible. We propose the Neural Conjugate Aggregation Model (NCAM), a hierarchical Bayesian framework that combines neural networks with conjugate Gaussian inference for unsupervised multi-source fusion. NCAM learns source-specific bias and reliability conditioned on contextual covariates, yielding an analytically tractable posterior over a latent target variable with decomposed epistemic and aleatoric uncertainty. Structural non-identifiability is resolved through sensor anchoring and variance regularization, enabling stable and interpretable posterior aggregation. To complement Bayesian uncertainty with finite-sample guarantees, we integrate locally adaptive Monte Carlo conformal prediction, producing heteroscedastic prediction intervals with coverage guarantees under exchangeability assumptions. Experiments on synthetic and real-world air-quality datasets demonstrate improved predictive accuracy and well-calibrated uncertainty compared to unsupervised baselines, including mean aggregation, probabilistic PCA, and Kalman filtering.