# Neural Conjugate Aggregation: Identifiable Unsupervised Multi-Sensor Regression under Heterogeneous Sensor Bias

arXiv: https://arxiv.org/abs/2606.22200 · HTML: https://mlsanity.com/paper/2606.22200/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 14 references that are in the map.
- First posted on arXiv 20 Jun 2026.

## Builds on (most cited first, 7 of 7)

- [Multimodal Machine Learning: A Survey and Taxonomy](https://mlsanity.com/paper/1705.09406/) (2017)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Conformal prediction under ambiguous ground truth](https://mlsanity.com/paper/2307.09302/) (2023)
- [Cocoon: Robust Multi-Modal Perception with Uncertainty-Aware Sensor Fusion](https://mlsanity.com/paper/2410.12592/) (2024)
- [Veli: Unsupervised Method and Unified Benchmark for Low-Cost Air Quality Sensor Correction](https://mlsanity.com/paper/2508.02724/) (2025)

## Abstract (arXiv)

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.