# BeliefPPG: Uncertainty-aware Heart Rate Estimation from PPG signals via Belief Propagation

arXiv: https://arxiv.org/abs/2306.07730 · HTML: https://mlsanity.com/paper/2306.07730/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 51 references that are in the map.
- First posted on arXiv 13 Jun 2023.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Practical Deep Learning with Bayesian Principles](https://mlsanity.com/paper/1906.02506/) (2019)
- [DeepPhys: Video-Based Physiological Measurement Using Convolutional Attention Networks](https://mlsanity.com/paper/1805.07888/) (2018)
- [Benchmarking Bayesian Deep Learning on Diabetic Retinopathy Detection Tasks](https://mlsanity.com/paper/2211.12717/) (2022)
- [SimPer: Simple Self-Supervised Learning of Periodic Targets](https://mlsanity.com/paper/2210.03115/) (2022)
- [TROIKA: A General Framework for Heart Rate Monitoring Using Wrist-Type Photoplethysmographic Signals During Intensive Physical Exercise](https://mlsanity.com/paper/1409.5181/) (2014)
- [CardioGAN: Attentive Generative Adversarial Network with Dual Discriminators for Synthesis of ECG from PPG](https://mlsanity.com/paper/2010.00104/) (2020)
- [Know Your Limits: Uncertainty Estimation with ReLU Classifiers Fails at Reliable OOD Detection](https://mlsanity.com/paper/2012.05329/) (2020)
- [Photoplethysmography-Based Heart Rate Monitoring in Physical Activities via Joint Sparse Spectrum Reconstruction](https://mlsanity.com/paper/1503.00688/) (2015)
- [Q-PPG: Energy-Efficient PPG-based Heart Rate Monitoring on Wearable Devices](https://mlsanity.com/paper/2203.14907/) (2022)
- [PPGnet: Deep Network for Device Independent Heart Rate Estimation from Photoplethysmogram](https://mlsanity.com/paper/1903.08912/) (2019)
- [Embedding Temporal Convolutional Networks for Energy-Efficient PPG-Based Heart Rate Monitoring](https://mlsanity.com/paper/2203.04396/) (2022)
- [Self-Supervised PPG Representation Learning Shows High Inter-Subject Variability](https://mlsanity.com/paper/2212.04902/) (2022)

## Built on by (most cited first, 8 of 8)

- [WildPPG: A Real-World PPG Dataset of Long Continuous Recordings](https://mlsanity.com/paper/2412.17540/) (2024)
- [GPT-PPG: A GPT-based Foundation Model for Photoplethysmography Signals](https://mlsanity.com/paper/2503.08015/) (2025)
- [KID-PPG: Knowledge Informed Deep Learning for Extracting Heart Rate from a Smartwatch](https://mlsanity.com/paper/2405.09559/) (2024)
- [SiamQuality: A ConvNet-Based Foundation Model for Imperfect Physiological Signals](https://mlsanity.com/paper/2404.17667/) (2024)
- [CAP: Towards PPG Universal Representation Learning with Patient-level Supervision](https://mlsanity.com/paper/2606.15284/) (2026)
- [Learning Without Augmenting: Unsupervised Time Series Representation Learning via Frame Projections](https://mlsanity.com/paper/2510.22655/) (2025)
- [Multi-site PPG: An In-the-Wild Physiological Dataset from Emerging Multi-site Wearables](https://mlsanity.com/paper/2605.17859/) (2026)
- [EgoHRV: Continuous Heart Rate Variability Estimation from Egocentric Systems for Autonomic Response and Skill Assessment](https://mlsanity.com/paper/2608.18711/) (2026)

## Abstract (arXiv)

We present a novel learning-based method that achieves state-of-the-art performance on several heart rate estimation benchmarks extracted from photoplethysmography signals (PPG). We consider the evolution of the heart rate in the context of a discrete-time stochastic process that we represent as a hidden Markov model. We derive a distribution over possible heart rate values for a given PPG signal window through a trained neural network. Using belief propagation, we incorporate the statistical distribution of heart rate changes to refine these estimates in a temporal context. From this, we obtain a quantized probability distribution over the range of possible heart rate values that captures a meaningful and well-calibrated estimate of the inherent predictive uncertainty. We show the robustness of our method on eight public datasets with three different cross-validation experiments.