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Valentin Bieri^*2, Paul Streli^*1, Berken Utku Demirel¹, Christian Holz¹

¹ Sensing, Interaction & Perception Lab, Department of Computer Science, ETH Zürich, Switzerland
² MSc Student, Department of Computer Science, ETH Zürich, Switzerland
^* These authors contributed equally to this work

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.

TL; DR
This repository contains instructions on how to install BeliefPPG for inference and code to run leave-one-session-out cross-validation experiments on multiple supported datasets. Taking multi-channel PPG and Accelerometer signals as input, BeliefPPG predicts the instantaneous heart rate and provides an uncertainty estimate for the prediction.

• Install
• Quick Start
• Datasets
• Training and Inference
• Citation
• License and Acknowledgement

You can install the pip package using:

pip install beliefppg

To start inferring heart rate from PPG and accelerometer data, you first need to import the infer_hr function from the beliefppg package.

from beliefppg import infer_hr

# Example of a simple function call (adjust 'ppg' and 'sampling_rate' as per your data)
hr, uncertainty, time_intervals = infer_hr(ppg, sampling_rate)

The accuracy of BeliefPPG can be enhanced by incorporating accelerometer data alongside the PPG signals. Additionally, users can choose between belief propagation and Viterbi decoding, specify the uncertainty measure, and decide whether to disable the time-domain backbone of the network architecture. Detailed explanations of these features can be found in our paper and supplementary material.

from beliefppg import infer_hr

ppg_sampling_rate = 128  # Hz (sampling rate of ppg sensor)
acc_sampling_rate = 128 # Hz (sampling rate of accelerometer)

# Load data item containing the PPG, HR, and IMU signals --- challenging custom dataset
data = np.load('Data/example.npy', allow_pickle=True).item()

ppg = data['PPG head'].reshape((-1,1)) # reshape ppg to (n_samples, n_channels)
IMU_X = data['IMU X head']
IMU_Y = data['IMU Y head']
IMU_Z = data['IMU Z head']
acc = np.stack([IMU_X,IMU_X, IMU_Z], axis=-1)

hr, uncertainty, time_intervals = infer_hr(
    ppg, # PPG signal data with shape (n_samples, n_channels)
    ppg_sampling_rate, # Sampling frequency of the PPG signal in Hz
    acc=acc, # Accelerometer signal data with shape (n_samples, n_channels). BeliefPPG to function without accelerometer signal data, but its accuracy may be reduced.
    acc_freq=acc_sampling_rate, # Sampling frequency of the accelerometer signal in Hz
    decoding='sumproduct', # Decoding method to use, either "sumproduct" or "viterbi"
    use_time_backbone=True, # Whether to use the time-domain backbone or not
    uncertainty='std' # Measure for predictive uncertainty, either "entropy" or "std"
)
# The function returns predicted heart rates in BPM, uncertainties (entropy or std), and time intervals in seconds.

For a complete example demonstrating how to use BeliefPPG for heart rate inference, see the tutorial notebook.

We provide a shell script which downloads the datasets DaLiA, WESAD, BAMI-1 and BAMI-2 from their original hosts. Run the following line in your terminal:

sh download_data.sh

• Note that WESAD does not natively include ground-truth HR. Labels can be generated from the provided ECG recordings instead.
• Support for the IEEE datasets is implemented, but the original data format seems to be no longer available. You can download it in the new format under https://zenodo.org/record/3902710#.ZGM9l3ZBy3C and restructure/convert the files or implement your own file reader.

Run the following in your terminal:

python train_eval.py --data_dir ${DATA_PATH} --dataset dalia 

This will run LoSo cross-validation on the DaLiA dataset. On a modern GPU, expect one full run to take roughly 10–14 hours. Results, that is the MAEs, predictions and models, are saved in the output directory, which can be specified with the --out_dir argument. Note that you may have to reinstall h5py in order for the models to be saved correctly.

We highly recommend that you use Weights&Biases to monitor model training. Make sure to log into W&B in the console and then simply add the argument --use_wandb to save additional plots and logging information.

If your find our paper or codes useful, please cite our work:

@InProceedings{uai2023-beliefppg,
    author={Bieri, Valentin and Streli, Paul and Demirel, Berken Utku and Holz, Christian},
    title = {BeliefPPG: Uncertainty-aware Heart Rate Estimation from PPG signals via Belief Propagation},
    year = {2023},
    organization={PMLR},
    booktitle = {Conference on Uncertainty in Artificial Intelligence (UAI)}
}

This project is released under the MIT license.