Advancing sleep detection by modelling weak label sets: A novel weakly
  supervised learning approach
Matthias Boeker Vajira Thambawita Michael Riegler Pål Halvorsen Hugo L. Hammer
Understanding sleep and activity patterns plays a crucial role in physical
and mental health. This study introduces a novel approach for sleep detection
using weakly supervised learning for scenarios where reliable ground truth
labels are unavailable. The proposed method relies on a set of weak labels,
derived from the predictions generated by conventional sleep detection
algorithms. Introducing a novel approach, we suggest a novel generalised
non-linear statistical model in which the number of weak sleep labels is
modelled as outcome of a binomial distribution. The probability of sleep in the
binomial distribution is linked to the outcomes of neural networks trained to
detect sleep based on actigraphy. We show that maximizing the likelihood
function of the model, is equivalent to minimizing the soft cross-entropy loss.
Additionally, we explored the use of the Brier score as a loss function for
weak labels. The efficacy of the suggested modelling framework was demonstrated
using the Multi-Ethnic Study of Atherosclerosis dataset. A \gls{lstm} trained
on the soft cross-entropy outperformed conventional sleep detection algorithms,
other neural network architectures and loss functions in accuracy and model
calibration. This research not only advances sleep detection techniques in
scenarios where ground truth data is scarce but also contributes to the broader
field of weakly supervised learning by introducing innovative approach in
modelling sets of weak labels.