# Incorporating sparse labels into hidden Markov models using weighted likelihoods improves accuracy and interpretability in biologging studies

## TL;DR

A new method improves hidden Markov models by using weighted likelihoods to better incorporate rare observations, enhancing accuracy in decoding animal behaviors from biologging data.

## Contribution

The novel weighted likelihood approach improves accuracy and interpretability when incorporating sparse labels into hidden Markov models.

## Key findings

- The weighted likelihood approach outperforms existing methods in decoding latent processes from biologging data.
- Cross-validated evaluation and simulations confirm improved accuracy and interpretability of decoded foraging behaviors in killer whales.
- The method effectively leverages sparse labels to enhance hidden process decoding across various fields.

## Abstract

Ecologists often use a hidden Markov model to decode a latent process, such as a sequence of an animal’s behaviours, from an observed biologging time series. Modern technological devices such as video recorders and drones now allow researchers to directly observe an animal’s behaviour. Using these observations as labels of the latent process can improve a hidden Markov model’s accuracy when decoding the latent process. However, many wild animals are observed infrequently. Including such rare labels often has a negligible influence on parameter estimates, which in turn does not meaningfully improve the accuracy of the decoded latent process. We introduce a weighted likelihood approach that increases the relative influence of labelled observations. We use this approach to develop hidden Markov models to decode the foraging behaviour of killer whales (Orcinus orca) off the coast of British Columbia, Canada. Using cross-validated evaluation metrics and a detailed simulation study, we show that our weighted likelihood approach produces more accurate and understandable decoded latent processes compared to existing hidden Markov models and single-frame machine learning methods. Thus, our method effectively leverages sparse labels to enhance researchers’ ability to accurately decode hidden processes across various fields.