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Currently, millions of individuals use wearables such as the Apple Watch to track their physical activity, heart rate, and other physiological signals. This has generated an unprecedented amount of wearable data, presenting an opportunity for digital medicine to unlock the next level of precision medicine. However, this wearable data is often noisy, making it seem unusable without new mathematical techniques to extract key signals from it. In this talk, I will describe several techniques that we have developed for analyzing this noisy time-series data. These techniques include a new state space estimation method called the level-set Kalman filter, which can be used to estimate the phase of circadian rhythms. I will also discuss a Kalman filter-assisted autoencoder for anomaly detection in time-series data, and feature engineering based on persistent homology and mathematical modeling. I will demonstrate how these techniques can be applied to scoring sleep, detecting aberrant physiological changes related to diseases such as COVID-19, and predicting daily mood. |