Tree-Based Regressors for Predicting Energy Expenditure from Heart Rate in Wearable Devices

Estimating energy expenditure from heart rate usually relies on population-based multiple linear regression equations, taking heart rate, age, gender, mass, height and, if available, VO2max into account. In this paper, we show that non-linear models, such as random forests and regression trees are suited for the deployment on memory constrained wearable devices and assess physical activity more accurately than linear regression models. We fitted linear regression models, regression trees, and random forests with data from 892 graded exercise tests on a treadmill with 857 participants and evaluated their performance, as well as memory consumption on a PineTime smartwatch and an Apple Watch. A regression tree with a tree depth of 11 performed the same (R2 = 0.825) as a widely used linear model by Keytel (R2 = 0.821) but does not depend on VO2max, which can be relevant for amateur athletes. The additional memory on the PineTime smartwach needed to store the tree increased the the original firmware size of 390 KiB to 416 KiB. If VO2max is available, then a tree with a depth of 11
achieves a coefficient of 0.877, and the total memory size is 418 KiB.