Temporally Multi-Scale Sparse Self-Attention for Physical Activity Data Imputation

TL;DR

This work constructs a novel and large scale data set consisting of a training set with over 3 million hourly step count observations and a test set with over 2.5 million hourly step count observations and proposes a domain knowledge-informed sparse self-attention model that captures the temporal multi-scale nature of step-count data.

Abstract

Wearable sensors enable health researchers to continuously collect data pertaining to the physiological state of individuals in real-world settings. However, such data can be subject to extensive missingness due to a complex combination of factors. In this work, we study the problem of imputation of missing step count data, one of the most ubiquitous forms of wearable sensor data. We construct a novel and large scale data set consisting of a training set with over 3 million hourly step count observations and a test set with over 2.5 million hourly step count observations. We propose a domain knowledge-informed sparse self-attention model for this task that captures the temporal multi-scale nature of step-count data. We assess the performance of the model relative to baselines and conduct ablation studies to verify our specific model designs.

Figures (11)

• Figure 1: Autocorrelation function (ACF) over all the participants of $\Delta t = 1, \ldots, 504$ hrs (within three weeks). Blue line: median ACF, Red line: $\Delta t=168 \times N$ hrs (i.e. $N$ weeks).
• Figure 2: Multi-timescale context window. The missing hourly block is at the center and indicated as red. Numbers are day differences between each day and the center day (i.e. difference is 0) which contains the missing hourly block. Letters indicate the day of the week for each day. The center day is Monday in this example.
• Figure 3: Histogram of observed hourly step counts between 6:00am and 10:00pm for the 100 training participants.
• Figure 4: Imputation results and model comparison on hourly blocks with various ground truth step counts. The first plot shows the proposed model's performance (evaluated by Micro MAE) by true step count bins. The first bin is for zero steps, while the rest have the bin width of 500 steps (i.e., [1, 500), [501, 1000), etc). The second to fourth plot show error ratios relative to the proposed model for several other models. Error ratios above 1 indicate that other models perform worse than the proposed model on the particular bin.
• Figure 5: Attention and relative time encoding visualization. We include attention weights regarding two days of the week as examples, and also show the attention difference between them (the fourth image). The attention scores are averaged over all completely held-out test samples, and relative time encoding is averaged over models from 10 training splits.