An official website of the United States government
Abstract Functional data with non-smooth features (e.g., discontinuities in the functional mean and/or covariance) and monotonicity arise frequently in practice. This paper develops simultaneous inference for concurrent functional linear regression in this setting. We construct a simultaneous confidence band for a functional covariate effect of interest. Along with a Wald-type formulation, our approach is based on a powerful nonparametric likelihood ratio method. Our procedures are flexible enough to allow discontinuities in the coefficient functions and the covariance structure, while accounting for discretization of the observed trajectories under a fixed dense design. A simulation study shows that the proposed likelihood ratio-based procedure outperforms the Wald-type procedure in moderate sample sizes. We apply the proposed methods to studying the effect of age on the occupation time curve derived from wearable device data obtained in an NHANES study.
more »
« less
Empirical Likelihood-Based Inference for Functional Means with Application to Wearable Device Data
Abstract This paper develops a nonparametric inference framework that is applicable to occupation time curves derived from wearable device data. These curves consider all activity levels within the range of device readings, which is preferable to the practice of classifying activity into discrete categories. Motivated by certain features of these curves, we introduce a powerful likelihood ratio approach to construct confidence bands and compare functional means. Notably, our approach allows discontinuities in the functional covariances while accommodating discretization of the observed trajectories. A simulation study shows that the proposed procedures outperform competing functional data procedures. We illustrate the proposed methods using wearable device data from an NHANES study.
more »
« less
- Award ID(s):
- 2112938
- PAR ID:
- 10429986
- Date Published:
- Journal Name:
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Volume:
- 84
- Issue:
- 5
- ISSN:
- 1369-7412
- Page Range / eLocation ID:
- 1947 to 1968
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Human activity recognition (HAR) and, more broadly, activities of daily life recognition using wearable devices have the potential to transform a number of applications, including mobile healthcare, smart homes, and fitness monitoring. Recent approaches for HAR use multiple sensors on various locations on the body to achieve higher accuracy for complex activities. While multiple sensors increase the accuracy, they are also susceptible to reliability issues when one or more sensors are unable to provide data to the application due to sensor malfunction, user error, or energy limitations. Training multiple activity classifiers that use a subset of sensors is not desirable, since it may lead to reduced accuracy for applications. To handle these limitations, we propose a novel generative approach that recovers the missing data of sensors using data available from other sensors. The recovered data are then used to seamlessly classify activities. Experiments using three publicly available activity datasets show that with data missing from one sensor, the proposed approach achieves accuracy that is within 10% of the accuracy with no missing data. Moreover, implementation on a wearable device prototype shows that the proposed approach takes about 1.5 ms for recovering data in the w-HAR dataset, which results in an energy consumption of 606 μJ. The low-energy consumption ensures that SensorGAN is suitable for effectively recovering data in tinyML applications on energy-constrained devices.more » « less
-
Abstract Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well if the data exhibits heavy-tailedness or outliers. To address this challenge, a new robust FPCA approach based on a functional pairwise spatial sign (PASS) operator, termed PASS FPCA, is introduced. We propose robust estimation procedures for eigenfunctions and eigenvalues. Theoretical properties of the PASS operator are established, showing that it adopts the same eigenfunctions as the standard covariance operator and also allows recovering ratios between eigenvalues. We also extend the proposed procedure to handle functional data measured with noise. Compared to existing robust FPCA approaches, the proposed PASS FPCA requires weaker distributional assumptions to conserve the eigenspace of the covariance function. Specifically, existing work are often built upon a class of functional elliptical distributions, which requires inherently symmetry. In contrast, we introduce a class of distributions called the weakly functional coordinate symmetry (weakly FCS), which allows for severe asymmetry and is much more flexible than the functional elliptical distribution family. The robustness of the PASS FPCA is demonstrated via extensive simulation studies, especially its advantages in scenarios with nonelliptical distributions. The proposed method was motivated by and applied to analysis of accelerometry data from the Objective Physical Activity and Cardiovascular Health Study, a large-scale epidemiological study to investigate the relationship between objectively measured physical activity and cardiovascular health among older women.more » « less
-
null (Ed.)Automated tracking of physical fitness has sparked a health revolution by allowing individuals to track their own physical activity and health in real time. This concept is beginning to be applied to tracking of cognitive load. It is well known that activity in the brain can be measured through changes in the body’s physiology, but current real-time measures tend to be unimodal and invasive. We therefore propose the concept of a wearable educational fitness (EduFit) tracker. We use machine learning with physiological data to understand how to develop a wearable device that tracks cognitive load accurately in real time. In an initial study, we found that body temperature, skin conductance, and heart rate were able to distinguish between (i) a problem solving activity (high cognitive load), (ii) a leisure activity (moderate cognitive load), and (iii) daydreaming (low cognitive load) with high accuracy in the test dataset. In a second study, we found that these physiological features can be used to predict accurately user-reported mental focus in the test dataset, even when relatively small numbers of training data were used. We explain how these findings inform the development and implementation of a wearable device for temporal tracking and logging a user’s learning activities and cognitive load.more » « less
-
null (Ed.)In this paper, we aimed to study the energy consumption problem in a collaborative activity monitoring system (CAMS) that consists of a compan- ion robot and a wearable device. First, we tested the energy consumption in different operation modes of the system. Based on that, we analyzed the effect of band- width on the time cost and energy consumption which allowed us to combine WiFi and Bluetooth together for data transmission to improve the performance of the system. Second, we preprocessed the image data on the wearable device to reduce the size of images before sending them to the robot, and analyzed the time and energy consumption cost by local computing and data transmission. Third, based on the bandwidth of WiFi and Bluetooth, the requirement of time and energy consumption, we proposed an optimization problem on image sizes in which the wearable device decides how to send the data to the robot to reduce the energy and time cost. The results showed that the relations between the bandwidth, time cost, image resolutions and energy consumption could be used to improve the performance of CAMS.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1111/rssb.12543
