arXiv subjects

Hongxiao Zhu

Publications and source records attributed to Hongxiao Zhu.

5 recordsLinked to original sources

arXiv2024

Semiparametric quantile functional regression analysis of adolescent physical activity distributions in the presence of missing data

In the age of digital healthcare, passively collected physical activity profiles from wearable sensors are a preeminent tool for evaluating health outcomes. In order to fully leverage the vast amounts of data collected through wearable accelerometers, we propose to use quantile functional regression to model activity profiles as distributional outcomes through quantile responses, which can be used to evaluate activity level differences across covariates based on any desired distributional summary. Our proposed framework addresses two key problems not handled in existing distributional regression literature. First, we use spline mixed model formulations in the basis space to model nonparametric effects of continuous predictors on the distributional response. Second, we address the underlying missingness problem that is common in these types of wearable data but typically not addressed. We show that the missingness can induce bias in the subject-specific distributional summaries that leads to biased distributional regression estimates and even bias the frequently used scalar summary measures, and introduce a nonparametric function-on-function modeling approach that adjusts for each subject's missingness profile to address this problem. We evaluate our nonparametric modeling and missing data adjustment using simulation studies based on realistically simulated activity profiles and use it to gain insights into adolescent activity profiles from the Teen Environment and Neighborhood study.

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arXiv2020

Recreating Bat Behavior on Quad-rotor UAVs-A Simulation Approach

We develop an effective computer model to simulate sensing environments that consist of natural trees. The simulated environments are random and contain full geometry of the tree foliage. While this simulated model can be used as a general platform for studying the sensing mechanism of different flying species, our ultimate goal is to build bat-inspired Quad-rotor UAVs- UAVs that can recreate bat's flying behavior (e.g., obstacle avoidance, path planning) in dense vegetation. To this end, we also introduce an foliage echo simulator that can produce simulated echoes by mimicking bat's biosonar. In our current model, a few realistic model choices or assumptions are made. First, in order to create natural looking trees, the branching structures of trees are modeled by L-systems, whereas the detailed geometry of branches, sub-branches and leaves is created by randomizing a reference tree in a CAD object file. Additionally, the foliage echo simulator is simplified so that no shading effect is considered. We demonstrate our developed model by simulating real-world scenarios with multiple trees and compute the corresponding impulse responses along a Quad-rotor trajectory.

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arXiv2020

Simulate forest trees by integrating L-system and 3D CAD files

In this article, we propose a new approach for simulating trees, including their branches, sub-branches, and leaves. This approach combines the theory of biological development, mathematical models, and computer graphics, producing simulated trees and forest with full geometry. Specifically, we adopt the Lindenmayer process to simulate the branching pattern of trees and modify the available measurements and dimensions of 3D CAD developed object files to create natural looking sub-branches and leaves. Randomization has been added to the placement of all branches, sub branches and leaves. To simulate a forest, we adopt Inhomogeneous Poisson process to generate random locations of trees. Our approach can be used to create complex structured 3D virtual environment for the purpose of testing new sensors and training robotic algorithms. We look forward to applying this approach to test biosonar sensors that mimick bats' fly in the simulated environment.

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arXiv2016

Bayesian Graphical Models for Multivariate Functional Data

Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional independence between random functions, and construct a framework for Bayesian inference of undirected, decomposable graphs in the multivariate functional data context. This framework is based on extending Markov distributions and hyper Markov laws from random variables to random processes, providing a principled alternative to naive application of multivariate methods to discretized functional data. Markov properties facilitate the composition of likelihoods and priors according to the decomposition of a graph. Our focus is on Gaussian process graphical models using orthogonal basis expansions. We propose a hyper-inverse-Wishart-process prior for the covariance kernels of the infinite coefficient sequences of the basis expansion, establish existence, uniqueness, strong hyper Markov property, and conjugacy. Stochastic search Markov chain Monte Carlo algorithms are developed for posterior inference, assessed through simulations, and applied to a study of brain activity and alcoholism.

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arXiv2015

Smoothing and mean-covariance estimation of functional data with a Bayesian hierarchical model

Functional data, with basic observational units being functions (e.g., curves, surfaces) varying over a continuum, are frequently encountered in various applications. While many statistical tools have been developed for functional data analysis, the issue of smoothing all functional observations simultaneously is less studied. Existing methods often focus on smoothing each individual function separately, at the risk of removing important systematic patterns common across functions. We propose a nonparametric Bayesian approach to smooth all functional observations simultaneously and nonparametrically. In the proposed approach, we assume that the functional observations are independent Gaussian processes subject to a common level of measurement errors, enabling the borrowing of strength across all observations. Unlike most Gaussian process regression models that rely on pre-specified structures for the covariance kernel, we adopt a hierarchical framework by assuming a Gaussian process prior for the mean function and an Inverse-Wishart process prior for the covariance function. These prior assumptions induce an automatic mean-covariance estimation in the posterior inference in addition to the simultaneous smoothing of all observations. Such a hierarchical framework is flexible enough to incorporate functional data with different characteristics, including data measured on either common or uncommon grids, and data with either stationary or nonstationary covariance structures. Simulations and real data analysis demonstrate that, in comparison with alternative methods, the proposed Bayesian approach achieves better smoothing accuracy and comparable mean-covariance estimation results. Furthermore, it can successfully retain the systematic patterns in the functional observations that are usually neglected by the existing functional data analyses based on individual-curve smoothing.

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