Life's most valuable asset is health. Continuously understanding the state of our health and modeling how it evolves is essential if we wish to improve it. Given the opportunity that people live with more data about their life today than any other time in history, the challenge rests in interweaving this data with the growing body of knowledge to compute and model the health state of an individual continually. This dissertation presents an approach to build a personal model and dynamically estimate the health state of an individual by fusing multi-modal data and domain knowledge. The system is stitched together from four essential abstraction elements: 1. the events in our life, 2. the layers of our biological systems (from molecular to an organism), 3. the functional utilities that arise from biological underpinnings, and 4. how we interact with these utilities in the reality of daily life. Connecting these four elements via graph network blocks forms the backbone by which we instantiate a digital twin of an individual. Edges and nodes in this graph structure are then regularly updated with learning techniques as data is continuously digested. Experiments demonstrate the use of dense and heterogeneous real-world data from a variety of personal and environmental sensors to monitor individual cardiovascular health state. State estimation and individual modeling is the fundamental basis to depart from disease-oriented approaches to a total health continuum paradigm. Precision in predicting health requires understanding state trajectory. By encasing this estimation within a navigational approach, a systematic guidance framework can plan actions to transition a current state towards a desired one. This work concludes by presenting this framework of combining the health state and personal graph model to perpetually plan and assist us in living life towards our goals.

We propose novel dynamic multiscale graph neural networks (DMGNN) to predict 3D skeleton-based human motions. The core idea of DMGNN is to use a multiscale graph to comprehensively model the internal relations of a human body for motion feature learning. This multiscale graph is adaptive during training and dynamic across network layers. Based on this graph, we propose a multiscale graph computational unit (MGCU) to extract features at individual scales and fuse features across scales. The entire model is action-category-agnostic and follows an encoder-decoder framework. The encoder consists of a sequence of MGCUs to learn motion features. The decoder uses a proposed graph-based gate recurrent unit to generate future poses. Extensive experiments show that the proposed DMGNN outperforms state-of-the-art methods in both short and long-term predictions on the datasets of Human 3.6M and CMU Mocap. We further investigate the learned multiscale graphs for the interpretability. The codes could be downloaded from https://github.com/limaosen0/DMGNN.

The wide spread use of positioning and photographing devices gives rise to a deluge of traffic trajectory data (e.g., vehicle passage records and taxi trajectory data), with each record having at least three attributes: object ID, location ID, and time-stamp. In this paper, we propose a novel mobility pattern embedding model called MPE to shed the light on people's mobility patterns in traffic trajectory data from multiple aspects, including sequential, personal, and temporal factors. MPE has two salient features: (1) it is capable of casting various types of information (object, location and time) to an integrated low-dimensional latent space; (2) it considers the effect of ``phantom transitions'' arising from road networks in traffic trajectory data. This embedding model opens the door to a wide range of applications such as next location prediction and visualization. Experimental results on two real-world datasets show that MPE is effective and outperforms the state-of-the-art methods significantly in a variety of tasks.

The widespread use of positioning devices (e.g., GPS) has given rise to a vast body of human movement data, often in the form of trajectories. Understanding human mobility patterns could benefit many location-based applications. In this paper, we propose a novel generative model called TraLFM via latent factor modeling to mine human mobility patterns underlying traffic trajectories. TraLFM is based on three key observations: (1) human mobility patterns are reflected by the sequences of locations in the trajectories; (2) human mobility patterns vary with people; and (3) human mobility patterns tend to be cyclical and change over time. Thus, TraLFM models the joint action of sequential, personal and temporal factors in a unified way, and brings a new perspective to many applications such as latent factor analysis and next location prediction. We perform thorough empirical studies on two real datasets, and the experimental results confirm that TraLFM outperforms the state-of-the-art methods significantly in these applications.

In recent biomedical scientific problems, it is a fundamental issue to integratively cluster a set of objects from multiple sources of datasets. Such problems are mostly encountered in genomics, where data is collected from various sources, and typically represent distinct yet complementary information. Integrating these data sources for multi-source clustering is challenging due to their complex dependence structure including directional dependency. Particularly in genomics studies, it is known that there is certain directional dependence between DNA expression, DNA methylation, and RNA expression, widely called The Central Dogma. Most of the existing multi-view clustering methods either assume an independent structure or pair-wise (non-directional) dependency, thereby ignoring the directional relationship. Motivated by this, we propose a copula-based multi-view clustering model where a copula enables the model to accommodate the directional dependence existing in the datasets. We conduct a simulation experiment where the simulated datasets exhibiting inherent directional dependence: it turns out that ignoring the directional dependence negatively affects the clustering performance. As a real application, we applied our model to the breast cancer tumor samples collected from The Cancer Genome Altas (TCGA).

We address the problem of policy evaluation in discounted Markov decision processes, and provide instance-dependent guarantees on the $\ell_\infty$-error under a generative model. We establish both asymptotic and non-asymptotic versions of local minimax lower bounds for policy evaluation, thereby providing an instance-dependent baseline by which to compare algorithms. Theory-inspired simulations show that the widely-used temporal difference (TD) algorithm is strictly suboptimal when evaluated in a non-asymptotic setting, even when combined with Polyak-Ruppert iterate averaging. We remedy this issue by introducing and analyzing variance-reduced forms of stochastic approximation, showing that they achieve non-asymptotic, instance-dependent optimality up to logarithmic factors.

The lack of interpretability is an inevitable problem when using neural network models in real applications. In this paper, a new explainable neural network called GAMI-Net, based on generalized additive models with structured interactions, is proposed to pursue a good balance between prediction accuracy and model interpretability. The GAMI-Net is a disentangled feedforward network with multiple additive subnetworks, where each subnetwork is designed for capturing either one main effect or one pairwise interaction effect. It takes into account three kinds of interpretability constraints, including a) sparsity constraint for selecting the most significant effects for parsimonious representations; b) heredity constraint such that a pairwise interaction could only be included when at least one of its parent effects exists; and c) marginal clarity constraint, in order to make the main and pairwise interaction effects mutually distinguishable. For model estimation, we develop an adaptive training algorithm that firstly fits the main effects to the responses, then fits the structured pairwise interactions to the residuals. Numerical experiments on both synthetic functions and real-world datasets show that the proposed explainable GAMI-Net enjoys superior interpretability while maintaining competitive prediction accuracy in comparison to the explainable boosting machine and other benchmark machine learning models.

Hot stellar systems (HSS) are a collection of stars bound together by gravitational attraction. These systems hold clues to many mysteries of outer space so understanding their origin, evolution and physical properties is important but remains a huge challenge. We used multivariate $t$-mixtures model-based clustering to analyze 13456 hot stellar systems from Misgeld & Hilker (2011) that included 12763 candidate globular clusters and found eight homogeneous groups using the Bayesian Information Criterion (BIC). A nonparametric bootstrap procedure was used to estimate the confidence of each of our clustering assignments. The eight obtained groups can be characterized in terms of the correlation, mass, effective radius and surface density. Using conventional correlation-mass-effective radius-surface density notation, the largest group, Group 1, can be described as having positive-low-low-moderate characteristics. The other groups, numbered in decreasing sizes are similarly characterised, with Group 2 having positive-low-low-high characteristics, Group 3 displaying positive-low-low-moderate characteristics, Group 4 having positive-low-low-high characteristic, Group 5 displaying positive-low-moderate-moderate characteristic and Group 6 showing positive-moderate-low-high characteristic. The smallest group (Group 8) shows negative-low-moderate-moderate characteristic. Group 7 has no candidate clusters and so cannot be similarly labeled but the mass, effective radius correlation for these non-candidates indicates that they zare larger than typical globular clusters. Assertions drawn for each group are ambiguous for a few HSS having low confidence in classification. Our analysis identifies distinct kinds of HSS with varying confidence and provides novel insight into their physical and evolutionary properties.

Reproducing kernel Hilbert spaces (RKHSs) play an important role in many statistics and machine learning applications ranging from support vector machines to Gaussian processes and kernel embeddings of distributions. Operators acting on such spaces are, for instance, required to embed conditional probability distributions in order to implement the kernel Bayes rule and build sequential data models. It was recently shown that transfer operators such as the Perron-Frobenius or Koopman operator can also be approximated in a similar fashion using covariance and cross-covariance operators and that eigenfunctions of these operators can be obtained by solving associated matrix eigenvalue problems. The goal of this paper is to provide a solid functional analytic foundation for the eigenvalue decomposition of RKHS operators and to extend the approach to the singular value decomposition. The results are illustrated with simple guiding examples.

Cognitive impairment has become epidemic in older adult population. The recent advent of tiny wearable and ambient devices, a.k.a Internet of Things (IoT) provides ample platforms for continuous functional and cognitive health assessment of older adults. In this paper, we design, implement and evaluate AutoCogniSys, a context-aware automated cognitive health assessment system, combining the sensing powers of wearable physiological (Electrodermal Activity, Photoplethysmography) and physical (Accelerometer, Object) sensors in conjunction with ambient sensors. We design appropriate signal processing and machine learning techniques, and develop an automatic cognitive health assessment system in a natural older adults living environment. We validate our approaches using two datasets: (i) a naturalistic sensor data streams related to Activities of Daily Living and mental arousal of 22 older adults recruited in a retirement community center, individually living in their own apartments using a customized inexpensive IoT system (IRB #HP-00064387) and (ii) a publicly available dataset for emotion detection. The performance of AutoCogniSys attests max. 93\% of accuracy in assessing cognitive health of older adults.