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.

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).

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.

Bayesian statistical inference loses predictive optimality when generative models are misspecified. Working within an existing coherent loss-based generalisation of Bayesian inference, we show existing Modular/Cut-model inference is coherent, and write down a new family of Semi-Modular Inference (SMI) schemes, indexed by an influence parameter, with Bayesian inference and Cut-models as special cases. We give a meta-learning criterion and estimation procedure to choose the inference scheme. This returns Bayesian inference when there is no misspecification. The framework applies naturally to Multi-modular models. Cut-model inference allows directed information flow from well-specified modules to misspecified modules, but not vice versa. An existing alternative power posterior method gives tunable but undirected control of information flow, improving prediction in some settings. In contrast, SMI allows tunable and directed information flow between modules. We illustrate our methods on two standard test cases from the literature and a motivating archaeological data set.

Modelling uncertainty arising from input-dependent label noise is an increasingly important problem. A state-of-the-art approach for classification [Kendall and Gal, 2017] places a normal distribution over the softmax logits, where the mean and variance of this distribution are learned functions of the inputs. This approach achieves impressive empirical performance but lacks theoretical justification. We show that this model is a special case of a well known and theoretically understood model studied in econometrics. Under this view the softmax over the logit distribution is a smooth approximation to an argmax, where the approximation is exact in the zero temperature limit. We further illustrate that the softmax temperature controls a bias-variance trade-off and the optimal point on this trade-off is not always found at 1.0. By tuning the softmax temperature, we achieve improved performance on well known image classification benchmarks with controlled label noise. For image segmentation, where input-dependent label noise naturally arises, we show that tuning the temperature increases the mean IoU on the PASCAL VOC and Cityscapes datasets by more than 1% over the state-of-the-art model and a strong baseline that does not model this noise source.

Bayes' theorem (alternatively Bayes' law or Bayes' rule) has been called the most powerful rule of probability and statistics. It describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if a disease is related to age, then, using Bayes' theorem, a person's age can be used to more accurately assess the probability that they have the disease, compared to the assessment of the probability of disease made without knowledge of the person's age. It is a powerful law of probability that brings in the concept of'subjectivity' or'the degree of belief' into the cold, hard statistical modeling. Bayes' rule is the only mechanism that can be used to gradually update the probability of an event as the evidence or data is gathered sequentially.

Change point detection is an important part of time series analysis, as the presence of a change point indicates an abrupt and significant change in the data generating process. While many algorithms for change point detection exist, little attention has been paid to evaluating their performance on real-world time series. Algorithms are typically evaluated on simulated data and a small number of commonly-used series with unreliable ground truth. Clearly this does not provide sufficient insight into the comparative performance of these algorithms. Therefore, instead of developing yet another change point detection method, we consider it vastly more important to properly evaluate existing algorithms on real-world data. To achieve this, we present the first data set specifically designed for the evaluation of change point detection algorithms, consisting of 37 time series from various domains. Each time series was annotated by five expert human annotators to provide ground truth on the presence and location of change points. We analyze the consistency of the human annotators, and describe evaluation metrics that can be used to measure algorithm performance in the presence of multiple ground truth annotations. Subsequently, we present a benchmark study where 13 existing algorithms are evaluated on each of the time series in the data set. This study shows that binary segmentation (Scott and Knott, 1974) and Bayesian online change point detection (Adams and MacKay, 2007) are among the best performing methods. Our aim is that this data set will serve as a proving ground in the development of novel change point detection algorithms.