Covariance Estimation with Missing and Dependent Data

The estimation of conditional dependence graphs and precision matrices is one of the most relevant problems in modern statistics. There is a large body of work for estimation with fully observed and independent data. These are, however, often unrealistic assumptions for real-world data applications. So extensions are needed to accommodate data complications more suited for actual data analysis. In this thesis we address the methodology, theory, and applications of covariance estimation with these complications. We focus on a data setting with both dependence and missingness. To model this, we use a matrix-variate model with a Kronecker product covariance structure and missing values. This model allows for correlations to exist both between the rows and between the columns, and is commonly used in fields as diverse as genetics, neuroimaging, psychology, and environmental science, where estimating and/or accounting for dependence is often a primary concern. We develop prototypical column- and row-wise precision matrix estimators for single data matrices with missing data. We show initial concentration of measure bounds on entry-wise consistency for data with mean structure and multiplicative errors, and develop corresponding rates of convergence for the joint mean and covariance estimation in high-dimensional settings. To implement these estimators, we first solve a general implementation issue with graphical Lasso-type estimators designed for use with noisy and missing data. These estimators often result in non-positive semidefinite input matrices to the graphical Lasso, which can result in pathological optimization issues. We show how this problem can be fixed with modified objective functions and develop a feasible and efficient algorithm for solving the graphical Lasso with these modifications. This algorithm can be used not only for our method, but also to implement a wide variety of graphical Lasso extensions that involve non-positive semidefinite inputs. Finally, we use our methods to explore a dataset of voting records from the U.S. Senate, where we expect there to be connections both between similar or opposed senators as well as between bills that may share characteristics or topics. This dataset exhibits missing data and has mean structure due to the two-party system, and in particular we are interested in estimating relationships beyond just those dictated by this party structure.PHDStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163035/1/rogerfan_1.pd

Spectral Study of Soil-Pile-Structure Interaction Based on Observed Data

Spectral analysis and system identification algorithm are used to analyze a set of acceleration response records obtained from a shaking table test. The method is based on the linear discrete time systems theory, and the soil-pile system can be represented as a linear filter of a finite order with time-varying coefficients. The recorded ground motion at the pile tip is the input, and the motion at the different level along the pile and the structure is the output of the filter. Knowing the input and output, the time varying parameters of the filter can be determined by using the system identification method. Once the filter parameters are known, the transfer function, and the kinematic interaction between the soil-pile-structure can be determined

Magnetoelectric domains and their switching mechanism in a Y-type hexaferrite

By employing resonant X-ray microdiffraction, we image the magnetisation and magnetic polarity domains of the Y-type hexaferrite Ba$_{0.5}$Sr$_{1.5}$Mg$_2$Fe$_{12}$O$_{22}$. We show that the magnetic polarity domain structure can be controlled by both magnetic and electric fields, and that full inversion of these domains can be achieved simply by reversal of an applied magnetic field in the absence of an electric field bias. Furthermore, we demonstrate that the diffraction intensity measured in different X-ray polarisation channels cannot be reproduced by the accepted model for the polar magnetic structure, known as the 2-fan transverse conical (TC) model. We propose a modification to this model, which achieves good quantitative agreement with all of our data. We show that the deviations from the TC model are large, and may be the result of an internal magnetic chirality, most likely inherited from the parent helical (non-polar) phase.Comment: 9 figure

Towards Unifying Diffusion Models for Probabilistic Spatio-Temporal Graph Learning

Spatio-temporal graph learning is a fundamental problem in the Web of Things era, which enables a plethora of Web applications such as smart cities, human mobility and climate analysis. Existing approaches tackle different learning tasks independently, tailoring their models to unique task characteristics. These methods, however, fall short of modeling intrinsic uncertainties in the spatio-temporal data. Meanwhile, their specialized designs limit their universality as general spatio-temporal learning solutions. In this paper, we propose to model the learning tasks in a unified perspective, viewing them as predictions based on conditional information with shared spatio-temporal patterns. Based on this proposal, we introduce Unified Spatio-Temporal Diffusion Models (USTD) to address the tasks uniformly within the uncertainty-aware diffusion framework. USTD is holistically designed, comprising a shared spatio-temporal encoder and attention-based denoising networks that are task-specific. The shared encoder, optimized by a pre-training strategy, effectively captures conditional spatio-temporal patterns. The denoising networks, utilizing both cross- and self-attention, integrate conditional dependencies and generate predictions. Opting for forecasting and kriging as downstream tasks, we design Gated Attention (SGA) and Temporal Gated Attention (TGA) for each task, with different emphases on the spatial and temporal dimensions, respectively. By combining the advantages of deterministic encoders and probabilistic diffusion models, USTD achieves state-of-the-art performances compared to deterministic and probabilistic baselines in both tasks, while also providing valuable uncertainty estimates

On the Distribution of Neutral Tone in Southern Min: LCC and Beyond

The aim of this paper is to address an often-overlooked topic in Southern Min tonology: neutral tone. We show that the tone sandhi domain in Southern Min is not always isomorphic with an XP in syntax or a phonological phrase. In fact, this domain may be smaller than what has been predicted, as evidenced in the phrase-final functional morphemes as well as in the rhythmic effect. We propose that the tone sandhi domain in Southern Min is defined by a constituent Tone Sandhi Domain (TSD, τ) between the p-phrase and the p-word. A TSD is required to bear a final prominence, and only a p-word, mapped from a contentive or focused element in syntax, can be a “prominence-bearing unit.

Are Hylobates lar Extirpated from China?

The Nangunhe Nature Reserve in Southwest Yunnan (PRC) has long been presumed to be the last stronghold of lar (or white-handed) gibbons (Hylobates lar) in China and the likely last place of occurrence of Hylobates lar yunnanensis. We conducted a comprehensive survey to assess the status of lar gibbons at Nangunhe. We found no visual or auditory evidence of them still residing at the reserve and therefore tentatively conclude that lar gibbons have become extinct in China. It appears that large-scale destruction of primary forests in the 1960s and 1970s brought about an initial decline in their numbers, and subsequent uncontrolled hunting has resulted in their extirpation. The situation for the six Chinese ape taxa is nothing less than disastrous, with 1 taxon assumed to have become extinct during the last few years, 1 taxon not having been confirmed since the 1980s, and 2 species at the very brink of extinction with only tens of individuals remaining in Chin