Causal Inference with Covariate Balance Optimization

Causal inference is a popular problem in biostatistics, economics, and health science studies. The goal of this thesis is to develop new methods for the estimation of causal effects using propensity scores or inverse probability weights where weights are chosen in such a way to achieve balance in covariates across the treatment groups. In Chapter 1, we introduce Neyman-Rubin Causal framework and causal inference with propensity scores. The importance of covariate balancing in causal inference is furthered discussed in this chapter. Besides, some general definitions and notations for causal inference are provided with many other popular propensity score approaches or weighting techniques in Chapter 2. In Chapter 3, we describe a new model averaging approach to propensity score estimation in which parametric and nonparametric estimates are combined to achieve covariate balance. Simulation studies are conducted across different scenarios varying in the degree of interactions and nonlinearity in the treatment model. The results show that the proposed method produces less bias and smaller standard errors than existing approaches. They also show that a model averaging approach with the objective of minimizing the average Kolmogorov-Smirnov statistic leads to the best performance. The proposed approach is applied to a real data set in evaluating the causal effect of formula or mixed feeding versus exclusive breastfeeding in the first month of life on a child's BMI Z-score at age 4. The data analysis shows that formula or mixed feeding is more likely to lead to obesity at age 4, compared to exclusive breastfeeding. In Chapter 4, we propose using kernel distance to measure balance across different treatment groups and propose a new propensity score estimator by setting the kernel distance to be zero. Compared to other balance measures, such as absolute standardized mean difference (ASMD) and Kolmogorov Smirnov (KS) statistic, kernel distance is one of the best bias indicators in estimating the causal effect. That is, the balance metric based on kernel distance is shown to have the strongest correlation with the absolute bias in estimating the causal effect, compared to several commonly used balance metrics. The kernel distance constraints are solved by generalized method of moments. Simulation studies are conducted across different scenarios varying in the degree of nonlinearity in both the propensity score model and outcome model. The proposed approach produces smaller mean squared error in estimating causal treatment effects than many existing approaches including the well-known covariate balance propensity score (CBPS) approach when the propensity score model is misspecified. An application to data from the International Tobacco Control (ITC) policy evaluation project is provided. Often interest lies in the estimation of quantiles other than the average causal effect. Other quantities such as quantiles or the quantile treatment effect may be of interest. In Chapter 5, we propose a multiply robust method for estimating marginal quantiles of potential outcomes by achieving mean balance in (1) the propensity score, and (2) the conditional distributions of potential outcomes. An empirical likelihood or entropy measure can be utilized instead of using inverse probability weighting. Simulation studies are conducted across different scenarios of correctness in both the propensity score models and outcome models. Our estimator is consistent if any of the models are correctly specified

Joint estimation of multiple dependent Gaussian graphical models with applications to mouse genomics

Gaussian graphical models are widely used to represent conditional dependence among random variables. In this paper, we propose a novel estimator for data arising from a group of Gaussian graphical models that are themselves dependent. A motivating example is that of modeling gene expression collected on multiple tissues from the same individual: here the multivariate outcome is affected by dependencies acting not only at the level of the specific tissues, but also at the level of the whole body; existing methods that assume independence among graphs are not applicable in this case. To estimate multiple dependent graphs, we decompose the problem into two graphical layers: the systemic layer, which affects all outcomes and thereby induces cross-graph dependence, and the category-specific layer, which represents graph-specific variation. We propose a graphical EM technique that estimates both layers jointly, establish estimation consistency and selection sparsistency of the proposed estimator, and confirm by simulation that the EM method is superior to a simple one-step method. We apply our technique to mouse genomics data and obtain biologically plausible results

ROLE OF EPIDERMAL GROWTH FACTOR RECEPTOR ON CARDIAC FUNCTION

The epidermal growth factor receptor (EGFR/ERBB1) was the first discovered member of the ERBB family of tyrosine kinas receptors that includes ERBB2, ERBB3 and ERBB4. After binding by EGF-related ligands, EGFR is activated to induce homodimerization or heterodimerization with other ERBB receptors, resulting in tyrosine kinase activity. Subsequently, autophosphorylation or transphosphorylation of tyrosine residues in the C-terminal tail of the receptor allows the binding of adaptor proteins to trigger intracellular signaling cascades that can lead to proliferation, survival, and anti-apoptosis. As EGFR is expressed in the majority of developing and adult tissues including heart, dysfunction of EGFR activity can cause severe damage in different tissues and even initiate cancers. Several anti-EGFR drugs are already available in the clinic for late stage cancer patients with activated EGFR activity. However, in cancer therapy using anti-ERBB2 drugs, severe cardiotoxicity among patients has been reported, emphasizing the importance of ERBB signaling in cardiac homeostasis. Also with the increases in life expectancy of patients, some types of cancers tend to be treated as a chronic disease. Therefore it is importance to understanding possible cardiac toxicity under chronic suppression of EGFR pathway. We propose the use of conditional knockout mice lacking EGFR activity in cardiomyocytes to understand the role of EGFR signaling in normal cardiac function. We demonstrated that chronic repression of EGFR pathway would cause severe cardiac dysfunction with chamber dilations, left ventricular wall thinning and depressed cardiac function. Left ventricular hypertrophy (LVH) is associated with many cardiovascular diseases and is a risk factor for cardiac related morbidity and mortality. Mice homozygous with EGFR hypomorphic mutation display various background dependent phenotypes including left ventricle hypertrophy. Using two different strains, we mapped a quantitative trait locus (QTL) associated with cardiac hypertrophy. These studies should be useful in understanding the development of LVH and in predicting patients susceptible to cardiatoxicity induced by chronic use of anti-EGFR drugs.Doctor of Philosoph

Estimation of Graphical Models with Biological Applications

Graphical models are widely used to represent the dependency relationship among random variables. In this dissertation, we have developed three statistical methodologies for estimating graphical models using high dimensional genomic data. In the first two, we estimate undirected Gaussian graphical models (GGMs) which capture the conditional dependence among variables, and in the third, we describe a novel method to estimate a Gaussian Directed Acyclic Graph (DAG). In the first project, we focus on estimating GGMs from a group of dependent data. A motivating example is that of modeling gene expression collected on multiple tissues from the same individual. Existing methods that assume independence among graphs are not applicable in this setting. To estimate multiple dependent graphs, we decompose the problem into two graphical layers: the systemic layer, which is the network affecting all outcomes and therefore describing cross-graph dependency, and the category-specific layer, which represents the graph-specific variation. We propose a new graphical EM technique that estimates the two layers jointly; and also establish the estimation consistency and selection sparsistency of the proposed estimator. We confirm by simulation and real data analysis that our EM method is superior to a naive one-step method Next, we consider estimating GGMs from noisy data. A notable drawback of existing methods for estimating GGMs is that they ignore the existence of measurement error which is common in biological data. We propose a new experimental design using technical replicates, and develop a new methodology using an EM algorithm to efficiently estimate the sparse GGM by taking account the measurement error. We systematically study the asymptotic properties of the proposed method in high dimensional settings. Simulation study suggests that our method have substantially higher sensitivity and specificity to estimate the underlying graph than existing methods. Lastly, we consider the estimation of the skeleton of a Directed Acyclic Graph (DAG) using observational data. We propose a novel method named AdaPC to efficiently estimate the skeleton of a DAG by a two-step approach. The performance of our method is systematically evaluated by numerical examples.Doctor of Philosoph

Disentangled Speech Representation Learning Based on Factorized Hierarchical Variational Autoencoder with Self-Supervised Objective

Disentangled representation learning aims to extract explanatory features or factors and retain salient information. Factorized hierarchical variational autoencoder (FHVAE) presents a way to disentangle a speech signal into sequential-level and segmental-level features, which represent speaker identity and speech content information, respectively. As a self-supervised objective, autoregressive predictive coding (APC), on the other hand, has been used in extracting meaningful and transferable speech features for multiple downstream tasks. Inspired by the success of these two representation learning methods, this paper proposes to integrate the APC objective into the FHVAE framework aiming at benefiting from the additional self-supervision target. The main proposed method requires neither more training data nor more computational cost at test time, but obtains improved meaningful representations while maintaining disentanglement. The experiments were conducted on the TIMIT dataset. Results demonstrate that FHVAE equipped with the additional self-supervised objective is able to learn features providing superior performance for tasks including speech recognition and speaker recognition. Furthermore, voice conversion, as one application of disentangled representation learning, has been applied and evaluated. The results show performance similar to baseline of the new framework on voice conversion.Comment: Published in: 2021 IEEE 31st International Workshop on Machine Learning for Signal Processing (MLSP

Superiority of GNN over NN in generalizing bandlimited functions

Graph Neural Network (GNN) with its ability to integrate graph information has been widely used for data analyses. However, the expressive power of GNN has only been studied for graph-level tasks but not for node-level tasks, such as node classification, where one tries to interpolate missing nodal labels from the observed ones. In this paper, we study the expressive power of GNN for the said classification task, which is in essence a function interpolation problem. Explicitly, we derive the number of weights and layers needed for a GNN to interpolate a band-limited function in $\mathbb{R}^d$. Our result shows that, the number of weights needed to $\epsilon$-approximate a bandlimited function using the GNN architecture is much fewer than the best known one using a fully connected neural network (NN) - in particular, one only needs $O((\log \epsilon^{-1})^{d})$ weights using a GNN trained by $O((\log \epsilon^{-1})^{d})$ samples to $\epsilon$-approximate a discretized bandlimited signal in $\mathbb{R}^d$. The result is obtained by drawing a connection between the GNN structure and the classical sampling theorems, making our work the first attempt in this direction

Complex Recurrent Variational Autoencoder for Speech Enhancement

Commonly-used methods in speech enhancement are based on short-time fourier transform (STFT) representation, in particular on the magnitude of the STFT. This is because phase is naturally unstructured and intractable, and magnitude has shown more importance in speech enhancement. Nevertheless, phase has shown its significance in some research and cannot be ignored. Complex neural networks, with their inherent advantage, provide a solution for complex spectrogram processing. Complex variational autoencoder (VAE), as an extension of vanilla \acrshort{vae}, has shown positive results in complex spectrogram representation. However, the existing work on complex \acrshort{vae} only uses linear layers and merely applies the model on direct spectra representation. This paper extends the linear complex \acrshort{vae} to a non-linear one. Furthermore, on account of the temporal property of speech signals, a complex recurrent \acrshort{vae} is proposed. The proposed model has been applied on speech enhancement. As far as we know, it is the first time that a complex generative model is applied to speech enhancement. Experiments are based on the TIMIT dataset, while speech intelligibility and speech quality have been evaluated. The results show that, for speech enhancement, the proposed method has better performance on speech intelligibility and comparable performance on speech quality.Comment: submitted to INTERSPEECH 202