arXiv subjects

Dehan Kong

Publications and source records attributed to Dehan Kong.

46 records · Page 3Linked to original sources

arXiv2022

Covariance Estimation for Matrix-valued Data

Covariance estimation for matrix-valued data has received an increasing interest in applications. Unlike previous works that rely heavily on matrix normal distribution assumption and the requirement of fixed matrix size, we propose a class of distribution-free regularized covariance estimation methods for high-dimensional matrix data under a separability condition and a bandable covariance structure. Under these conditions, the original covariance matrix is decomposed into a Kronecker product of two bandable small covariance matrices representing the variability over row and column directions. We formulate a unified framework for estimating bandable covariance, and introduce an efficient algorithm based on rank one unconstrained Kronecker product approximation. The convergence rates of the proposed estimators are established, and the derived minimax lower bound shows our proposed estimator is rate-optimal under certain divergence regimes of matrix size. We further introduce a class of robust covariance estimators and provide theoretical guarantees to deal with heavy-tailed data. We demonstrate the superior finite-sample performance of our methods using simulations and real applications from a gridded temperature anomalies dataset and a S&P 500 stock data analysis.

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arXiv2022

Ultra-high Dimensional Variable Selection for Doubly Robust Causal Inference

Causal inference has been increasingly reliant on observational studies with rich covariate information. To build tractable causal procedures, such as the doubly robust estimators, it is imperative to first extract important features from high or even ultra-high dimensional data. In this paper, we propose causal ball screening for confounder selection from modern ultra-high dimensional data sets. Unlike the familiar task of variable selection for prediction modeling, our confounder selection procedure aims to control for confounding while improving efficiency in the resulting causal effect estimate. Previous empirical and theoretical studies suggest excluding causes of the treatment that are not confounders. Motivated by these results, our goal is to keep all the predictors of the outcome in both the propensity score and outcome regression models. A distinctive feature of our proposal is that we use an outcome model-free procedure for propensity score model selection, thereby maintaining double robustness in the resulting causal effect estimator. Our theoretical analyses show that the proposed procedure enjoys a number of properties, including model selection consistency and point-wise normality. Synthetic and real data analysis show that our proposal performs favorably with existing methods in a range of realistic settings. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.

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arXiv2020

Identifiability of causal effects with multiple causes and a binary outcome

Unobserved confounding presents a major threat to causal inference from observational studies. Recently, several authors suggest that this problem may be overcome in a shared confounding setting where multiple treatments are independent given a common latent confounder. It has been shown that under a linear Gaussian model for the treatments, the causal effect is not identifiable without parametric assumptions on the outcome model. In this paper, we show that the causal effect is indeed identifiable if we assume a general binary choice model for the outcome with a non-probit link. Our identification approach is based on the incongruence between Gaussianity of the treatments and latent confounder, and non-Gaussianity of a latent outcome variable. We further develop a two-step likelihood-based estimation procedure.

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arXiv2020

Multivariate functional responses low rank regression with an application to brain imaging data

We propose a multivariate functional responses low rank regression model with possible high dimensional functional responses and scalar covariates. By expanding the slope functions on a set of sieve basis, we reconstruct the basis coefficients as a matrix. To estimate these coefficients, we propose an efficient procedure using nuclear norm regularization. We also derive error bounds for our estimates and evaluate our method using simulations. We further apply our method to the Human Connectome Project neuroimaging data to predict cortical surface motor task-evoked functional magnetic resonance imaging signals using various clinical covariates to illustrate the usefulness of our results.

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arXiv2020

Federated Learning for Computational Pathology on Gigapixel Whole Slide Images

Deep Learning-based computational pathology algorithms have demonstrated profound ability to excel in a wide array of tasks that range from characterization of well known morphological phenotypes to predicting non-human-identifiable features from histology such as molecular alterations. However, the development of robust, adaptable, and accurate deep learning-based models often rely on the collection and time-costly curation large high-quality annotated training data that should ideally come from diverse sources and patient populations to cater for the heterogeneity that exists in such datasets. Multi-centric and collaborative integration of medical data across multiple institutions can naturally help overcome this challenge and boost the model performance but is limited by privacy concerns amongst other difficulties that may arise in the complex data sharing process as models scale towards using hundreds of thousands of gigapixel whole slide images. In this paper, we introduce privacy-preserving federated learning for gigapixel whole slide images in computational pathology using weakly-supervised attention multiple instance learning and differential privacy. We evaluated our approach on two different diagnostic problems using thousands of histology whole slide images with only slide-level labels. Additionally, we present a weakly-supervised learning framework for survival prediction and patient stratification from whole slide images and demonstrate its effectiveness in a federated setting. Our results show that using federated learning, we can effectively develop accurate weakly supervised deep learning models from distributed data silos without direct data sharing and its associated complexities, while also preserving differential privacy using randomized noise generation.

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arXiv2020

Stochastic Generalized Lotka-Volterra Model with An Application to Learning Microbial Community Structures

Inferring microbial community structure based on temporal metagenomics data is an important goal in microbiome studies. The deterministic generalized Lotka-Volterra differential (GLV) equations have been used to model the dynamics of microbial data. However, these approaches fail to take random environmental fluctuations into account, which may negatively impact the estimates. We propose a new stochastic GLV (SGLV) differential equation model, where the random perturbations of Brownian motion in the model can naturally account for the external environmental effects on the microbial community. We establish new conditions and show various mathematical properties of the solutions including general existence and uniqueness, stationary distribution, and ergodicity. We further develop approximate maximum likelihood estimators based on discrete observations and systematically investigate the consistency and asymptotic normality of the proposed estimators. Our method is demonstrated through simulation studies and an application to the well-known "moving picture" temporal microbial dataset.

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arXiv2020

Nonparametric Matrix Response Regression with Application to Brain Imaging Data Analysis

With the rapid growth of neuroimaging technologies, a great effort has been dedicated recently to investigate the dynamic changes in brain activity. Examples include time course calcium imaging and dynamic brain functional connectivity. In this paper, we propose a novel nonparametric matrix response regression model to characterize the nonlinear association between 2D image outcomes and predictors such as time and patient information. Our estimation procedure can be formulated as a nuclear norm regularization problem, which can capture the underlying low-rank structure of the dynamic 2D images. We present a computationally efficient algorithm, derive the asymptotic theory and show that the method outperforms other existing approaches in simulations. We then apply the proposed method to a calcium imaging study for estimating the change of fluorescent intensities of neurons, and an electroencephalography study for a comparison in the dynamic connectivity covariance matrices between alcoholic and control individuals. For both studies, the method leads to a substantial improvement in prediction error.

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arXiv2019

Nonparametric principal subspace regression

In scientific applications, multivariate observations often come in tandem with temporal or spatial covariates, with which the underlying signals vary smoothly. The standard approaches such as principal component analysis and factor analysis neglect the smoothness of the data, while multivariate linear or nonparametric regression fail to leverage the correlation information among multivariate response variables. We propose a novel approach named nonparametric principal subspace regression to overcome these issues. By decoupling the model discrepancy, a simple and general two-step framework is introduced, which leaves much flexibility in choice of model fitting. We establish theoretical property of the general framework, and offer implementation procedures that fulfill requirements and enjoy the theoretical guarantee. We demonstrate the favorable finite-sample performance of the proposed method through simulations and a real data application from an electroencephalogram study.

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arXiv2019

Modeling Symmetric Positive Definite Matrices with An Application to Functional Brain Connectivity

In neuroscience, functional brain connectivity describes the connectivity between brain regions that share functional properties. Neuroscientists often characterize it by a time series of covariance matrices between functional measurements of distributed neuron areas. An effective statistical model for functional connectivity and its changes over time is critical for better understanding the mechanisms of brain and various neurological diseases. To this end, we propose a matrix-log mean model with an additive heterogeneous noise for modeling random symmetric positive definite matrices that lie in a Riemannian manifold. The heterogeneity of error terms is introduced specifically to capture the curved nature of the manifold. We then propose to use the local scan statistics to detect change patterns in the functional connectivity. Theoretically, we show that our procedure can recover all change points consistently. Simulation studies and an application to the Human Connectome Project lend further support to the proposed methodology.

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arXiv2019

Matrix Linear Discriminant Analysis

We propose a novel linear discriminant analysis approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional linear discriminant analysis and the ordinary least squares, we consider an efficient nuclear norm penalized regression that encourages a low-rank structure. Theoretical properties including a non-asymptotic risk bound and a rank consistency result are established. Simulation studies and an application to electroencephalography data show the superior performance of the proposed method over the existing approaches.

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