arXiv subjects

Fang Yao

Publications and source records attributed to Fang Yao.

At least 37 records · Page 2Linked to original sources

arXiv2024

Fast Signal Region Detection with Application to Whole Genome Association Studies

Research on the localization of the genetic basis associated with diseases or traits has been widely conducted in the last a few decades. Scan methods have been developed for region-based analysis in whole-genome association studies, helping us better understand how genetics influences human diseases or traits, especially when the aggregated effects of multiple causal variants are present. In this paper, we propose a fast and effective algorithm coupling with high-dimensional test for simultaneously detecting multiple signal regions, which is distinct from existing methods using scan or knockoff statistics. The idea is to conduct binary splitting with re-search and arrangement based on a sequence of dynamic critical values to increase detection accuracy and reduce computation. Theoretical and empirical studies demonstrate that our approach enjoys favorable theoretical guarantees with fewer restrictions and exhibits superior numerical performance with faster computation. Utilizing the UK Biobank data to identify the genetic regions related to breast cancer, we confirm previous findings and meanwhile, identify a number of new regions which suggest strong association with risk of breast cancer and deserve further investigation.

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arXiv2024

Spatial Interference Detection in Treatment Effect Model

Modeling the interference effect is an important issue in the field of causal inference. Existing studies rely on explicit and often homogeneous assumptions regarding interference structures. In this paper, we introduce a low-rank and sparse treatment effect model that leverages data-driven techniques to identify the locations of interference effects. A profiling algorithm is proposed to estimate the model coefficients, and based on these estimates, global test and local detection methods are established to detect the existence of interference and the interference neighbor locations for each unit. We derive the non-asymptotic bound of the estimation error, and establish theoretical guarantees for the global test and the accuracy of the detection method in terms of Jaccard index. Simulations and real data examples are provided to demonstrate the usefulness of the proposed method.

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arXiv2024

Physics-encoded Spatio-temporal Regression

Physics-informed methods have gained a great success in analyzing data with partial differential equation (PDE) constraints, which are ubiquitous when modeling dynamical systems. Different from the common penalty-based approach, this work promotes adherence to the underlying physical mechanism that facilitates statistical procedures. The motivating application concerns modeling fluorescence recovery after photobleaching, which is used for characterization of diffusion processes. We propose a physics-encoded regression model for handling spatio-temporally distributed data, which enables principled interpretability, parsimonious computation and efficient estimation by exploiting the structure of solutions of a governing evolution equation. The rate of convergence attaining the minimax optimality is theoretically demonstrated, generalizing the result obtained for the spatial regression. We conduct simulation studies to assess the performance of our proposed estimator and illustrate its usage in the aforementioned real data example.

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arXiv2024

Theory of functional principal component analysis for discretely observed data

Functional data analysis is an important research field in statistics which treats data as random functions drawn from some infinite-dimensional functional space, and functional principal component analysis (FPCA) based on eigen-decomposition plays a central role for data reduction and representation. After nearly three decades of research, there remains a key problem unsolved, namely, the perturbation analysis of covariance operator for diverging number of eigencomponents obtained from noisy and discretely observed data. This is fundamental for studying models and methods based on FPCA, while there has not been substantial progress since Hall, Müller and Wang (2006)'s result for a fixed number of eigenfunction estimates. In this work, we aim to establish a unified theory for this problem, obtaining upper bounds for eigenfunctions with diverging indices in both the $\mathcal{L}^2$ and supremum norms, and deriving the asymptotic distributions of eigenvalues for a wide range of sampling schemes. Our results provide insight into the phenomenon when the $\mathcal{L}^{2}$ bound of eigenfunction estimates with diverging indices is minimax optimal as if the curves are fully observed, and reveal the transition of convergence rates from nonparametric to parametric regimes in connection to sparse or dense sampling. We also develop a double truncation technique to handle the uniform convergence of estimated covariance and eigenfunctions. The technical arguments in this work are useful for handling the perturbation series with noisy and discretely observed functional data and can be applied in models or those involving inverse problems based on FPCA as regularization, such as functional linear regression.

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arXiv2023

Policy Evaluation for Temporal and/or Spatial Dependent Experiments

The aim of this paper is to establish a causal link between the policies implemented by technology companies and the outcomes they yield within intricate temporal and/or spatial dependent experiments. We propose a novel temporal/spatio-temporal Varying Coefficient Decision Process (VCDP) model, capable of effectively capturing the evolving treatment effects in situations characterized by temporal and/or spatial dependence. Our methodology encompasses the decomposition of the Average Treatment Effect (ATE) into the Direct Effect (DE) and the Indirect Effect (IE). We subsequently devise comprehensive procedures for estimating and making inferences about both DE and IE. Additionally, we provide a rigorous analysis of the statistical properties of these procedures, such as asymptotic power. To substantiate the effectiveness of our approach, we carry out extensive simulations and real data analyses.

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arXiv2023

Robust Functional Data Analysis for Discretely Observed Data

This paper examines robust functional data analysis for discretely observed data, where the underlying process encompasses various distributions, such as heavy tail, skewness, or contaminations. We propose a unified robust concept of functional mean, covariance, and principal component analysis, while existing methods and definitions often differ from one another or only address fully observed functions (the ``ideal'' case). Specifically, the robust functional mean can deviate from its non-robust counterpart and is estimated using robust local linear regression. Moreover, we define a new robust functional covariance that shares useful properties with the classic version. Importantly, this covariance yields the robust version of Karhunen--Loève decomposition and corresponding principal components beneficial for dimension reduction. The theoretical results of the robust functional mean, covariance, and eigenfunction estimates, based on pooling discretely observed data (ranging from sparse to dense), are established and aligned with their non-robust counterparts. The newly-proposed perturbation bounds for estimated eigenfunctions, with indexes allowed to grow with sample size, lay the foundation for further modeling based on robust functional principal component analysis.

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arXiv2022

Non-Asymptotic Guarantees for Robust Statistical Learning under Infinite Variance Assumption

There has been a surge of interest in developing robust estimators for models with heavy-tailed and bounded variance data in statistics and machine learning, while few works impose unbounded variance. This paper proposes two type of robust estimators, the ridge log-truncated M-estimator and the elastic net log-truncated M-estimator. The first estimator is applied to convex regressions such as quantile regression and generalized linear models, while the other one is applied to high dimensional non-convex learning problems such as regressions via deep neural networks. Simulations and real data analysis demonstrate the {robustness} of log-truncated estimations over standard estimations.

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arXiv2022

Dynamic Principal Component Analysis in High Dimensions

Principal component analysis is a versatile tool to reduce dimensionality which has wide applications in statistics and machine learning. It is particularly useful for modeling data in high-dimensional scenarios where the number of variables $p$ is comparable to, or much larger than the sample size $n$. Despite an extensive literature on this topic, researchers have focused on modeling static principal eigenvectors, which are not suitable for stochastic processes that are dynamic in nature. To characterize the change in the entire course of high-dimensional data collection, we propose a unified framework to directly estimate dynamic eigenvectors of covariance matrices. Specifically, we formulate an optimization problem by combining the local linear smoothing and regularization penalty together with the orthogonality constraint, which can be effectively solved by manifold optimization algorithms. We show that our method is suitable for high-dimensional data observed under both common and irregular designs, and theoretical properties of the estimators are investigated under $l_q (0 \leq q \leq 1)$ sparsity. Extensive experiments demonstrate the effectiveness of the proposed method in both simulated and real data examples.

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arXiv2022

Intrinsic Riemannian Functional Data Analysis for Sparse Longitudinal Observations

A new framework is developed to intrinsically analyze sparsely observed Riemannian functional data. It features four innovative components: a frame-independent covariance function, a smooth vector bundle termed covariance vector bundle, a parallel transport and a smooth bundle metric on the covariance vector bundle. The introduced intrinsic covariance function links estimation of covariance structure to smoothing problems that involve raw covariance observations derived from sparsely observed Riemannian functional data, while the covariance vector bundle provides a rigorous mathematical foundation for formulating such smoothing problems. The parallel transport and the bundle metric together make it possible to measure fidelity of fit to the covariance function. They also play a critical role in quantifying the quality of estimators for the covariance function. As an illustration, based on the proposed framework, we develop a local linear smoothing estimator for the covariance function, analyze its theoretical properties, and provide numerical demonstration via simulated and real datasets. The intrinsic feature of the framework makes it applicable to not only Euclidean submanifolds but also manifolds without a canonical ambient space.

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arXiv2021

Online Generalized Additive Model

Additive models and generalized additive models are effective semiparametric tools for multidimensional data. In this article we propose an online smoothing backfitting method for generalized additive models with local polynomial smoothers. The main idea is to use a second order expansion to approximate the nonlinear integral equations to maximize the local quasilikelihood and store the coefficients as the sufficient statistics which can be updated in an online manner by a dynamic candidate bandwidth method. The updating procedure only depends on the stored sufficient statistics and the current data block. We derive the asymptotic normality as well as the relative efficiency lower bounds of the online estimates, which provides insight into the relationship between estimation accuracy and computational cost driven by the length of candidate bandwidth sequence. Simulations and real data examples are provided to validate our findings.

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arXiv2021

Test of Weak Separability for Spatially Stationary Functional Field

For spatially dependent functional data, a generalized Karhunen-Loève expansion is commonly used to decompose data into an additive form of temporal components and spatially correlated coefficients. This structure provides a convenient model to investigate the space-time interactions, but may not hold for complex spatio-temporal processes. In this work, we introduce the concept of weak separability, and propose a formal test to examine its validity for non-replicated spatially stationary functional field. The asymptotic distribution of the test statistic that adapts to potentially diverging ranks is derived by constructing lag covariance estimation, which is easy to compute for practical implementation. We demonstrate the efficacy of the proposed test via simulations and illustrate its usefulness in two real examples: China PM$_{2.5}$ data and Harvard Forest data.

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arXiv2021

Online Estimation for Functional Data

Functional data analysis has attracted considerable interest and is facing new challenges, one of which is the increasingly available data in a streaming manner. In this article we develop an online nonparametric method to dynamically update the estimates of mean and covariance functions for functional data. The kernel-type estimates can be decomposed into two sufficient statistics depending on the data-driven bandwidths. We propose to approximate the future optimal bandwidths by a sequence of dynamically changing candidates and combine the corresponding statistics across blocks to form the updated estimation. The proposed online method is easy to compute based on the stored sufficient statistics and the current data block. We derive the asymptotic normality and, more importantly, the relative efficiency lower bounds of the online estimates of mean and covariance functions. This provides insight into the relationship between estimation accuracy and computational cost driven by the length of candidate bandwidth sequence. Simulations and real data examples are provided to support such findings.

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arXiv2021

Intrinsic Wasserstein Correlation Analysis

We develop a framework of canonical correlation analysis for distribution-valued functional data within the geometry of Wasserstein spaces. Specifically, we formulate an intrinsic concept of correlation between random distributions, propose estimation methods based on functional principal component analysis (FPCA) and Tikhonov regularization, respectively, for the correlation and its corresponding weight functions, and establish the minimax convergence rates of the estimators. The key idea is to extend the framework of tensor Hilbert spaces to distribution-valued functional data to overcome the challenging issue raised by nonlinearity of Wasserstein spaces. The finite-sample performance of the proposed estimators is illustrated via simulation studies, and the practical merit is demonstrated via a study on the association of distributions of brain activities between two brain regions.

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arXiv2021

Sparse Functional Principal Component Analysis in High Dimensions

Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with a single or finite number of random functions (much smaller than the sample size $n$). In this work, we focus on high-dimensional functional processes where the number of random functions $p$ is comparable to, or even much larger than $n$. Such data are ubiquitous in various fields such as neuroimaging analysis, and cannot be properly modeled by existing methods. We propose a new algorithm, called sparse FPCA, which is able to model principal eigenfunctions effectively under sensible sparsity regimes. While sparsity assumptions are standard in multivariate statistics, they have not been investigated in the complex context where not only is $p$ large, but also each variable itself is an intrinsically infinite-dimensional process. The sparsity structure motivates a thresholding rule that is easy to compute without nonparametric smoothing by exploiting the relationship between univariate orthonormal basis expansions and multivariate Kahunen-Loève (K-L) representations. We investigate the theoretical properties of the resulting estimators, and illustrate the performance with simulated and real data examples.

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arXiv2020

Functional Regression on Manifold with Contamination

We propose a new method for functional nonparametric regression with a predictor that resides on a finite-dimensional manifold but is only observable in an infinite-dimensional space. Contamination of the predictor due to discrete/noisy measurements is also accounted for. By using functional local linear manifold smoothing, the proposed estimator enjoys a polynomial rate of convergence that adapts to the intrinsic manifold dimension and the contamination level. This is in contrast to the logarithmic convergence rate in the literature of functional nonparametric regression. We also observe a phase transition phenomenon regarding the interplay of the manifold dimension and the contamination level. We demonstrate that the proposed method has favorable numerical performance relative to commonly used methods via simulated and real data examples.

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arXiv2019

Intrinsic Riemannian Functional Data Analysis

In this work we develop a novel and foundational framework for analyzing general Riemannian functional data, in particular a new development of tensor Hilbert spaces along curves on a manifold. Such spaces enable us to derive Karhunen-Loeve expansion for Riemannian random processes. This framework also features an approach to compare objects from different tensor Hilbert spaces, which paves the way for asymptotic analysis in Riemannian functional data analysis. Built upon intrinsic geometric concepts such as vector field, Levi-Civita connection and parallel transport on Riemannian manifolds, the developed framework applies to not only Euclidean submanifolds but also manifolds without a natural ambient space. As applications of this framework, we develop intrinsic Riemannian functional principal component analysis (iRFPCA) and intrinsic Riemannian functional linear regression (iRFLR) that are distinct from their traditional and ambient counterparts. We also provide estimation procedures for iRFPCA and iRFLR, and investigate their asymptotic properties within the intrinsic geometry. Numerical performance is illustrated by simulated and real examples.

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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

Distribution and correlation free two-sample test of high-dimensional means

We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This two-sample test based on a nontrivial extension of the one-sample central limit theorem (Chernozhukov et al., 2017) provides a practically useful procedure with rigorous theoretical guarantees on its size and power assessment. In particular, the proposed test is easy to compute and does not require the independently and identically distributed assumption, which is allowed to have different distributions and arbitrary correlation structures. Further desired features include weaker moments and tail conditions than existing methods, allowance for highly unequal sample sizes, consistent power behavior under fairly general alternative, data dimension allowed to be exponentially high under the umbrella of such general conditions. Simulated and real data examples are used to demonstrate the favorable numerical performance over existing methods.

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