arXiv subjects

Elynn Y. Chen

Publications and source records attributed to Elynn Y. Chen.

10 recordsLinked to original sources

arXiv2024

Time-Varying Matrix Factor Models

Matrix-variate data of high dimensions are frequently observed in finance and economics, spanning extended time periods, such as the long-term data on international trade flows among numerous countries. To address potential structural shifts and explore the matrix structure's informational context, we propose a time-varying matrix factor model. This model accommodates changing factor loadings over time, revealing the underlying dynamic structure through nonparametric principal component analysis and facilitating dimension reduction. We establish the consistency and asymptotic normality of our estimators under general conditions that allow for weak correlations across time, rows, or columns of the noise. A novel approach is introduced to overcome rotational ambiguity in the estimators, enhancing the clarity and interpretability of the estimated loading matrices. Our simulation study highlights the merits of the proposed estimators and the effective of the smoothing operation. In an application to international trade flow, we investigate the trading hubs, centrality, patterns, and trends in the trading network.

stat.ME↗

arXiv2024

Semi-parametric TEnsor Factor Analysis by Iteratively Projected Singular Value Decomposition

This paper introduces a general framework of Semi-parametric TEnsor Factor Analysis (STEFA) that focuses on the methodology and theory of low-rank tensor decomposition with auxiliary covariates. Semi-parametric TEnsor Factor Analysis models extend tensor factor models by incorporating auxiliary covariates in the loading matrices. We propose an algorithm of iteratively projected singular value decomposition (IP-SVD) for the semi-parametric estimation. It iteratively projects tensor data onto the linear space spanned by the basis functions of covariates and applies singular value decomposition on matricized tensors over each mode. We establish the convergence rates of the loading matrices and the core tensor factor. The theoretical results only require a sub-exponential noise distribution, which is weaker than the assumption of sub-Gaussian tail of noise in the literature. Compared with the Tucker decomposition, IP-SVD yields more accurate estimators with a faster convergence rate. Besides estimation, we propose several prediction methods with new covariates based on the STEFA model. On both synthetic and real tensor data, we demonstrate the efficacy of the STEFA model and the IP-SVD algorithm on both the estimation and prediction tasks.

stat.ME↗

arXiv2022

Constrained Factor Models for High-Dimensional Matrix-Variate Time Series

High-dimensional matrix-variate time series data are becoming widely available in many scientific fields, such as economics, biology, and meteorology. To achieve significant dimension reduction while preserving the intrinsic matrix structure and temporal dynamics in such data, Wang et al. (2017) proposed a matrix factor model that is shown to provide effective analysis. In this paper, we establish a general framework for incorporating domain or prior knowledge in the matrix factor model through linear constraints. The proposed framework is shown to be useful in achieving parsimonious parameterization, facilitating interpretation of the latent matrix factor, and identifying specific factors of interest. Fully utilizing the prior-knowledge-induced constraints results in more efficient and accurate modeling, inference, dimension reduction as well as a clear and better interpretation of the results. In this paper, constrained, multi-term, and partially constrained factor models for matrix-variate time series are developed, with efficient estimation procedures and their asymptotic properties. We show that the convergence rates of the constrained factor loading matrices are much faster than those of the conventional matrix factor analysis under many situations. Simulation studies are carried out to demonstrate the finite-sample performance of the proposed method and its associated asymptotic properties. We illustrate the proposed model with three applications, where the constrained matrix-factor models outperform their unconstrained counterparts in the power of variance explanation under the out-of-sample 10-fold cross-validation setting.

stat.ME↗

arXiv2022

Statistical Inference for High-Dimensional Matrix-Variate Factor Model

This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of observations ($T$). We propose an estimation method called $α$-PCA that preserves the matrix structure and aggregates mean and contemporary covariance through a hyper-parameter $α$. We develop an inferential theory, establishing consistency, the rate of convergence, and the limiting distributions, under general conditions that allow for correlations across time, rows, or columns of the noise. We show both theoretical and empirical methods of choosing the best $α$, depending on the use-case criteria. Simulation results demonstrate the adequacy of the asymptotic results in approximating the finite sample properties. The $α$-PCA compares favorably with the existing ones. Finally, we illustrate its applications with a real numeric data set and two real image data sets. In all applications, the proposed estimation procedure outperforms previous methods in the power of variance explanation using out-of-sample 10-fold cross-validation.

math.ST↗

arXiv2022

Reinforcement Learning with Heterogeneous Data: Estimation and Inference

Reinforcement Learning (RL) has the promise of providing data-driven support for decision-making in a wide range of problems in healthcare, education, business, and other domains. Classical RL methods focus on the mean of the total return and, thus, may provide misleading results in the setting of the heterogeneous populations that commonly underlie large-scale datasets. We introduce the K-Heterogeneous Markov Decision Process (K-Hetero MDP) to address sequential decision problems with population heterogeneity. We propose the Auto-Clustered Policy Evaluation (ACPE) for estimating the value of a given policy, and the Auto-Clustered Policy Iteration (ACPI) for estimating the optimal policy in a given policy class. Our auto-clustered algorithms can automatically detect and identify homogeneous sub-populations, while estimating the Q function and the optimal policy for each sub-population. We establish convergence rates and construct confidence intervals for the estimators obtained by the ACPE and ACPI. We present simulations to support our theoretical findings, and we conduct an empirical study on the standard MIMIC-III dataset. The latter analysis shows evidence of value heterogeneity and confirms the advantages of our new method.

cs.LG↗

arXiv2021

On Projection Robust Optimal Transport: Sample Complexity and Model Misspecification

Optimal transport (OT) distances are increasingly used as loss functions for statistical inference, notably in the learning of generative models or supervised learning. Yet, the behavior of minimum Wasserstein estimators is poorly understood, notably in high-dimensional regimes or under model misspecification. In this work we adopt the viewpoint of projection robust (PR) OT, which seeks to maximize the OT cost between two measures by choosing a $k$-dimensional subspace onto which they can be projected. Our first contribution is to establish several fundamental statistical properties of PR Wasserstein distances, complementing and improving previous literature that has been restricted to one-dimensional and well-specified cases. Next, we propose the integral PR Wasserstein (IPRW) distance as an alternative to the PRW distance, by averaging rather than optimizing on subspaces. Our complexity bounds can help explain why both PRW and IPRW distances outperform Wasserstein distances empirically in high-dimensional inference tasks. Finally, we consider parametric inference using the PRW distance. We provide an asymptotic guarantee of two types of minimum PRW estimators and formulate a central limit theorem for max-sliced Wasserstein estimator under model misspecification. To enable our analysis on PRW with projection dimension larger than one, we devise a novel combination of variational analysis and statistical theory.

math.ST↗

arXiv2020

Community Network Auto-Regression for High-Dimensional Time Series

Modeling responses on the nodes of a large-scale network is an important task that arises commonly in practice. This paper proposes a community network vector autoregressive (CNAR) model, which utilizes the network structure to characterize the dependence and intra-community homogeneity of the high dimensional time series. The CNAR model greatly increases the flexibility and generality of the network vector autoregressive (Zhu et al, 2017, NAR) model by allowing heterogeneous network effects across different network communities. In addition, the non-community-related latent factors are included to account for unknown cross-sectional dependence. The number of network communities can diverge as the network expands, which leads to estimating a diverging number of model parameters. We obtain a set of stationary conditions and develop an efficient two-step weighted least-squares estimator. The consistency and asymptotic normality properties of the estimators are established. The theoretical results show that the two-step estimator improves the one-step estimator by an order of magnitude when the error admits a factor structure. The advantages of the CNAR model are further illustrated on a variety of synthetic and real datasets.

stat.ME↗

arXiv2020

Modeling Multivariate Spatial-Temporal Data with Latent Low-Dimensional Dynamics

High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies in large data sets. In this paper, we propose a new approach to utilize the correlations in variable, space and time to achieve dimension reduction and to facilitate spatial/temporal predictions in the high-dimensional settings. The multivariate spatial-temporal process is represented as a linear transformation of a lower-dimensional latent factor process. The spatial dependence structure of the factor process is further represented non-parametrically in terms of latent empirical orthogonal functions. The low-dimensional structure is completely unknown in our setting and is learned entirely from data collected irregularly over space but regularly over time. We propose innovative estimation and prediction methods based on the latent low-rank structures. Asymptotic properties of the estimators and predictors are established. Extensive experiments on synthetic and real data sets show that, while the dimensions are reduced significantly, the spatial, temporal and variable-wise covariance structures are largely preserved. The efficacy of our method is further confirmed by the prediction performances on both synthetic and real data sets.

stat.ME↗

arXiv2019

Low-Rank Principal Eigenmatrix Analysis

Sparse PCA is a widely used technique for high-dimensional data analysis. In this paper, we propose a new method called low-rank principal eigenmatrix analysis. Different from sparse PCA, the dominant eigenvectors are allowed to be dense but are assumed to have a low-rank structure when matricized appropriately. Such a structure arises naturally in several practical cases: Indeed the top eigenvector of a circulant matrix, when matricized appropriately is a rank-1 matrix. We propose a matricized rank-truncated power method that could be efficiently implemented and establish its computational and statistical properties. Extensive experiments on several synthetic data sets demonstrate the competitive empirical performance of our method.

stat.ML↗

arXiv2019

Modeling Dynamic Transport Network with Matrix Factor Models: with an Application to International Trade Flow

International trade research plays an important role to inform trade policy and shed light on wider issues relating to poverty, development, migration, productivity, and economy. With recent advances in information technology, global and regional agencies distribute an enormous amount of internationally comparable trading data among a large number of countries over time, providing a goldmine for empirical analysis of international trade. Meanwhile, an array of new statistical methods are recently developed for dynamic network analysis. However, these advanced methods have not been utilized for analyzing such massive dynamic cross-country trading data. International trade data can be viewed as a dynamic transport network because it emphasizes the amount of goods moving across a network. Most literature on dynamic network analysis concentrates on the connectivity network that focuses on link formation or deformation rather than the transport moving across the network. We take a different perspective from the pervasive node-and-edge level modeling: the dynamic transport network is modeled as a time series of relational matrices. We adopt a matrix factor model of \cite{wang2018factor}, with a specific interpretation for the dynamic transport network. Under the model, the observed surface network is assumed to be driven by a latent dynamic transport network with lower dimensions. The proposed method is able to unveil the latent dynamic structure and achieve the objective of dimension reduction. We applied the proposed framework and methodology to a data set of monthly trading volumes among 24 countries and regions from 1982 to 2015. Our findings shed light on trading hubs, centrality, trends and patterns of international trade and show matching change points to trading policies. The dataset also provides a fertile ground for future research on international trade.

econ.EM↗