arXiv subjects

Haipeng Shen

Publications and source records attributed to Haipeng Shen.

15 recordsLinked to original sources

arXiv2024

Nested Deep Learning Model Towards A Foundation Model for Brain Signal Data

Epilepsy affects around 50 million people globally. Electroencephalography (EEG) or Magnetoencephalography (MEG) based spike detection plays a crucial role in diagnosis and treatment. Manual spike identification is time-consuming and requires specialized training that further limits the number of qualified professionals. To ease the difficulty, various algorithmic approaches have been developed. However, the existing methods face challenges in handling varying channel configurations and in identifying the specific channels where the spikes originate. A novel Nested Deep Learning (NDL) framework is proposed to overcome these limitations. NDL applies a weighted combination of signals across all channels, ensuring adaptability to different channel setups, and allows clinicians to identify key channels more accurately. Through theoretical analysis and empirical validation on real EEG/MEG datasets, NDL is shown to improve prediction accuracy, achieve channel localization, support cross-modality data integration, and adapt to various neurophysiological applications.

stat.ML↗

arXiv2023

Optimal Functional Bilinear Regression with Two-way Functional Covariates via Reproducing Kernel Hilbert Space

Traditional functional linear regression usually takes a one-dimensional functional predictor as input and estimates the continuous coefficient function. Modern applications often generate two-dimensional covariates, which become matrices when observed at grid points. To avoid the inefficiency of the classical method involving estimation of a two-dimensional coefficient function, we propose a functional bilinear regression model, and introduce an innovative three-term penalty to impose roughness penalty in the estimation. The proposed estimator exhibits minimax optimal property for prediction under the framework of reproducing kernel Hilbert space. An iterative generalized cross-validation approach is developed to choose tuning parameters, which significantly improves the computational efficiency over the traditional cross-validation approach. The statistical and computational advantages of the proposed method over existing methods are further demonstrated via simulated experiments, the Canadian weather data, and a biochemical long-range infrared light detection and ranging data.

stat.ME↗

arXiv2022

Nonparametric Independent Component Analysis for the Sources with Mixed Spectra

Independent component analysis (ICA) is a blind source separation method to recover source signals of interest from their mixtures. Most existing ICA procedures assume independent sampling. Second-order-statistics-based source separation methods have been developed based on parametric time series models for the mixtures from the autocorrelated sources. However, the second-order-statistics-based methods cannot separate the sources accurately when the sources have temporal autocorrelations with mixed spectra. To address this issue, we propose a new ICA method by estimating spectral density functions and line spectra of the source signals using cubic splines and indicator functions, respectively. The mixed spectra and the mixing matrix are estimated by maximizing the Whittle likelihood function. We illustrate the performance of the proposed method through simulation experiments and an EEG data application. The numerical results indicate that our approach outperforms existing ICA methods, including SOBI algorithms. In addition, we investigate the asymptotic behavior of the proposed method.

stat.ML↗

arXiv2021

Network regression and supervised centrality estimation

The centrality in a network is often used to measure nodes' importance and model network effects on a certain outcome. Empirical studies widely adopt a two-stage procedure, which first estimates the centrality from the observed noisy network and then infers the network effect from the estimated centrality, even though it lacks theoretical understanding. We propose a unified modeling framework to study the properties of centrality estimation and inference and the subsequent network regression analysis with noisy network observations. Furthermore, we propose a supervised centrality estimation methodology, which aims to simultaneously estimate both centrality and network effect. We showcase the advantages of our method compared with the two-stage method both theoretically and numerically via extensive simulations and a case study in predicting currency risk premiums from the global trade network.

econ.EM↗

arXiv2021

Testing and Support Recovery of Correlation Structures for Matrix-Valued Observations with an Application to Stock Market Data

Estimation of the covariance matrix of asset returns is crucial to portfolio construction. As suggested by economic theories, the correlation structure among assets differs between emerging markets and developed countries. It is therefore imperative to make rigorous statistical inference on correlation matrix equality between the two groups of countries. However, if the traditional vector-valued approach is undertaken, such inference is either infeasible due to limited number of countries comparing to the relatively abundant assets, or invalid due to the violations of temporal independence assumption. This highlights the necessity of treating the observations as matrix-valued rather than vector-valued. With matrix-valued observations, our problem of interest can be formulated as statistical inference on covariance structures under sub-Gaussian distributions, i.e., testing non-correlation and correlation equality, as well as the corresponding support estimations. We develop procedures that are asymptotically optimal under some regularity conditions. Simulation results demonstrate the computational and statistical advantages of our procedures over certain existing state-of-the-art methods for both normal and non-normal distributions. Application of our procedures to stock market data reveals interesting patterns and validates several economic propositions via rigorous statistical testing.

stat.ME↗

arXiv2017

To Wait or Not to Wait: Two-way Functional Hazards Model for Understanding Waiting in Call Centers

Telephone call centers offer a convenient communication channel between businesses and their customers. Efficient management of call centers needs accurate modeling of customer waiting behavior, which contains important information about customer patience (how long a customer is willing to wait) and service quality (how long a customer needs to wait to get served). Hazard functions offer dynamic characterization of customer waiting behavior, and provide critical inputs for agent scheduling. Motivated by this application, we develop a two-way functional hazards (tF-Hazards) model to study customer waiting behavior as a function of two timescales, waiting duration and the time of day that a customer calls in. The model stems from a two-way piecewise constant hazard function, and imposes low-rank structure and smoothness on the hazard rates to enhance interpretability. We exploit an alternating direction method of multipliers (ADMM) algorithm to optimize a penalized likelihood function of the model. We carefully analyze the data from a US bank call center, and provide informative insights about customer patience and service quality patterns along waiting time and across different times of a day. The findings provide primitive inputs for call center agent staffing and scheduling, as well as for call center practitioners to understand the effect of system protocols on customer waiting behavior.

stat.AP↗

arXiv2013

Robust regularized singular value decomposition with application to mortality data

We develop a robust regularized singular value decomposition (RobRSVD) method for analyzing two-way functional data. The research is motivated by the application of modeling human mortality as a smooth two-way function of age group and year. The RobRSVD is formulated as a penalized loss minimization problem where a robust loss function is used to measure the reconstruction error of a low-rank matrix approximation of the data, and an appropriately defined two-way roughness penalty function is used to ensure smoothness along each of the two functional domains. By viewing the minimization problem as two conditional regularized robust regressions, we develop a fast iterative reweighted least squares algorithm to implement the method. Our implementation naturally incorporates missing values. Furthermore, our formulation allows rigorous derivation of leave-one-row/column-out cross-validation and generalized cross-validation criteria, which enable computationally efficient data-driven penalty parameter selection. The advantages of the new robust method over nonrobust ones are shown via extensive simulation studies and the mortality rate application.

stat.AP↗

arXiv2013

A General Framework For Consistency of Principal Component Analysis

A general asymptotic framework is developed for studying consis- tency properties of principal component analysis (PCA). Our frame- work includes several previously studied domains of asymptotics as special cases and allows one to investigate interesting connections and transitions among the various domains. More importantly, it enables us to investigate asymptotic scenarios that have not been considered before, and gain new insights into the consistency, subspace consistency and strong inconsistency regions of PCA and the boundaries among them. We also establish the corresponding convergence rate within each region. Under general spike covariance models, the dimension (or the number of variables) discourages the consistency of PCA, while the sample size and spike information (the relative size of the population eigenvalues) encourages PCA consistency. Our framework nicely illustrates the relationship among these three types of information in terms of dimension, sample size and spike size, and rigorously characterizes how their relationships affect PCA consistency.

math.ST↗

arXiv2013

Surprising Asymptotic Conical Structure in Critical Sample Eigen-Directions

The aim of this paper is to establish several deep theoretical properties of principal component analysis for multiple-component spike covariance models. Our new results reveal a surprising asymptotic conical structure in critical sample eigendirections under the spike models with distinguishable (or indistinguishable) eigenvalues, when the sample size and/or the number of variables (or dimension) tend to infinity. The consistency of the sample eigenvectors relative to their population counterparts is determined by the ratio between the dimension and the product of the sample size with the spike size. When this ratio converges to a nonzero constant, the sample eigenvector converges to a cone, with a certain angle to its corresponding population eigenvector.In the High Dimension, Low Sample Size case, the angle between the sample eigenvector and its population counterpart converges to a limiting distribution.Several generalizations of the multi-spike covariance models are also explored, and additional theoretical results are presented.

math.ST↗

arXiv2012

High Dimensional Principal Component Scores and Data Visualization

Principal component analysis is a useful dimension reduction and data visualization method. However, in high dimension, low sample size asymptotic contexts, where the sample size is fixed and the dimension goes to infinity,a paradox has arisen. In particular, despite the useful real data insights commonly obtained from principal component score visualization, these scores are not consistent even when the sample eigen-vectors are consistent. This paradox is resolved by asymptotic study of the ratio between the sample and population principal component scores. In particular, it is seen that this proportion converges to a non-degenerate random variable. The realization is the same for each data point, i.e. there is a common random rescaling, which appears for each eigen-direction. This then gives inconsistent axis labels for the standard scores plot, yet the relative positions of the points (typically the main visual content) are consistent. This paradox disappears when the sample size goes to infinity.

stat.AP↗

arXiv2012

A two-way regularization method for MEG source reconstruction

The MEG inverse problem refers to the reconstruction of the neural activity of the brain from magnetoencephalography (MEG) measurements. We propose a two-way regularization (TWR) method to solve the MEG inverse problem under the assumptions that only a small number of locations in space are responsible for the measured signals (focality), and each source time course is smooth in time (smoothness). The focality and smoothness of the reconstructed signals are ensured respectively by imposing a sparsity-inducing penalty and a roughness penalty in the data fitting criterion. A two-stage algorithm is developed for fast computation, where a raw estimate of the source time course is obtained in the first stage and then refined in the second stage by the two-way regularization. The proposed method is shown to be effective on both synthetic and real-world examples.

stat.AP↗

arXiv2012

Functional dynamic factor models with application to yield curve forecasting

Accurate forecasting of zero coupon bond yields for a continuum of maturities is paramount to bond portfolio management and derivative security pricing. Yet a universal model for yield curve forecasting has been elusive, and prior attempts often resulted in a trade-off between goodness of fit and consistency with economic theory. To address this, herein we propose a novel formulation which connects the dynamic factor model (DFM) framework with concepts from functional data analysis: a DFM with functional factor loading curves. This results in a model capable of forecasting functional time series. Further, in the yield curve context we show that the model retains economic interpretation. Model estimation is achieved through an expectation-maximization algorithm, where the time series parameters and factor loading curves are simultaneously estimated in a single step. Efficient computing is implemented and a data-driven smoothing parameter is nicely incorporated. We show that our model performs very well on forecasting actual yield data compared with existing approaches, especially in regard to profit-based assessment for an innovative trading exercise. We further illustrate the viability of our model to applications outside of yield forecasting.

stat.AP↗

arXiv2011

Consistency of Sparse PCA in High Dimension, Low Sample Size Contexts

Sparse Principal Component Analysis (PCA) methods are efficient tools to reduce the dimension (or the number of variables) of complex data. Sparse principal components (PCs) are easier to interpret than conventional PCs, because most loadings are zero. We study the asymptotic properties of these sparse PC directions for scenarios with fixed sample size and increasing dimension (i.e. High Dimension, Low Sample Size (HDLSS)). Under the previously studied spike covariance assumption, we show that Sparse PCA remains consistent under the same large spike condition that was previously established for conventional PCA. Under a broad range of small spike conditions, we find a large set of sparsity assumptions where Sparse PCA is consistent, but PCA is strongly inconsistent. The boundaries of the consistent region are clarified using an oracle result.

math.ST↗

arXiv2008

Functional principal components analysis via penalized rank one approximation

Two existing approaches to functional principal components analysis (FPCA) are due to Rice and Silverman (1991) and Silverman (1996), both based on maximizing variance but introducing penalization in different ways. In this article we propose an alternative approach to FPCA using penalized rank one approximation to the data matrix. Our contributions are four-fold: (1) by considering invariance under scale transformation of the measurements, the new formulation sheds light on how regularization should be performed for FPCA and suggests an efficient power algorithm for computation; (2) it naturally incorporates spline smoothing of discretized functional data; (3) the connection with smoothing splines also facilitates construction of cross-validation or generalized cross-validation criteria for smoothing parameter selection that allows efficient computation; (4) different smoothing parameters are permitted for different FPCs. The methodology is illustrated with a real data example and a simulation.

math.ST↗

arXiv2008

Forecasting time series of inhomogeneous Poisson processes with application to call center workforce management

We consider forecasting the latent rate profiles of a time series of inhomogeneous Poisson processes. The work is motivated by operations management of queueing systems, in particular, telephone call centers, where accurate forecasting of call arrival rates is a crucial primitive for efficient staffing of such centers. Our forecasting approach utilizes dimension reduction through a factor analysis of Poisson variables, followed by time series modeling of factor score series. Time series forecasts of factor scores are combined with factor loadings to yield forecasts of future Poisson rate profiles. Penalized Poisson regressions on factor loadings guided by time series forecasts of factor scores are used to generate dynamic within-process rate updating. Methods are also developed to obtain distributional forecasts. Our methods are illustrated using simulation and real data. The empirical results demonstrate how forecasting and dynamic updating of call arrival rates can affect the accuracy of call center staffing.

stat.AP↗