arXiv subjects

Peijun Sang

Publications and source records attributed to Peijun Sang.

22 records · Page 2Linked to original sources

arXiv2022

Two Gaussian regularization methods for time-varying networks

We model time-varying network data as realizations from multivariate Gaussian distributions with precision matrices that change over time. To facilitate parameter estimation, we require not only that each precision matrix at any given time point be sparse, but also that precision matrices at neighboring time points be similar. We accomplish this with two different algorithms, by generalizing the elastic net and the fused LASSO, respectively. Our main focuses are efficient computational algorithms and convenient degree-of-freedom formulae for choosing tuning parameters. We illustrate our methods with two simulation studies. By applying them to an fMRI data set, we also detect some interesting differences in brain connectivity between healthy individuals and ADHD patients.

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arXiv2022

Statistical Inference for Functional Linear Quantile Regression

We propose inferential tools for functional linear quantile regression where the conditional quantile of a scalar response is assumed to be a linear functional of a functional covariate. In contrast to conventional approaches, we employ kernel convolution to smooth the original loss function. The coefficient function is estimated under a reproducing kernel Hilbert space framework. A gradient descent algorithm is designed to minimize the smoothed loss function with a roughness penalty. With the aid of the Banach fixed-point theorem, we show the existence and uniqueness of our proposed estimator as the minimizer of the regularized loss function in an appropriate Hilbert space. Furthermore, we establish the convergence rate as well as the weak convergence of our estimator. As far as we know, this is the first weak convergence result for a functional quantile regression model. Pointwise confidence intervals and a simultaneous confidence band for the true coefficient function are then developed based on these theoretical properties. Numerical studies including both simulations and a data application are conducted to investigate the performance of our estimator and inference tools in finite sample.

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arXiv2021

A reproducing kernel Hilbert space framework for functional data classification

We encounter a bottleneck when we try to borrow the strength of classical classifiers to classify functional data. The major issue is that functional data are intrinsically infinite dimensional, thus classical classifiers cannot be applied directly or have poor performance due to the curse of dimensionality. To address this concern, we propose to project functional data onto one specific direction, and then a distance-weighted discrimination DWD classifier is built upon the projection score. The projection direction is identified through minimizing an empirical risk function that contains the particular loss function in a DWD classifier, over a reproducing kernel Hilbert space. Hence our proposed classifier can avoid overfitting and enjoy appealing properties of DWD classifiers. This framework is further extended to accommodate functional data classification problems where scalar covariates are involved. In contrast to previous work, we establish a non-asymptotic estimation error bound on the relative misclassification rate. In finite sample case, we demonstrate that the proposed classifiers compare favorably with some commonly used functional classifiers in terms of prediction accuracy through simulation studies and a real-world application.

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arXiv2021

Continuum centroid classifier for functional data

Aiming at the binary classification of functional data, we propose the continuum centroid classifier (CCC) built upon projections of functional data onto one specific direction. This direction is obtained via bridging the regression and classification. Controlling the extent of supervision, our technique is neither unsupervised nor fully supervised. Thanks to the intrinsic infinite dimension of functional data, one of two subtypes of CCC enjoys the (asymptotic) zero misclassification rate. Our proposal includes an effective algorithm that yields a consistent empirical counterpart of CCC. Simulation studies demonstrate the performance of CCC in different scenarios. Finally, we apply CCC to two real examples.

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