arXiv subjects

Shuhao Jiao

Publications and source records attributed to Shuhao Jiao.

11 recordsLinked to original sources

arXiv2026

Filtration-Based Learning of Multiscale Shared Structures for Multiple Functional Predictors

It is crucial to learn the shared structures among functional predictors, as these structures characterize how predictor components exert common effects and, more generally, how predictors are homogeneously associated with the response. However, learning from multiple functional predictors is challenging because response-predictor dependencies may vary across representation dimensions and emerge at multiple resolutions, ranging from globally shared effects to predictor-specific effects. To address this issue, we propose a filtration-based shared structure learning framework for multiple functional predictors. The proposed framework organizes predictors through a hierarchical forest structure, in which shared and predictor-specific components are progressively identified from coarse to fine filtration layers. Building on this structure, we develop a filtration-based pursuit pipeline for shared structure discovery, together with a filtrated functional partial least squares method for shared component extraction and coefficient estimation under the learned shared structures. Simulation studies show that the proposed framework is able to recover the dominant coarse-to-fine organization of the underlying shared structures and yield improved prediction performance relative to competing methods. Applied to lower-limb angular kinematics, the proposed framework improves evaluation accuracy and reveals interpretable joint coordination patterns associated with aging. More broadly, it provides a new multiscale representation-learning perspective for complex data consisting of multiple multidimensional objects.

stat.ME↗

arXiv2025

Coefficient Shape Transfer Learning for Functional Linear Regression

The shapes of functions provide highly interpretable summaries of their trajectories. This article develops a novel transfer learning methodology to tackle the challenge of data scarcity in functional linear models. The methodology incorporates samples from the target model (target domain) alongside those from auxiliary models (source domains), transferring knowledge of coefficient shape from the source domains to the target domain. This shape-based transfer learning framework enhances robustness and generalizability: by being invariant to covariate scaling and signal strength, it ensures reliable knowledge transfer even when data from different sources differ in magnitude, and by formalizing the notion of coefficient shape homogeneity, it extends beyond traditional coefficient-equality assumptions to incorporate information from a broader range of source domains. We rigorously analyze the convergence rates of the proposed estimator and examine the minimax optimality. Our findings show that the degree of improvement depends not only on the similarity of coefficient shapes between the target and source domains, but also on coefficient magnitudes and the spectral decay rates of the functional covariates covariance operators. To address situations where only a subset of auxiliary models is informative for the target model, we further develop a data-driven procedure for identifying such informative sources. The effectiveness of the proposed methodology is demonstrated through comprehensive simulation studies and an application to occupation time analysis using physical activity data from the U.S. National Health and Nutrition Examination Survey.

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arXiv2024

Coefficient Shape Alignment in Multiple Functional Linear Regression

In multivariate functional data analysis, different functional covariates often exhibit homogeneity. The covariates with pronounced homogeneity can be analyzed jointly within the same group, offering a parsimonious approach to modeling multivariate functional data. In this paper, a novel grouped multiple functional regression model with a new regularization approach termed {\it ``coefficient shape alignment"} is developed to tackle functional covariates homogeneity. The modeling procedure includes two steps: first aggregate covariates into disjoint groups using the new regularization approach; then the grouped multiple functional regression model is established based on the detected grouping structure. In this grouped model, the coefficient functions of covariates in the same group share the same shape, invariant to scaling. The new regularization approach works by penalizing differences in the shape of the coefficients. We establish conditions under which the true grouping structure can be accurately identified and derive the asymptotic properties of the model estimates. Extensive simulation studies are conducted to assess the finite-sample performance of the proposed methods. The practical applicability of the model is demonstrated through real data analysis in the context of sugar quality evaluation. This work offers a novel framework for analyzing the homogeneity of functional covariates and constructing parsimonious models for multivariate functional data.

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arXiv2023

Spectral Topological Data Analysis of Brain Signals

Topological analyses of brain functional connectivity usually reduce each pair of channels to a single scalar dependence, typically the Pearson correlation, and so cannot resolve the frequency-specific synchronisation that organises electrophysiology. We propose a topological summary that keeps the frequency information. The spectral landscape indexes the persistence landscape of Bubenik (2015) by Fourier frequency, building each filtration from a coherence-based distance, so that it is a function of both the filtration scale and the frequency. It is Lipschitz-stable in the coherence matrix and feeds a functional two-sample test over a chosen frequency band, whose limiting null distribution and consistency follow from standard functional-data arguments. In simulations the test recovers a topological difference in the band where it lives while holding its nominal level under the null. Applied to electroencephalography from 53 control and 51 ADHD children, a global test rejects equality of the two groups' cycle topology at the 95% level (p = 0.019); a band-by-band follow-up localises the difference to the gamma and theta bands, although none survives family-wise correction at this sample size. The pattern is consistent with the established role of these bands in ADHD.

q-bio.NC↗

arXiv2022

Filtrated Common Functional Principal Components for Multivariate Functional data

Local field potentials (LFPs) are signals that measure electrical activity in localized cortical regions from implanted tetrodes in the human or animal brain. The LFP signals are curves observed at multiple tetrodes which are implanted across a patch on the surface of the cortex. Hence, they can be treated as multi-group functional data, where the trajectories collected across temporal epochs from one tetrode are viewed as a group of functions. In many cases, multi-tetrode LFP trajectories contain both global variation patterns (which are shared in common to all groups, due to signal synchrony) and isolated variation patterns (common only to a small subset of groups), and such structure is very informative to the analysis of such data. Therefore, one goal in this paper is to develop an efficient procedure that is able to capture and quantify both global and isolated features. We propose a novel tree-structured functional principal components (filt-fPC) analysis through finite-dimensional functional representation - specifically via filtration. A major advantage of the proposed filt-fPC method is the ability to extract the components that are common to multiple groups (or tetrodes) in a flexible "multi-resolution" manner and simultaneously preserve the idiosyncratic individual components of different tetrodes. The proposed filt-fPC approach is highly data-driven and no "ground-truth" model pre-specification is needed, making it a suitable approach for analyzing multi-group functional data that is complex. In addition, the filt-fPC method is able to produce a parsimonious, interpretable, and efficient low dimensional representation of multi-group functional data with orthonormal basis functions. Here, the proposed filt-fPCA method is employed to study the impact of a shock (induced stroke) on the synchrony structure of the rat brain.

stat.ME↗

arXiv2022

Enhanced Change-Point Detection in Functional Means

A new dimension reduction methodology for change-point detection in functional means is developed in this paper. The major advantage and novelty of the proposed method is its efficiency in selecting basis functions that capture the change, or jump, of functional means, leading to higher detection power, especially when the functions cannot be sufficiently explained by a small number of basis functions or are contaminated by random noises. The throughly developed theoretical results demonstrate that, even when the change shrinks to zero, the proposed approach can still detect the change asymptotically almost surely. The numerical simulation studies justify the superiority of the proposed approach to the method based on functional principal components and the fully functional approach without dimension reduction. An application to annual humidity trajectories was also included to illustrate the practical superiority of the developed approach.

stat.ME↗

arXiv2022

Variation Pattern Classification of Functional Data

A new classification method for functional data is proposed in this paper. This work is motivated by the need to identify features that discriminate between neurological conditions on which local field potentials (LFPs) were recorded. Regardless of the condition, these local field potentials have zero mean and thus the first moments of these random processes do not have discriminating power. We propose the variation pattern classification (VPC) method {which employs the (auto-)covariance operators as the discriminating features} and uses the Hilbert-Schmidt norm to measure the discrepancy between the (auto-)covariance operators of different groups. The proposed VPC method is demonstrated to be sensitive to the discrepancy, {potentially leading to a higher rate of classification}. One important innovation lies in the dimension reduction where the VPC method data-adaptively determines the basis functions (discriminative feature functions) that account for the major discrepancy. In addition, the selected discriminative feature functions provide insights on the discrepancy between different groups because they reveal the features of variation pattern that differentiate groups. Consistency properties are established and, furthermore, simulation studies and the analysis of rat brain LFP trajectories empirically demonstrate the advantages and effectiveness of the proposed method.

stat.ME↗

arXiv2022

Functional time series prediction under partial observation of the future curve

This paper tackles one of the most fundamental goals in functional time series analysis which is to provide reliable predictions for future functions. Existing methods for predicting a complete future functional observation use only completely observed trajectories. We develop a new method, called partial functional prediction (PFP), which uses both completely observed trajectories and partial information (available partial data) on the trajectory to be predicted. The PFP method includes an automatic selection criterion for tuning parameters based on minimizing the prediction error, and the convergence rate of the PFP prediction is established. Simulation studies demonstrate that incorporating partially observed trajectory in the prediction outperforms existing methods with respect to mean squared prediction error. The PFP method is illustrated to be superior in the analysis of environmental data and traffic flow data.

stat.ME↗

arXiv2022

Break Point Detection for Functional Covariance

Many experiments record sequential trajectories where each trajectory consists of oscillations and fluctuations around zero. Such trajectories can be viewed as zero-mean functional data. When there are structural breaks (on the sequence of trajectories) in higher order moments, it is not always easy to spot these by mere visual inspection. Motivated by this challenging problem in brain signal analysis, we propose a detection and testing procedure to find the change point in functional covariance. The detection procedure is based on the cumulative sum statistics (CUSUM). The classical testing procedure for functional data depends on a null distribution which depends on infinitely many unknown parameters, though in practice only a finite number of these can be included for the hypothesis test of the existence of change point. This paper provides some theoretical insights on the influence of the number of parameters. Meanwhile, the asymptotic properties of the estimated change point are developed. The effectiveness of the proposed method is numerically validated in simulation studies and an application to investigate changes in rat brain signals following an experimentally-induced stroke.

stat.ME↗

arXiv2022

Shape-Preserving Prediction for Stationary Functional Time Series

This article presents a novel method for prediction of stationary functional time series, in particular for trajectories that share a similar pattern but display variable phases. The limitation of most of the existing prediction methodologies for functional time series is that they only consider vertical variation (amplitude, scale, or vertical shift). To overcome this limitation, we develop a shape-preserving (SP) prediction method that incorporates both vertical and horizontal variation. One major advantage of our proposed method is the ability to preserve the shape of functions. Moreover, our proposed SP method does not involve unnatural transformations and can be easily implemented using existing software packages. The utility of the SP method is demonstrated in the analysis of non-metanic hydrocarbons (NMHC) concentration. The analysis demonstrates that the prediction by the SP method captures the common pattern better than the existing prediction methods and also provides competitive prediction accuracy.

stat.ME↗

arXiv2021

Change-point detection using spectral PCA for multivariate time series

We propose a two-stage approach Spec PC-CP to identify change points in multivariate time series. In the first stage, we obtain a low-dimensional summary of the high-dimensional time series by Spectral Principal Component Analysis (Spec-PCA). In the second stage, we apply cumulative sum-type test on the Spectral PCA component using a binary segmentation algorithm. Compared with existing approaches, the proposed method is able to capture the lead-lag relationship in time series. Our simulations demonstrate that the Spec PC-CP method performs significantly better than competing methods for detecting change points in high-dimensional time series. The results on epileptic seizure EEG data and stock data also indicate that our new method can efficiently {detect} change points corresponding to the onset of the underlying events.

stat.AP↗