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This paper concerns the development of an inferential framework for high-dimensional linear mixed effect models. These are suitable models, for instance, when we have $n$ repeated measurements for $M$ subjects. We consider a scenario where…
For mechanical systems subject to periodic excitation, forced response curves (FRCs) depict the relationship between the amplitude of the periodic response and the forcing frequency. For nonlinear systems, this functional relationship is…
This paper considers statistical inference for the explained variance $\beta^{\intercal}\Sigma \beta$ under the high-dimensional linear model $Y=X\beta+\epsilon$ in the semi-supervised setting, where $\beta$ is the regression vector and…
In the realm of machine and deep learning regression tasks, the role of effective feature engineering (FE) is pivotal in enhancing model performance. Traditional approaches of FE often rely on domain expertise to manually design features…
Measurement error is an important problem that has not been very well studied in the context of Functional Data Analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors…
Modeling and analysis of spectroscopy data is an active area of research with applications to chemistry and biology. This paper focuses on analyzing Raman spectra obtained from a bone fracture healing experiment, although the functional…
In this paper, a functional partial quantile regression approach, a quantile regression analog of the functional partial least squares regression, is proposed to estimate the function-on-function linear quantile regression model. A partial…
This paper studies transfer learning for ridge-regularized robust linear regression in the moderate-dimensional regime, where the number of predictors is of the same order as the sample size and the regression coefficients are not assumed…
We develop a Fisher-consistent redescending robust estimator for the spatial scalar-on-function regression model, where a scalar response depends on both a functional predictor and a spatial autoregressive lag. Existing estimation…
We investigate the feature compression of high-dimensional ridge regression using the optimal subsampling technique. Specifically, based on the basic framework of random sampling algorithm on feature for ridge regression and the A-optimal…
This paper introduces a novel supervised classification strategy that integrates functional data analysis (FDA) with tree-based methods, addressing the challenges of high-dimensional data and enhancing the classification performance of…
In this study, we propose a function-on-function linear quantile regression model that allows for more than one functional predictor to establish a more flexible and robust approach. The proposed model is first transformed into a…
In performative learning, the data distribution reacts to the deployed model - for example, because strategic users adapt their features to game it - which creates a more complex dynamic than in classical supervised learning. One should…
Functional data analysis tools, such as function-on-function regression models, have received considerable attention in various scientific fields because of their observed high-dimensional and complex data structures. Several statistical…
High-dimensional functional data have become increasingly prevalent in modern applications such as high-frequency financial data and neuroimaging data analysis. We investigate a class of high-dimensional linear regression models, where each…
Meshfree radial basis function (RBF) methods are popular tools used to numerically solve partial differential equations (PDEs). They take advantage of being flexible with respect to geometry, easy to implement in higher dimensions, and can…
Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…
Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…
Rule-based models are essential for high-stakes decision-making due to their transparency and interpretability, but their discrete nature creates challenges for optimization and scalability. In this work, we present the Fuzzy Rule-based…
We develop a continuous-time penalized regression framework for the estimation of time-varying coefficients and variable selection when both the response and covariates are It\^o semimartingales with jumps. The coefficient paths are…