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Real-world problems are often dependent on multiple data modalities, making multimodal fusion essential for leveraging diverse information sources. In high-stakes domains, such as in healthcare, understanding how each modality contributes…
Statistical depth, a commonly used analytic tool in non-parametric statistics, has been extensively studied for multivariate and functional observations over the past few decades. Although various forms of depth were introduced, they are…
Principal Component Analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in Statistics, Machine Learning, Computer Vision, and related fields. However, PCA is well-known…
Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are…
The efficient extraction of force constants (FCs) is crucial for the analysis of many thermodynamic materials properties. Approaches based on the systematic enumeration of finite differences scale poorly with system size and can rarely…
We introduce a method called multi-scale local shape analysis, or MLSA, for extracting features that describe the local structure of points within a dataset. The method uses both geometric and topological features at multiple levels of…
In a world increasingly awash with data, the need to extract meaningful insights from data has never been more crucial. Functional Data Analysis (FDA) goes beyond traditional data points, treating data as dynamic, continuous functions,…
Patient representation learning based on electronic health records (EHR) is a critical task for disease prediction. This task aims to effectively extract useful information on dynamic features. Although various existing works have achieved…
Functional linear discriminant analysis (FLDA) is a powerful tool that extends LDA-mediated multiclass classification and dimension reduction to univariate time-series functions. However, in the age of large multivariate and incomplete…
Functional approximation as a high-order continuous representation provides a more accurate value and gradient query compared to the traditional discrete volume representation. Volume visualization directly rendered from functional…
Dynamic factor models are often estimated by point-estimation methods, disregarding parameter uncertainty. We propose a method accounting for parameter uncertainty by means of posterior approximation, using variational inference. Our…
Biological image analysis has traditionally focused on measuring specific visual properties of interest for cells or other entities. A complementary paradigm gaining increasing traction is image-based profiling - quantifying many distinct…
Long-range correlations are essential across numerous machine learning tasks, especially for data embedded in Euclidean space, where the relative positions and orientations of distant components are often critical for accurate predictions.…
Deformable fractured porous media appear in many geoscience applications. While the extended finite element (XFEM) has been successfully developed within the computational mechanics community for accurate modeling of the deformation, its…
The multipole-expansion (MPE) model is an implicit solvation model used to efficiently incorporate solvent effects in quantum chemistry. Even within the recent direct approach, the multipole basis used in MPE to express the dielectric…
How to effectively and reliably guarantee the correct functioning of safety-critical cyber-physical systems in uncertain conditions is a challenging problem. This paper presents a data-driven algorithm to derive approximate abstractions for…
Many modern datasets, from areas such as neuroimaging and geostatistics, come in the form of a random sample of tensor-valued data which can be understood as noisy observations of a smooth multidimensional random function. Most of the…
Modern multiscale type segmentation methods are known to detect multiple change-points with high statistical accuracy, while allowing for fast computation. Underpinning theory has been developed mainly for models that assume the signal as a…
Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable…
Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with a single or finite number of random functions (much smaller…