Related papers: Representation of Functional Data in Neural Networ…

Radial basis function (RBF) network is a third layered neural network that is widely used in function approximation and data classification. Here we propose a quantum model of the RBF network. Similar to the classical case, we still use the…

The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…

Random feature (RF) method is a powerful kernel approximation technique, but is typically equipped with fixed activation functions, limiting its adaptability across diverse tasks. To overcome this limitation, we introduce the Random Feature…

This paper describes opportunities and challenges of using functional data analysis (FDA) for the exploration and analysis of data originating from electronic commerce (eCommerce). We discuss the special data structures that arise in the…

Many real-world applications involve analyzing time-dependent phenomena, which are intrinsically functional, consisting of curves varying over a continuum (e.g., time). When analyzing continuous data, functional data analysis (FDA) provides…

Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is…

It is common practice in deep learning to represent a measurement of the world on a discrete grid, e.g. a 2D grid of pixels. However, the underlying signal represented by these measurements is often continuous, e.g. the scene depicted in an…

Statistical analysis of functional data is challenging due to their complex patterns, for which functional depth provides an effective means of reflecting their ordering structure. In this work, we investigate practical aspects of the…

Functional data analysis in a mixed-effects model framework is done using operator calculus. In this approach the functional parameters are treated as serially correlated effects giving an alternative to the penalized likelihood approach,…

Foundation Models (FMs) are models trained on large corpora of data that, at very large scale, can generalize to new tasks without any task-specific finetuning. As these models continue to grow in size, innovations continue to push the…

Functional data play a pivotal role across science and engineering, yet their infinite-dimensional nature makes representation learning challenging. Conventional statistical models depend on pre-chosen basis expansions or kernels, limiting…

We introduce FDApy, an open-source Python package for the analysis of functional data. The package provides tools for the representation of (multivariate) functional data defined on different dimensional domains and for functional data that…

Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…

We present a new method based on Functional Data Analysis (FDA) for detecting associations between one or more scalar covariates and a longitudinal response, while correcting for other variables. Our methods exploit the temporal structure…

Recent advances in acquisition equipment is providing experiments with growing amounts of precise yet affordable sensors. At the same time an improved computational power, coming from new hardware resources (GPU, FPGA, ACAP), has been made…

Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal…

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…

The focus of this paper is to extend Fisher's linear discriminant analysis (LDA) to both densely re-corded functional data and sparsely observed longitudinal data for general $c$-category classification problems. We propose an efficient…

Linear discriminant analysis (LDA) is a popular tool for classification and dimension reduction. Limited by its linear form and the underlying Gaussian assumption, however, LDA is not applicable in situations where the data distribution is…

Federated Domain Adaptation (FDA) is a federated learning (FL) approach that improves model performance at the target client by collaborating with source clients while preserving data privacy. FDA faces two primary challenges: domain shifts…