Related papers: Multivariate Functional Linear Discriminant Analys…
We propose the Fourier Adaptive Lite Diffusion Architecture (FALDA), a novel probabilistic framework for time series forecasting. First, we introduce the Diffusion Model for Residual Regression (DMRR) framework, which unifies…
Functional Data Analysis (FDA) is a statistical domain developed to handle functional data characterized by high dimensionality and complex data structures. Sequential Neural Networks (SNNs) are specialized neural networks capable of…
In practical applications, we often have to deal with high order data, such as a grayscale image and a video sequence are intrinsically 2nd-order tensor and 3rd-order tensor, respectively. For doing clustering or classification of these…
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…
In many social, economical, biological and medical studies, one objective is to classify a subject into one of several classes based on a set of variables observed from the subject. Because the probability distribution of the variables is…
In many phenomena, data are collected on a large scale and of different frequencies. In this context, functional data analysis (FDA) has become an important statistical methodology for analyzing and modeling such data. The approach of FDA…
Quadratic and Linear Discriminant Analysis (QDA/LDA) are the most often applied classification rules under normality. In QDA, a separate covariance matrix is estimated for each group. If there are more variables than observations in the…
Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…
In large-scale few-shot learning for classification problems, often there are a large number of classes and few high-dimensional observations per class. Previous model-based methods, such as Fisher's linear discriminant analysis (LDA),…
We provide a MATLAB toolbox, BFDA, that implements a Bayesian hierarchical model to smooth multiple functional data with the assumptions of the same underlying Gaussian process distribution, a Gaussian process prior for the mean function,…
Time series analysis is crucial in fields like finance, economics, environmental science, and biomedical engineering, aiding in forecasting, pattern identification, and understanding underlying mechanisms. While traditional time-domain…
Functional data analysis (FDA) deals with high-resolution data recorded over a continuum, such as time, space or frequency. Device-based assessments of physical activity or sleep are objective yet still prone to measurement error. We…
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…
We address classification of distributional data, where units are described by histogram or interval-valued variables. The proposed approach uses a linear discriminant function where distributions or intervals are represented by quantile…
Factor models are widely applied to the analysis of multivariate data across disparate fields of research. However, modern scientific data are often incomplete, and estimating a factor model from partially observed data can be very…
Feature selection is a crucial step in large-scale industrial machine learning systems, directly affecting model accuracy, efficiency, and maintainability. Traditional feature selection methods rely on labeled data and statistical…
Few-shot learning for image classification comes up as a hot topic in computer vision, which aims at fast learning from a limited number of labeled images and generalize over the new tasks. In this paper, motivated by the idea of Fisher…
This paper considers the problem of manifold functional multiple regression with functional response, time--varying scalar regressors, and functional error term displaying Long Range Dependence (LRD) in time. Specifically, the error term is…
Functional data analysis (FDA) methods have computational and theoretical appeals for some high dimensional data, but lack the scalability to modern large sample datasets. To tackle the challenge, we develop randomized algorithms for two…
We present a new mixture model-based discriminant analysis approach for functional data using a specific hidden process regression model. The approach allows for fitting flexible curve-models to each class of complex-shaped curves…