Related papers: An Understanding of Principal Differential Analysi…

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…

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…

To detect differences between the mean curves of two samples in longitudinal study or functional data analysis, we usually need to partition the temporal or spatial domain into several pre-determined sub-areas. In this paper we apply the…

Understanding and predicting the electric consumption patterns in the short-, mid- and long-term, at the distribution and transmission level, is a fundamental asset for smart grids infrastructure planning, dynamic network reconfiguration,…

Functional data analysis, which handles data arising from curves, surfaces, volumes, manifolds and beyond in a variety of scientific fields, is a rapidly developing area in modern statistics and data science in the recent decades. The…

Regularized discriminant analysis (RDA), proposed by Friedman (1989), is a widely popular classifier that lacks interpretability and is impractical for high-dimensional data sets. Here, we present an interpretable and computationally…

Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used…

In our previous work, a reduced order model (ROM) for a stochastic system was made, where noisy data was projected onto principal component analysis (PCA)-derived basis vectors to obtain an accurate reconstruction of the noise-free data.…

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…

We develop a robust Bayesian functional principal component analysis (RB-FPCA) method that utilizes the skew elliptical class of distributions to model functional data, which are observed over a continuous domain. This approach effectively…

Researchers in the behavioral and social sciences use linear discriminant analysis (LDA) for predictions of group membership (classification) and for identifying the variables most relevant to group separation among a set of continuous…

We study regression using functional predictors in situations where these functions contain both phase and amplitude variability. In other words, the functions are misaligned due to errors in time measurements, and these errors can…

Linear discriminant analysis (LDA) is a classical method for dimensionality reduction, where discriminant vectors are sought to project data to a lower dimensional space for optimal separability of classes. Several recent papers have…

Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

Every organism in an environment, whether biological, robotic or virtual, must be able to predict certain aspects of its environment in order to survive or perform whatever task is intended. It needs a model that is capable of estimating…

We consider the problem of learning a linear factor model. We propose a regularized form of principal component analysis (PCA) and demonstrate through experiments with synthetic and real data the superiority of resulting estimates to those…

Ordinal measurements are common outcomes in studies within psychology, as well as in the social and behavioral sciences. Choosing an appropriate regression model for analysing such data poses a difficult task. This paper aims to facilitate…

Aggregation of large databases in a specific format is a frequently used process to make the data easily manageable. Interval-valued data is one of the data types that is generated by such an aggregation process. Using traditional methods…

The regression discontinuity design (RDD) is a quasi-experimental design that can be used to identify and estimate the causal effect of a treatment using observational data. In an RDD, a pre-specified rule is used for treatment assignment,…