Related papers: Efficiently transforming from values of a function…
In the papers dealing with derivation and applications of operational matrices of Bernstein polynomials, a basis transformation, commonly a transformation to power basis, is used. The main disadvantage of this method is that the…
Sparse functional data arise when measurements are observed infrequently and at irregular time points for each subject, often in the presence of measurement error. These characteristics introduce additional challenges for functional…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters…
We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
Several applications of slicing require a program to be sliced with respect to more than one slicing criterion. Program specialization, parallelization and cohesion measurement are examples of such applications. These applications can…
We introduce intrinsic interpolatory bases for data structured on graphs and derive properties of those bases. Polyharmonic Lagrange functions are shown to satisfy exponential decay away from their centers. The decay depends on the density…
In practice functional data are sampled on a discrete set of observation points and often susceptible to noise. We consider in this paper the setting where such data are used as explanatory variables in a regression problem. If the primary…
Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the…
Statistical methods for inference on spatial extremes of large datasets are yet to be developed. Motivated by standard dimension reduction techniques used in spatial statistics, we propose an approach based on empirical basis functions to…
Graph Neural Networks (GNN) exhibit superior performance in graph representation learning, but their inference cost can be high, due to an aggregation operation that can require a memory fetch for a very large number of nodes. This…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
Functional data analysis deals with data recorded densely over time (or any other continuum) with one or more observed curves per subject. Conceptually, functional data are continuously defined, but in practice, they are usually observed at…
In a number of previous papers, local (coarse grid) multiscale model reduction techniques are developed using a Generalized Multiscale Finite Element Method. In these approaches, multiscale basis functions are constructed using local…
We present a framework for networked state estimation, where systems encode their (possibly high dimensional) state vectors using a mutually agreed basis between the system and the estimator (in a remote monitoring unit). The basis…
In this paper, we develop a quantile functional regression modeling framework that models the distribution of a set of common repeated observations from a subject through the quantile function, which is regressed on a set of covariates to…
We define a new basis of the algebra of quasi-symmetric functions by lifting the cycle-index polynomials of symmetric groups to noncommutative polynomials with coefficients in the algebra of free quasi-symmetric functions, and then…
We propose a novel family of test statistics to detect the presence of changepoints in a sequence of dependent, possibly multivariate, functional-valued observations. Our approach allows to test for a very general class of changepoints,…
This paper addresses the problem of expressing a signal as a sum of frequency components (sinusoids) wherein each sinusoid may exhibit abrupt changes in its amplitude and/or phase. The Fourier transform of a narrow-band signal, with a…