Related papers: Research on Interpolation and Data Fitting: Basis …
Data assimilation is a method that combines observations (that is, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model…
Changepoint detection is commonly formulated by minimizing the sum of in-sample losses to quantify the model's overall fit. However, for flexible modeling procedures -- especially those involving high-dimensional parameter spaces or…
This paper introduces data augmentation for point clouds by interpolation between examples. Data augmentation by interpolation has shown to be a simple and effective approach in the image domain. Such a mixup is however not directly…
We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all…
The analysis of data sometimes requires fitting many free parameters in a theory to a large number of data points. Questions naturally arise about the compatibility of specific subsets of the data, such as those from a particular experiment…
One approach to parametric and adaptive model reduction is via the interpolation of orthogonal bases, subspaces or positive definite system matrices. In all these cases, the sampled inputs stem from matrix sets that feature a geometric…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…
Given a straight-line program whose output is a polynomial function of the inputs, we present a new algorithm to compute a concise representation of that unknown function. Our algorithm can handle any case where the unknown function is a…
Radio interferometry is an observational technique used to study astrophysical phenomena. Data gathered by an interferometer requires substantial processing before astronomers can extract the scientific information from it. Data processing…
Fitting models for non-Poisson point processes is complicated by the lack of tractable models for much of the data. By using large samples of independent and identically distributed realizations and statistical learning, it is possible to…
We develop a formal framework for the behavioral comparison of linear systems across different time domains. We accomplish this by introducing the notion of system interpolation, which determines whether the input-state trajectories of a…
The versatility of data-driven approximation by interpolatory methods, originally settled for model approximation purpose, is illustrated in the context of linear controller design and stability analysis of irrational models. To this aim,…
This paper introduces an interpolation-based method, called the reconstruction approach, for nonparametric regression. Based on the fact that interpolation usually has negligible errors compared to statistical estimation, the reconstruction…
Exploiting the deep generative model's remarkable ability of learning the data-manifold structure, some recent researches proposed a geometric data interpolation method based on the geodesic curves on the learned data-manifold. However,…
Consistent experiment data are crucial to adjust parameters of physics models and to determine best estimates of observables. However, often experiment data are not consistent due to unrecognized systematic errors. Standard methods of…
Fitting experiment data onto a curve is a common signal processing technique to extract data features and establish the relationship between variables. Often, we expect the curve to comply with some analytical function and then turn data…
Data imputation, the process of filling in missing feature elements for incomplete data sets, plays a crucial role in data-driven learning. A fundamental belief is that data imputation is helpful for learning performance, and it follows…
Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated…
Flow matching models typically use linear interpolants to define the forward/noise addition process. This, together with the independent coupling between noise and target distributions, yields a vector field which is often non-straight.…
We describe a general approach for constructing a broad class of operators approximating high-dimensional curves based on geometric Hermite data. The geometric Hermite data consists of point samples and their associated tangent vectors of…