Related papers: Research on Interpolation and Data Fitting: Basis …

Object data analysis is concerned with statistical methodology for datasets whose elements reside in an arbitrary, unspecified metric space. In this work we propose the object shape, a novel measure of shape/symmetry for object data. The…

Training classifiers under fairness constraints such as group fairness, regularizes the disparities of predictions between the groups. Nevertheless, even though the constraints are satisfied during training, they might not generalize at…

This paper investigates the problem of temporally interpolating dynamic 3D point clouds with large non-rigid deformation. We formulate the problem as estimation of point-wise trajectories (i.e., smooth curves) and further reason that…

Data clustering is an approach to seek for structure in sets of complex data, i.e., sets of "objects". The main objective is to identify groups of objects which are similar to each other, e.g., for classification. Here, an introduction to…

Most deep learning methods for video frame interpolation consist of three main components: feature extraction, motion estimation, and image synthesis. Existing approaches are mainly distinguishable in terms of how these modules are…

Interpolating functional method is a powerful tool for studying the behavior of a quantity in the intermediate region of the parameter space of interest by using its perturbative expansions at both ends. Recently several interpolating…

Among all data augmentation techniques proposed so far, linear interpolation of training samples, also called Mixup, has found to be effective for a large panel of applications. Along with improved predictive performance, Mixup is also a…

Mixup refers to interpolation-based data augmentation, originally motivated as a way to go beyond empirical risk minimization (ERM). Its extensions mostly focus on the definition of interpolation and the space (input or feature) where it…

Many machine/deep learning artificial neural networks are trained to simply be interpolation functions that map input variables to output values interpolated from the training data in a linear/nonlinear fashion. Even when the input/output…

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…

Often in real-world datasets, especially in high dimensional data, some feature values are missing. Since most data analysis and statistical methods do not handle gracefully missing values, the first step in the analysis requires the…

Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…

We introduce, analyze and test a new interpolation operator for use with continuous data assimilation (DA) of evolution equations that are discretized spatially with the finite element method. The interpolant is constructed as an…

As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…

A data matrix may be seen simply as a means of organizing observations into rows ( e.g., by measured object) and into columns ( e.g., by measured variable) so that the observations can be analyzed with mathematical tools. As a mathematical…

Deep learning is a machine learning methodology using multi-layer neural network. A multi-layer neural network can be regarded as a chain of complete bipartite graphs. The nodes of the first partita is the input layer and the last is the…

Learning Ising or Potts models from data has become an important topic in statistical physics and computational biology, with applications to predictions of structural contacts in proteins and other areas of biological data analysis. The…

Data mining is the task of discovering interesting patterns from large amounts of data. There are many data mining tasks, such as classification, clustering, association rule mining, and sequential pattern mining. Sequential pattern mining…

Interpolating between points is a problem connected simultaneously with finding geodesics and study of generative models. In the case of geodesics, we search for the curves with the shortest length, while in the case of generative models we…

For many use cases, combining information from different datasets can be of interest to improve a machine learning model's performance, especially when the number of samples from at least one of the datasets is small. However, a potential…