Related papers: Manifold Data Imputation
Most practical data science problems encounter missing data. A wide variety of solutions exist, each with strengths and weaknesses that depend upon the missingness-generating process. Here we develop a theoretical framework for training and…
While many phenomena in physics and engineering are formally high-dimensional, their long-time dynamics often live on a lower-dimensional manifold. The present work introduces an autoencoder framework that combines implicit regularization…
Widely used methods for analyzing missing data can be biased in small samples. To understand these biases, we evaluate in detail the situation where a small univariate normal sample, with values missing at random, is analyzed using either…
Experimental spatio-temporal flow data often contain gaps or other types of undesired artifacts. To reconstruct flow data in the compromised or missing regions, a data completion method based on spectral proper orthogonal decomposition…
In many machine learning applications, we are faced with incomplete datasets. In the literature, missing data imputation techniques have been mostly concerned with filling missing values. However, the existence of missing values is…
Missing data is a fundamental challenge in data science, significantly hindering analysis and decision-making across a wide range of disciplines, including healthcare, bioinformatics, social science, e-commerce, and industrial monitoring.…
Scattered data fitting is a frequently encountered problem for reconstructing an unknown function from given scattered data. Radial basis function (RBF) methods have proven to be highly useful to deal with this problem. We describe two…
Missing data theory deals with the statistical methods in the occurrence of missing data. Missing data occurs when some values are not stored or observed for variables of interest. However, most of the statistical theory assumes that data…
The ability to represent and compare machine learning models is crucial in order to quantify subtle model changes, evaluate generative models, and gather insights on neural network architectures. Existing techniques for comparing data…
An interpolation method to evaluate magnetic fields given unstructured, scattered magnetic data is presented. The method is based on the reconstruction of the global magnetic field using a superposition of orthogonal functions. The…
Classification is a core topic in functional data analysis. A large number of functional classifiers have been proposed in the literature, most of which are based on functional principal component analysis or functional regression. In…
Deep learning has had tremendous success at learning low-dimensional representations of high-dimensional data. This success would be impossible if there was no hidden low-dimensional structure in data of interest; this existence is posited…
Data imputation is the most popular method of dealing with missing values, but in most real life applications, large missing data can occur and it is difficult or impossible to evaluate whether data has been imputed accurately (lack of…
The paper demonstrates that invariant foliations are accurate, data-efficient and practical tools for data-driven modelling of physical systems. Invariant foliations can be fitted to data that either fill the phase space or cluster about an…
In topology inference from data, current approaches face two major problems. One concerns the selection of a correct parameter to build an appropriate complex on top of the data points; the other involves with the typical `large' size of…
We present a robust framework to perform linear regression with missing entries in the features. By considering an elliptical data distribution, and specifically a multivariate normal model, we are able to conditionally formulate a…
Recently, Hyperspectral Image (HSI) classification has attracted increasing attention in remote sensing. However, HSI data are inherently high-dimensional but low-rank, with discriminative information concentrated on a low-dimensional…
The challenge of missing data remains a significant obstacle across various scientific domains, necessitating the development of advanced imputation techniques that can effectively address complex missingness patterns. This study introduces…
Missing data is a ubiquitous challenge in data analysis, often leading to biased and inaccurate results. Traditional imputation methods usually assume that the missingness mechanism is missing-at-random (MAR), where the missingness is…
Missing data are frequently encountered in high-dimensional problems, but they are usually difficult to deal with using standard algorithms, such as the expectation-maximization (EM) algorithm and its variants. To tackle this difficulty,…