Related papers: Manifold Data Imputation
When analyzing empirical data, we often find that global linear models overestimate the number of parameters required. In such cases, we may ask whether the data lies on or near a manifold or a set of manifolds (a so-called multi-manifold)…
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…
Missing values are largely inevitable in gene expression microarray studies. Data sets often have significant omissions due to individuals dropping out of experiments, errors in data collection, image corruptions, and so on. Missing data…
When do gradient-based explanation algorithms provide perceptually-aligned explanations? We propose a criterion: the feature attributions need to be aligned with the tangent space of the data manifold. To provide evidence for this…
In this work, we propose a novel framework for estimating the dimension of the data manifold using a trained diffusion model. A diffusion model approximates the score function i.e. the gradient of the log density of a noise-corrupted…
We present single imputation method for missing values which borrows the idea of data depth---a measure of centrality defined for an arbitrary point of a space with respect to a probability distribution or data cloud. This consists in…
High-dimensional data are often assumed to lie on lower-dimensional manifolds. We study how to construct diffusion processes on this data manifold using only point cloud samples and without access to charts, projections, or other geometric…
Multiple imputation is a highly recommended technique to deal with missing data, but the application to longitudinal datasets can be done in multiple ways. When a new wave of longitudinal data arrives, we can treat the combined data of…
In this paper, we consider the problem of recovering a compactly supported multivariate function from a collection of pointwise samples of its Fourier transform taken nonuniformly. We do this by using the concept of weighted Fourier frames.…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
We propose a high-precision numerical quadrature framework based on local Fourier extension (LFE) approximations. The method constructs, on each subinterval, a truncated-SVD stabilized local Fourier continuation of the integrand on an…
We present a scalable low dimensional manifold model for the reconstruction of noisy and incomplete hyperspectral images. The model is based on the observation that the spatial-spectral blocks of a hyperspectral image typically lie close to…
This paper examines issues of data completion and location uncertainty, popular in many practical PDE-based inverse problems, in the context of option calibration via recovery of local volatility surfaces. While real data is usually more…
This paper investigates gradient recovery schemes for data defined on discretized manifolds. The proposed method, parametric polynomial preserving recovery (PPPR), does not require the tangent spaces of the exact manifolds, and they have…
In Functional Data Analysis, data are commonly assumed to be smooth functions on a fixed interval of the real line. In this work, we introduce a comprehensive framework for the analysis of functional data, whose domain is a two-dimensional…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
We introduce a comprehensive and statistical framework in a model free setting for a complete treatment of localized data corruptions due to severe noise sources, e.g., an occluder in the case of a visual recording. Within this framework,…
Non-parametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these…
Feature selection on incomplete datasets is an exceptionally challenging task. Existing methods address this challenge by first employing imputation methods to complete the incomplete data and then conducting feature selection based on the…
We introduce a new regression framework designed to deal with large-scale, complex data that lies around a low-dimensional manifold with noises. Our approach first constructs a graph representation, referred to as the skeleton, to capture…