Multi-Linear Kernel Regression and Imputation in Data Manifolds
This paper introduces an efficient multi-linear nonparametric (kernel-based) approximation framework for data regression and imputation, and its application to dynamic magnetic-resonance imaging (dMRI). Data features are assumed to reside in or close to a smooth manifold embedded in a reproducing kernel Hilbert space. Landmark points are identified to describe concisely the point cloud of features by linear approximating patches which mimic the concept of tangent spaces to smooth manifolds. The multi-linear model effects dimensionality reduction, enables efficient computations, and extracts data patterns and their geometry without any training data or additional information. Numerical tests on dMRI data under severe under-sampling demonstrate remarkable improvements in efficiency and accuracy of the proposed approach over its predecessors, popular data modeling methods, as well as recent tensor-based and deep-image-prior schemes.
Code (0)
등록된 구현이 없습니다.
Tasks
Dimensionality ReductionImputationregressionSimilar Papers 제목 키워드 기반
Statistical Inference after Kernel Ridge Regression Imputation under item nonresponse
Imputation is a popular technique for handling missing data. We consider a nonparametric approach to imputation using the kernel ridge regression technique and propose consistent variance estimation. The proposed varianc…
ImputationregressionMultilinear Kernel Regression and Imputation via Manifold Learning
This paper introduces a novel nonparametric framework for data imputation, coined multilinear kernel regression and imputation via the manifold assumption (MultiL-KRIM). Motivated by manifold learning, MultiL-KRIM models…
Dimensionality ReductionImputationregressionImputation of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learning
This paper extends the recently developed framework of multilinear kernel regression and imputation via manifold learning (MultiL-KRIM) to impute time-varying edge flows in a graph. MultiL-KRIM uses simplicial-complex ar…
Collaborative FilteringDimensionality ReductionImputationStatistical inference using Regularized M-estimation in the reproducing kernel Hilbert space for handling missing data
Imputation and propensity score weighting are two popular techniques for handling missing data. We address these problems using the regularized M-estimation techniques in the reproducing kernel Hilbert space. Specificall…
ImputationregressionPseudo-Labeling for Unsupervised Domain Adaptation with Kernel GLMs
We propose a principled framework for unsupervised domain adaptation under covariate shift in kernel Generalized Linear Models (GLMs), encompassing kernelized linear, logistic, and Poisson regression with ridge regulariz…
Unsupervised Domain Adaptation