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Reproducing kernel Hilbert spaces provide a foundational framework for kernel-based learning, where regularization and interpolation problems admit finite-dimensional solutions through classical representer theorems. Many modern learning…
We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and construct optimal sparse grids for scattered data…
Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…
Conditional kernel mean embeddings are nonparametric models that encode conditional expectations in a reproducing kernel Hilbert space. While they provide a flexible and powerful framework for probabilistic inference, their performance is…
We are interested in comparing probability distributions defined on Riemannian manifold. The traditional approach to study a distribution relies on locating its mean point and finding the dispersion about that point. On a general manifold…
We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression…
In recent years, transfer learning has garnered significant attention. Its ability to leverage knowledge from related studies to improve generalization performance in a target study has made it highly appealing. This paper focuses on…
This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information is unknown and can depend on both predictors and…
Euclidean representations distort data with intrinsic non-Euclidean structure. While Riemannian representation learning offers a solution by embedding data onto matching manifolds, it typically relies on an encoder to estimate densities on…
Random Forests and Gradient Boosting are among the most effective algorithms for supervised learning on tabular data. Both belong to the class of tree-based ensemble methods, where predictions are obtained by aggregating many randomized…
Data similarity is a key concept in many data-driven applications. Many algorithms are sensitive to similarity measures. To tackle this fundamental problem, automatically learning of similarity information from data via self-expression has…
``Benign overfitting'', the ability of certain algorithms to interpolate noisy training data and yet perform well out-of-sample, has been a topic of considerable recent interest. We show, using a fixed design setup, that an important class…
Despite extensive research spanning several decades, class imbalance is still considered a profound difficulty for both machine learning and deep learning models. While data oversampling is the foremost technique to address this issue,…
Many supervised learning problems involve high-dimensional data such as images, text, or graphs. In order to make efficient use of data, it is often useful to leverage certain geometric priors in the problem at hand, such as invariance to…
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 develop a framework for function classes generated by parametric ridge kernels: one-dimensional kernels composed with affine projections and averaged over a parameter measure. The induced kernels are positive definite, and the resulting…
In order to fully utilize "big data", it is often required to use "big models". Such models tend to grow with the complexity and size of the training data, and do not make strong parametric assumptions upfront on the nature of the…
In supervised learning with distributional inputs in the two-stage sampling setup, relevant to applications like learning-based medical screening or causal learning, the inputs (which are probability distributions) are not accessible in the…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
This study presents an efficient approach for incomplete data classification, where the entries of samples are missing or masked due to privacy preservation. To deal with these incomplete data, a new kernel function with asymmetric…