Related papers: On the Size and Approximation Error of Distilled S…

In this paper, we consider nonparametric estimation over general Dirichlet metric measure spaces. Unlike the more commonly studied reproducing kernel Hilbert space, whose elements may be defined pointwise, a Dirichlet space typically only…

The random feature (RF) approach is a well-established and efficient tool for scalable kernel methods, but existing literature has primarily focused on kernel ridge regression with random features (KRR-RF), which has limitations in handling…

Parameter reduction can enable otherwise infeasible design and uncertainty studies with modern computational science models that contain several input parameters. In statistical regression, techniques for sufficient dimension reduction…

Relational databases (RDBs) underpin the majority of global data management systems, where information is structured into multiple interdependent tables. To effectively use the knowledge within RDBs for predictive tasks, recent advances…

Dataset distillation aims to synthesize a compact yet representative dataset that preserves the essential characteristics of the original data for efficient model training. Existing methods mainly focus on improving data-synthetic alignment…

Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming…

Dataset distillation aims to distill the knowledge of a large-scale real dataset into small yet informative synthetic data such that a model trained on it performs as well as a model trained on the full dataset. Despite recent progress,…

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. Specifically, we first use the…

Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…

Residual connection has been extensively studied and widely applied at the model architecture level. However, its potential in the more challenging data-centric approaches remains unexplored. In this work, we introduce the concept of Data…

Regularization is an essential element of virtually all kernel methods for nonparametric regression problems. A critical factor in the effectiveness of a given kernel method is the type of regularization that is employed. This article…

Although the diffusion model has achieved remarkable performance in the field of image generation, its high inference delay hinders its wide application in edge devices with scarce computing resources. Therefore, many training-free sampling…

We focus on the distribution regression problem: regressing to a real-valued response from a probability distribution. Although there exist a large number of similarity measures between distributions, very little is known about their…

Recent advances in model compression have provided procedures for compressing large neural networks to a fraction of their original size while retaining most if not all of their accuracy. However, all of these approaches rely on access to…

Dataset distillation condenses large datasets into synthetic subsets, achieving performance comparable to training on the full dataset while substantially reducing storage and computation costs. Most existing dataset distillation methods…

Retinal image matching plays a crucial role in monitoring disease progression and treatment response. However, datasets with matched keypoints between temporally separated pairs of images are not available in abundance to train…

One approach to improving the running time of kernel-based machine learning methods is to build a small sketch of the input and use it in lieu of the full kernel matrix in the machine learning task of interest. Here, we describe a version…

Kernel ridge regression is an important nonparametric method for estimating smooth functions. We introduce a new set of conditions, under which the actual rates of convergence of the kernel ridge regression estimator under both the L_2 norm…

In this paper we introduce randomized $t$-type statistics that will be referred to as randomized pivots. We show that these randomized pivots yield central limit theorems with a significantly smaller magnitude of error as compared to that…

Model-based deep learning has achieved astounding successes due in part to the availability of large-scale real-world data. However, processing such massive amounts of data comes at a considerable cost in terms of computations, storage,…