Related papers: Linear-time Learning on Distributions with Approxi…

We consider the regret minimization problem in reinforcement learning (RL) in the episodic setting. In many real-world RL environments, the state and action spaces are continuous or very large. Existing approaches establish regret…

This work develops algorithms for non-parametric confidence regions for samples from a univariate distribution whose support is a discrete mesh bounded on the left. We generalize the theory of Learned-Miller to preorders over the sample…

In this paper, we study the angle testing problem in the context of similarity search in high-dimensional Euclidean spaces and propose two projection-based probabilistic kernel functions, one designed for angle comparison and the other for…

Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert space…

The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance…

Descriptive statistics for parametric models are currently highly sensative to departures, gross errors, and/or random errors. Here, leveraging the structures of parametric distributions and their central moment kernel distributions, a…

Conditional Maximum Mean Discrepancy (CMMD) can capture the discrepancy between conditional distributions by drawing support from nonlinear kernel functions, thus it has been successfully used for pattern classification. However, CMMD does…

We introduce two versions of a new sketch for approximately embedding the Gaussian kernel into Euclidean inner product space. These work by truncating infinite expansions of the Gaussian kernel, and carefully invoking the…

Efficient and accurate low-rank approximations of multiple data sources are essential in the era of big data. The scaling of kernel-based learning algorithms to large datasets is limited by the O(n^2) computation and storage complexity of…

We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…

Graph classification is a challenging problem owing to the difficulty in quantifying the similarity between graphs or representing graphs as vectors, though there have been a few methods using graph kernels or graph neural networks (GNNs).…

Random features provide a practical framework for large-scale kernel approximation and supervised learning. It has been shown that data-dependent sampling of random features using leverage scores can significantly reduce the number of…

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…

An increasing number of systems are being designed by gathering significant amounts of data and then optimizing the system parameters directly using the obtained data. Often this is done without analyzing the dataset structure. As task…

Kernel conditional mean embeddings (CMEs) offer a powerful framework for representing conditional distribution, but they often face scalability and expressiveness challenges. In this work, we propose a new method that effectively combines…

Kernel quadrature is widely used to approximate integrals of smooth functions, with worst-case error typically decaying at the minimax rate $n^{-\alpha/d}$ for smoothness $\alpha$ in dimension $d$. Existing rate-optimal methods often depend…

A central problem in machine learning is often formulated as follows: Given a dataset $\{(x_j, y_j)\}_{j=1}^M$, which is a sample drawn from an unknown probability distribution, the goal is to construct a functional model $f$ such that…

Kernels are often developed and used as implicit mapping functions that show impressive predictive power due to their high-dimensional feature space representations. In this study, we gradually construct a series of simple feature maps that…

This paper introduces an algorithm to select demonstration examples for in-context learning of a query set. Given a set of $n$ examples, how can we quickly select $k$ out of $n$ to best serve as the conditioning for downstream inference?…

Classifying large-scale image data into object categories is an important problem that has received increasing research attention. Given the huge amount of data, non-parametric approaches such as nearest neighbor classifiers have shown…