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Retrieval-Augmented Generation (RAG) has emerged as a powerful framework for knowledge-intensive tasks, yet its effectiveness in long-context scenarios is often bottlenecked by the retriever's inability to distinguish sparse yet crucial…

We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…

We consider the task of robust non-linear regression in the presence of both inlier noise and outliers. Assuming that the unknown non-linear function belongs to a Reproducing Kernel Hilbert Space (RKHS), our goal is to estimate the set of…

In this article, we introduce a kernel-based consensual aggregation method for regression problems. We aim to exibly combine individual regression estimators $r_1, \ldots, r_M$ using a weighted average where the weights are dened based on…

The classical kernel ridge regression problem aims to find the best fit for the output $Y$ as a function of the input data $X\in \mathbb{R}^d$, with a fixed choice of regularization term imposed by a given choice of a reproducing kernel…

Identifying patient cohorts is fundamental to numerous healthcare tasks, including clinical trial recruitment and retrospective studies. Current cohort retrieval methods in healthcare organizations rely on automated queries of structured…

Trust-region (TR) and adaptive regularization using cubics (ARC) have proven to have some very appealing theoretical properties for non-convex optimization by concurrently computing function value, gradient, and Hessian matrix to obtain the…

The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…

Gaussian process regression (GPR) or kernel ridge regression is a widely used and powerful tool for nonlinear prediction. Therefore, active learning (AL) for GPR, which actively collects data labels to achieve an accurate prediction with…

Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…

Reinforcement learning utilizing kernel ridge regression to predict the expected value function represents a powerful method with great representational capacity. This setting is a highly versatile framework amenable to analytical results.…

We introduce CUTS-GPR, a new method for performing numerically exact Gaussian process regression (GPR) in high-dimensional settings. The key component of CUTS-GPR is an extremely fast kernel matrix-vector product, which exhibits near-linear…

The ever-growing size of the datasets renders well-studied learning techniques, such as Kernel Ridge Regression, inapplicable, posing a serious computational challenge. Divide-and-conquer is a common remedy, suggesting to split the dataset…

Subspace clustering aims to group data points into multiple clusters of which each corresponds to one subspace. Most existing subspace clustering approaches assume that input data lie on linear subspaces. In practice, however, this…

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…

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…

In large-scale regression problems, random Fourier features (RFFs) have significantly enhanced the computational scalability and flexibility of Gaussian processes (GPs) by defining kernels through their spectral density, from which a finite…

Chunking is a crucial preprocessing step in retrieval-augmented generation (RAG) systems, significantly impacting retrieval effectiveness across diverse datasets. In this study, we systematically evaluate fixed-size chunking strategies and…

The Multi-Kink Quantile Regression (MKQR) model is an important tool for analyzing data with heterogeneous conditional distributions, especially when quantiles of response variable are of interest, due to its robustness to outliers and…

We concern computer model calibration problem where the goal is to find the parameters that minimize the discrepancy between the multivariate real-world and computer model outputs. We propose to solve an approximation using signed residuals…