Related papers: Generalized Local Polynomial Regression with Decom…

Local Polynomial Regression (LPR) is a widely used nonparametric method for modeling complex relationships due to its flexibility and simplicity. It estimates a regression function by fitting low-degree polynomials to localized subsets of…

Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various…

We develop a novel framework to accelerate Gaussian process regression (GPR). In particular, we consider localization kernels at each data point to down-weigh the contributions from other data points that are far away, and we derive the GPR…

LiDAR-based Place Recognition (LPR) remains a critical task in Embodied Artificial Intelligence (AI) and Autonomous Driving, primarily addressing localization challenges in GPS-denied environments and supporting loop closure detection.…

This paper provides ANOVA inference for nonparametric local polynomial regression (LPR) in analogy with ANOVA tools for the classical linear regression model. A surprisingly simple and exact local ANOVA decomposition is established, and a…

Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds,…

Frequency response function (FRF) estimation is a classical subject in system identification. In the past two decades, there have been remarkable advances in developing local methods for this subject, e.g., the local polynomial method,…

For supervised classification problems, this paper considers estimating the query's label probability through local regression using observed covariates. Well-known nonparametric kernel smoother and $k$-nearest neighbor ($k$-NN) estimator,…

Local Fr'echet Regression (LFR) is a nonparametric regression method for settings in which the explanatory variable lies in a Euclidean space and the response variable lies in a metric space. It is used to estimate smooth trajectories in…

Machine learning (ML) models for molecules and materials commonly rely on a decomposition of the global target quantity into local, atom-centered contributions. This approach is convenient from a computational perspective, enabling…

Although geographically weighted Poisson regression (GWPR) is a popular regression for spatially indexed count data, its development is relatively limited compared to that found for linear geographically weighted regression (GWR), where…

Over-parameterized models like deep nets and random forests have become very popular in machine learning. However, the natural goals of continuity and differentiability, common in regression models, are now often ignored in modern…

Geometric variations like rotation, scaling, and viewpoint changes pose a significant challenge to visual understanding. One common solution is to directly model certain intrinsic structures, e.g., using landmarks. However, it then becomes…

High-dimensional data analysis has been an active area, and the main focuses have been variable selection and dimension reduction. In practice, it occurs often that the variables are located on an unknown, lower-dimensional nonlinear…

Gaussian process regression (GPR) has been a well-known machine learning method for various applications such as uncertainty quantifications (UQ). However, GPR is inherently a data-driven method, which requires sufficiently large dataset.…

This paper proposes a novel discriminative regression method, called adaptive locality preserving regression (ALPR) for classification. In particular, ALPR aims to learn a more flexible and discriminative projection that not only preserves…

Convolutional Neural Networks (CNN) and the locally connected layer are limited in capturing the importance and relations of different local receptive fields, which are often crucial for tasks such as face verification, visual question…

In Earth sciences, unobserved factors exhibit non-stationary spatial distributions, causing the relationships between features and targets to display spatial heterogeneity. In geographic machine learning tasks, conventional statistical…

Pre-trained large-scale vision-language models (VLMs) have acquired profound understanding of general visual concepts. Recent advancements in efficient transfer learning (ETL) have shown remarkable success in fine-tuning VLMs within the…

Estimating software effort has been a largely unsolved problem for decades. One of the main reasons that hinders building accurate estimation models is the often heterogeneous nature of software data with a complex structure. Typically,…