Related papers: Improving Nonparametric Classification via Local R…
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…
Kernel ridge regression (KRR) is a widely used nonparametric method due to its strong theoretical guarantees and computational convenience. However, standard KRR does not distinguish between linear and nonlinear components in the signal,…
We propose a method for incorporating variable selection into local polynomial regression. This can improve the accuracy of the regression by extending the bandwidth in directions corresponding to those variables judged to be are…
This paper develops a general asymptotic theory of local polynomial (LP) regression for spatial data observed at irregularly spaced locations in a sampling region $R_n \subset \mathbb{R}^d$. We adopt a stochastic sampling design that can…
Local polynomial regression (Fan and Gijbels 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time…
In this study, we develop an asymptotic theory of nonparametric regression for locally stationary random fields (LSRFs) $\{{\bf X}_{{\bf s}, A_{n}}: {\bf s} \in R_{n} \}$ in $\mathbb{R}^{p}$ observed at irregularly spaced locations in…
A key issue in statistics and machine learning is to automatically select the "right" model complexity, e.g., the number of neighbors to be averaged over in k nearest neighbor (kNN) regression or the polynomial degree in regression with…
Kernel logistic regression (KLR) is a powerful classification method widely applied across diverse domains. In many real-world scenarios, indefinite kernels capture more domain-specific structural information than positive definite kernels.…
Multiple kernel methods less consider the intrinsic manifold structure of multiple kernel data and estimate the consensus kernel matrix with quadratic number of variables, which makes it vulnerable to the noise and outliers within multiple…
The propensity score is widely used for causal inference in observational studies, but common parametric estimators can produce biased and inefficient effect estimates when model assumptions are violated. Nonparametric approaches reduce…
Label Ranking (LR) corresponds to the problem of learning a hypothesis that maps features to rankings over a finite set of labels. We adopt a nonparametric regression approach to LR and obtain theoretical performance guarantees for this…
We study the problem of estimating the derivatives of a regression function, which has a wide range of applications as a key nonparametric functional of unknown functions. Standard analysis may be tailored to specific derivative orders, and…
Distance metric learning is a successful way to enhance the performance of the nearest neighbor classifier. In most cases, however, the distribution of data does not obey a regular form and may change in different parts of the feature…
Nystr\"om approximation is a fast randomized method that rapidly solves kernel ridge regression (KRR) problems through sub-sampling the n-by-n empirical kernel matrix appearing in the objective function. However, the performance of such a…
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…
We study the problem of learning local metrics for nearest neighbor classification. Most previous works on local metric learning learn a number of local unrelated metrics. While this "independence" approach delivers an increased flexibility…
Consider the nonparametric logistic regression problem. In the logistic regression, we usually consider the maximum likelihood estimator, and the excess risk is the expectation of the Kullback-Leibler (KL) divergence between the true and…
Local Polynomial Regression (LPR) is a powerful tool for nonparametric smoothing, yet it traditionally suffers from a "Euclidean tautology": the variables used to define the local neighborhood are identical to those used in the polynomial…
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,…
We present Label Space Reduction (LSR), a novel method for improving zero-shot classification performance of Large Language Models (LLMs). LSR iteratively refines the classification label space by systematically ranking and reducing…