Related papers: Bayesian Kernel and Mutual $k$-Nearest Neighbor Re…
The $k$-nearest neighbor classification method ($k$-NNC) is one of the simplest nonparametric classification methods. The mutual $k$-NN classification method (M$k$NNC) is a variant of $k$-NNC based on mutual neighborship. We propose another…
Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick…
Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…
In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
K-Nearest neighbor classifier (k-NNC) is simple to use and has little design time like finding k values in k-nearest neighbor classifier, hence these are suitable to work with dynamically varying data-sets. There exists some fundamental…
This paper proposes a spatial k-nearest neighbor method for nonparametric prediction of real-valued spatial data and supervised classification for categorical spatial data. The proposed method is based on a double nearest neighbor rule…
Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of…
Multiple kernel learning algorithms are proposed to combine kernels in order to obtain a better similarity measure or to integrate feature representations coming from different data sources. Most of the previous research on such methods is…
Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…
Kernel methods are ubiquitous tools in machine learning. However, there is often little reason for the common practice of selecting a kernel a priori. Even if a universal approximating kernel is selected, the quality of the finite sample…
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and…
Data-driven neighborhood definitions and graph constructions are often used in machine learning and signal processing applications. k-nearest neighbor~(kNN) and $\epsilon$-neighborhood methods are among the most common methods used for…
We propose a kernel mixture of polynomials prior for Bayesian nonparametric regression. The regression function is modeled by local averages of polynomials with kernel mixture weights. We obtain the minimax-optimal rate of contraction of…
K-Nearest Neighbours (k-NN) is a popular classification and regression algorithm, yet one of its main limitations is the difficulty in choosing the number of neighbours. We present a Bayesian algorithm to compute the posterior probability…
Kernel Bayesian inference is a principled approach to nonparametric inference in probabilistic graphical models, where probabilistic relationships between variables are learned from data in a nonparametric manner. Various algorithms of…
There is a rich literature on Bayesian methods for density estimation, which characterize the unknown density as a mixture of kernels. Such methods have advantages in terms of providing uncertainty quantification in estimation, while being…
This paper develops a class of Bayesian non- and semiparametric methods for estimating regression curves and surfaces. The main idea is to model the regression as locally linear, and then place suitable local priors on the local parameters.…
We establish the first nonasymptotic error bounds for Kaplan-Meier-based nearest neighbor and kernel survival probability estimators where feature vectors reside in metric spaces. Our bounds imply rates of strong consistency for these…