Maximum pseudo-likelihood estimator for nearest-neighbours Gibbs point processes

协变量偏移下的迁移学习：重尾设计的局部 $k$-近邻回归

Transfer Learning under Covariate Shift: Local $k$-Nearest Neighbours Regression with Heavy-Tailed Design

针对无界支撑与重尾目标分布下的协变量偏移迁移学习，提出密度比指数与按样本边缘似然调节近邻数的局部 k-近邻回归器，并证明其更快收敛速率。

Efficient multivariate entropy estimation via $k$-nearest neighbour distances

Many statistical procedures, including goodness-of-fit tests and methods for independent component analysis, rely critically on the estimation of the entropy of a distribution. In this paper, we seek entropy estimators that are efficient and achieve the local asymptotic minimax lower bound with respect to squared error loss. To this end, we study weighted averages of the estimators originally proposed by Kozachenko and Leonenko (1987), based on the $k$-nearest neighbour distances of a sample of $n$ independent and identically distributed random vectors in $\mathbb{R}^d$. A careful choice of we…

Minimax rates for cost-sensitive learning on manifolds with approximate nearest neighbours

We study the approximate nearest neighbour method for cost-sensitive classification on low-dimensional manifolds embedded within a high-dimensional feature space. We determine the minimax learning rates for distributions on a smooth manifold, in a cost-sensitive setting. This generalises a classic result of Audibert and Tsybakov. Building upon recent work of Chaudhuri and Dasgupta we prove that these minimax rates are attained by the approximate nearest neighbour algorithm, where neighbours are computed in a randomly projected low-dimensional space. In addition, we give a bound on the number o…

Classification using distance nearest neighbours

This paper proposes a new probabilistic classification algorithm using a Markov random field approach. The joint distribution of class labels is explicitly modelled using the distances between feature vectors. Intuitively, a class label should depend more on class labels which are closer in the feature space, than those which are further away. Our approach builds on previous work by Holmes and Adams (2002, 2003) and Cucala et al. (2008). Our work shares many of the advantages of these approaches in providing a probabilistic basis for the statistical inference. In comparison to previous work, w…

Optimal weighted nearest neighbour classifiers

We derive an asymptotic expansion for the excess risk (regret) of a weighted nearest-neighbour classifier. This allows us to find the asymptotically optimal vector of nonnegative weights, which has a rather simple form. We show that the ratio of the regret of this classifier to that of an unweighted k-nearest neighbour classifier depends asymptotically only on the dimension d of the feature vectors, and not on the underlying populations. The improvement is greatest when d=4, but thereafter decreases as $d\rightarrow\infty$. The popular bagged nearest neighbour classifier can also be regarded a…

图上具有欧几里得边的最近邻马尔可夫点过程

Nearest-neighbour Markov point processes on graphs with Euclidean edges

本文提出了一种在具有欧几里得边的图上定义的最近邻马尔可夫点过程，并证明了其满足一致性条件。