Related papers: Infinite-dimensional Mahalanobis Distance with App…
Rotated object detection in aerial images is a meaningful yet challenging task as objects are densely arranged and have arbitrary orientations. The eight-parameter (coordinates of box vectors) methods in rotated object detection usually use…
We present a fast, differentially private algorithm for high-dimensional covariance-aware mean estimation with nearly optimal sample complexity. Only exponential-time estimators were previously known to achieve this guarantee. Given $n$…
The distance metric plays an important role in nearest neighbor (NN) classification. Usually the Euclidean distance metric is assumed or a Mahalanobis distance metric is optimized to improve the NN performance. In this paper, we study the…
Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…
This paper focuses on the problem of kernelizing an existing supervised Mahalanobis distance learner. The following features are included in the paper. Firstly, three popular learners, namely, "neighborhood component analysis", "large…
This work introduces the Matrix Minimum Covariance Determinant (MMCD) method, a novel robust location and covariance estimation procedure designed for data that are naturally represented in the form of a matrix. Unlike standard robust…
Recent work in metric learning has significantly improved the state-of-the-art in k-nearest neighbor classification. Support vector machines (SVM), particularly with RBF kernels, are amongst the most popular classification algorithms that…
A collection of robust Mahalanobis distances for multivariate outlier detection is proposed, based on the notion of shrinkage. Robust intensity and scaling factors are optimally estimated to define the shrinkage. Some properties are…
The estimation of covariance operators of spatio-temporal data is in many applications only computationally feasible under simplifying assumptions, such as separability of the covariance into strictly temporal and spatial factors.Powerful…
Statistical distance measures have found wide applicability in information retrieval tasks that typically involve high dimensional datasets. In order to reduce the storage space and ensure efficient performance of queries, dimensionality…
In this paper, we study distance covariance, Hilbert-Schmidt covariance (aka Hilbert-Schmidt independence criterion [Gretton et al. (2008)]) and related independence tests under the high dimensional scenario. We show that the sample…
A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert…
Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…
Effectively applying the K-means algorithm to clustering tasks with incomplete features remains an important research area due to its impact on real-world applications. Recent work has shown that unifying K-means clustering and imputation…
Analyzing the covariance structure of data is a fundamental task of statistics. While this task is simple for low-dimensional observations, it becomes challenging for more intricate objects, such as multivariate functions. Here, the…
We develop a kernel-based approach for estimating the spatially varying Sobolev regularity~$s$ of an unknown $d$-variate function~$f$ from scattered sampling data, which quantifies the degree of local differentiability supported by the…
While likelihood-based inference and its variants provide a statistically efficient and widely applicable approach to parametric inference, their application to models involving intractable likelihoods poses challenges. In this work, we…
Kernel regression is a popular non-parametric fitting technique. It aims at learning a function which estimates the targets for test inputs as precise as possible. Generally, the function value for a test input is estimated by a weighted…
Distance covariance is a popular dependence measure for two random vectors $X$ and $Y$ of possibly different dimensions and types. Recent years have witnessed concentrated efforts in the literature to understand the distributional…
We consider the supervised classification problem of machine learning in Cayley-Klein projective geometries: We show how to learn a curved Mahalanobis metric distance corresponding to either the hyperbolic geometry or the elliptic geometry…