Related papers: Online Adaptive Mahalanobis Distance Estimation

Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…

Despite the enormous success of Hamiltonian Monte Carlo and related Markov Chain Monte Carlo (MCMC) methods, sampling often still represents the computational bottleneck in scientific applications. Availability of parallel resources can…

The ability of deep learning models to learn continuously is essential for adapting to new data categories and evolving data distributions. In recent years, approaches leveraging frozen feature extractors after an initial learning phase…

Clustering is an important part of many modern data analysis pipelines, including network analysis and data retrieval. There are many different clustering algorithms developed by various communities, and it is often not clear which…

Robust estimators of location and dispersion are often used in the elliptical model to obtain an uncontaminated and highly representative subsample by trimming the data outside an ellipsoid based in the associated Mahalanobis distance. Here…

Sampling from high dimensional distributions is a computational bottleneck in many scientific applications. Hamiltonian Monte Carlo (HMC), and in particular the No-U-Turn Sampler (NUTS), are widely used, yet they struggle on problems with a…

k-means has recently been recognized as one of the best algorithms for clustering unsupervised data. Since k-means depends mainly on distance calculation between all data points and the centers, the time cost will be high when the size of…

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…

We employ unsupervised machine learning to enhance the accuracy of our recently presented scaling method for wave confinement analysis [1]. We employ the standard k-means++ algorithm as well as our own model-based algorithm. We investigate…

The crucial importance of metrics in machine learning algorithms has led to an increasing interest in optimizing distance and similarity functions, an area of research known as metric learning. When data consist of feature vectors, a large…

The emergence of Big Data has enabled new research perspectives in the discrete choice community. While the techniques to estimate Machine Learning models on a massive amount of data are well established, these have not yet been fully…

Bateni et al. has recently introduced the weak-strong distance oracle model to study clustering problems in settings with limited distance information. Given query access to the strong-oracle and weak-oracle in the weak-strong oracle model,…

Metric magnitude is a measure of the "size" of point clouds with many desirable geometric properties. It has been adapted to various mathematical contexts and recent work suggests that it can enhance machine learning and optimization…

The horseshoe prior is frequently employed in Bayesian analysis of high-dimensional models, and has been shown to achieve minimax optimal risk properties when the truth is sparse. While optimization-based algorithms for the extremely…

Geodesic distance serves as a reliable means of measuring distance in nonlinear spaces, and such nonlinear manifolds are prevalent in the current multimodal learning. In these scenarios, some samples may exhibit high similarity, yet they…

We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…

In many modern data sets, High dimension low sample size (HDLSS) data is prevalent in many fields of studies. There has been an increased focus recently on using machine learning and statistical methods to mine valuable information out of…

Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…

The most widely used internal measure for clustering evaluation is the silhouette coefficient, whose naive computation requires a quadratic number of distance calculations, which is clearly unfeasible for massive datasets. Surprisingly,…

Ensembling deep learning models is a shortcut to promote its implementation in new scenarios, which can avoid tuning neural networks, losses and training algorithms from scratch. However, it is difficult to collect sufficient accurate and…