arXiv research

Extends Mahalanobis distance to Banach spaces for anomaly detection.

A new algorithm estimates mean adaptively to covariance, faster and more flexible than existing methods.

Study robustness of early-stopping GD for linear regression attacks.

Extends metrics for SPD matrices to infinite dimensions.

New algorithm estimates robust Gaussian covariance in nearly matrix multiplication time.

This paper presents a general notion of Mahalanobis distance for functional data that extends the classical multivariate concept to situations where the observed data are points belonging to curves generated by a stochastic process. More precisely, a new semi-distance for functional observations that generalize the usu…

Flexible classifier using Mahalanobis distances for non-elliptical distributions.

Mahalanobis distance detects anomalies well, but not for classification.

A method uses Shapley values and Mahalanobis distances to explain multivariate outliers.

A new algorithm reduces online exp-concave optimization runtime.

FF algorithm uses goodness as a likelihood-ratio test for scalar normalization.

A new method detects anomalies in multivariate streams without unit dependence.

The paper connects neural networks to Mahalanobis distance for interpretability.

Compressing data helps learn Mahalanobis metrics effectively.

Learning Mahalanobis metric spaces is an important problem that has found numerous applications. Several algorithms have been designed for this problem, including Information Theoretic Metric Learning (ITML) [Davis et al. 2007] and Large Margin Nearest Neighbor (LMNN) classification [Weinberger and Saul 2009]. We study…

Enhances forecasting of complex systems using FKMD.

Connects robust optimization to conformal prediction for uncertainty sets.

We propose a low-rank approach to learning a Mahalanobis metric from data. Inspired by the recent geometric mean metric learning (GMML) algorithm, we propose a low-rank variant of the algorithm. This allows to jointly learn a low-dimensional subspace where the data reside and the Mahalanobis metric that appropriately f…

Iterative reweighted algorithms, as a class of algorithms for sparse signal recovery, have been found to have better performance than their non-reweighted counterparts. However, for solving the problem of multiple measurement vectors (MMVs), all the existing reweighted algorithms do not account for temporal correlation…

Bayesian nonparametric models improve OOD detection, especially with complex covariance structures.

Metric learning seeks a transformation of the feature space that enhances prediction quality for the given task at hand. In this work we provide PAC-style sample complexity rates for supervised metric learning. We give matching lower- and upper-bounds showing that the sample complexity scales with the representation di…

For many tasks and data types, there are natural transformations to which the data should be invariant or insensitive. For instance, in visual recognition, natural images should be insensitive to rotation and translation. This requirement and its implications have been important in many machine learning applications, a…

This paper learns user preferences from comparisons using Mahalanobis metrics.

Proposes ridge regression on Riemannian manifolds for time-series prediction.

Metric learning for classification has been intensively studied over the last decade. The idea is to learn a metric space induced from a normed vector space on which data from different classes are well separated. Different measures of the separation thus lead to various designs of the objective function in the metric …

This paper quantifies how hard it is to identify specific data points in machine learning models.

Boosts kernel two-sample test power with multiple kernels.

Develops a computationally tractable differentially private mean estimator called the balloon mean.

2L-FUSE enhances feature sparsity through kernel learning.

Proposes a text perturbation method using a Mahalanobis metric to balance privacy and utility.

Polynomial-time private algorithm for robust estimation of mean and covariance in the presence of outliers.

We derive a new radial link for binary classification under shared elliptical distributions.

Adam's bias shifts from full-batch to max-margin of different norms for separable data.

A new test validates ensemble models against the null hypothesis.

Bayesian framework identifies dynamical systems from noisy data.

Develops a method for stress testing correlations of financial portfolios.

Single particle reconstruction (SPR) from cryo-electron microscopy (EM) is a technique in which the 3D structure of a molecule needs to be determined from its contrast transfer function (CTF) affected, noisy 2D projection images taken at unknown viewing directions. One of the main challenges in cryo-EM is the typically…

This paper explores a new framework for reinforcement learning based on online convex optimization, in particular mirror descent and related algorithms. Mirror descent can be viewed as an enhanced gradient method, particularly suited to minimization of convex functions in highdimensional spaces. Unlike traditional grad…

FF algorithm uses goodness as a measure of input quality, derived from likelihood-ratio tests.

Kernel functions in support vector machines (SVM) are needed to assess the similarity of input samples in order to classify these samples, for instance. Besides standard kernels such as Gaussian (i.e., radial basis function, RBF) or polynomial kernels, there are also specific kernels tailored to consider structure in t…

Paper proposes a robust metric learning algorithm.

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 problem of embedding arbitrary metric spaces into a Euclidean space with the goal…

The paper tackles learning smooth distance functions using query-based methods.

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 uses distance metrics to compare examples. This paper provides an empirical analy…

The paper evaluates and improves uncertainty estimates in neural networks for safety-critical applications.

In the classical Gaussian SVM classification we use the feature space projection transforming points to normal distributions with fixed covariance matrices (identity in the standard RBF and the covariance of the whole dataset in Mahalanobis RBF). In this paper we add additional information to Gaussian SVM by considerin…

Robust multivariate linear regression methods for online and offline use.

A fundamental question in data analysis, machine learning and signal processing is how to compare between data points. The choice of the distance metric is specifically challenging for high-dimensional data sets, where the problem of meaningfulness is more prominent (e.g. the Euclidean distance between images). In this…