arXiv research

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

A new algorithm reduces online exp-concave optimization runtime.

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.

Extends Mahalanobis distance to Banach spaces for anomaly detection.

Mahalanobis distance detects anomalies well, but not for classification.

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

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…

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

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.

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

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.

2L-FUSE enhances feature sparsity through kernel learning.

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

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

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

A new test validates ensemble models against the null hypothesis.

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…

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.

Extends metrics for SPD matrices to infinite dimensions.

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

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…

There is an increasingly apparent need for validating the classifications made by deep learning systems in safety-critical applications like autonomous vehicle systems. A number of recent papers have proposed methods for detecting anomalous image data that appear different from known inlier data samples, including reco…

Bayesian method selects subsets for LMMs with structured dependence.

Elliptical Attention improves transformer performance by focusing on contextually relevant features.

Improved anomaly detection for launch vehicle propulsion systems using LSTM and statistical relabeling.

Algorithm learns similarity metrics for individual fairness.

Study metric learning from limited preference comparisons, showing how low-dimensional structure can still reveal metric information.

Proposes GMOTE for better handling imbalanced data.

Study quantifies distribution shifts and uncertainties to improve machine learning model robustness.

Tests if vertices in graphs have the same latent positions.

The objective of this study is to investigate the efficient determination of $C$ and $γ$ for Support Vector Regression with RBF or mahalanobis kernel based on numerical and statistician considerations, which indicates the connection between $C$ and kernels and demonstrates that the deviation of geometric distance of ne…