Related papers: Choosing the parameter of the Fermat distance: nav…
A number of machine learning algorithms are using a metric, or a distance, in order to compare individuals. The Euclidean distance is usually employed, but it may be more efficient to learn a parametric distance such as Mahalanobis metric.…
Density-based distances (DBDs) provide a principled approach to metric learning by defining distances in terms of the underlying data distribution. By employing a Riemannian metric that increases in regions of low probability density,…
Finding the point in an algebraic variety that is closest to a given point is an optimization problem with many applications. We study the case when the variety is a Fermat hypersurface. Our formula for its Euclidean distance degree is a…
Pairwise Euclidean distance calculation is a fundamental step in many machine learning and data analysis algorithms. In real-world applications, however, these distances are frequently distorted by heteroskedastic noise$\unicode{x2014}$a…
Matrix Factorization plays an important role in machine learning such as Non-negative Matrix Factorization, Principal Component Analysis, Dictionary Learning, etc. However, most of the studies aim to minimize the loss by measuring the…
Machine Learning has attracted considerable attention throughout the past decade due to its potential to solve far-reaching tasks, such as image classification, object recognition, anomaly detection, and data forecasting. A standard…
To optimize a neural network one often thinks of optimizing its parameters, but it is ultimately a matter of optimizing the function that maps inputs to outputs. Since a change in the parameters might serve as a poor proxy for the change in…
The success of machine learning on a given task dependson, among other things, which learning algorithm is selected and its associated hyperparameters. Selecting an appropriate learning algorithm and setting its hyperparameters for a given…
Given a probability measure with density, Fermat distances and density-driven metrics are conformal transformations of the Euclidean metric that shrink distances in high density areas and enlarge distances in low density areas. Although…
In this work we discuss the impact of nuisance parameters on the effectiveness of machine learning in high-energy physics problems, and provide a review of techniques that allow to include their effect and reduce their impact in the search…
Parameter estimation is of fundamental importance in areas from atomic spectroscopy and atomic clocks to gravitational wave detection. Entangled probes provide a significant precision gain over classical strategies in the absence of noise.…
In machine learning, accurately predicting the probability that a specific input is correct is crucial for risk management. This process, known as uncertainty (or confidence) estimation, is particularly important in mission-critical…
Distances are fundamental primitives whose choice significantly impacts the performances of algorithms in machine learning and signal processing. However selecting the most appropriate distance for a given task is an endeavor. Instead of…
Fourier extensions have been shown to be an effective means for the approximation of smooth, nonperiodic functions on bounded intervals given their values on an equispaced, or in general, scattered grid. Related to this method are two…
Consider an i.i.d. sample from an unknown density function supported on an unknown manifold embedded in a high dimensional Euclidean space. We tackle the problem of learning a distance between points, able to capture both the geometry of…
In many data analysis applications the following scenario is commonplace: we are given a point set that is supposed to sample a hidden ground truth $K$ in a metric space, but it got corrupted with noise so that some of the data points lie…
This paper relates parameter distance to gradient breakdown for a broad class of nonlinear compositional functions. The analysis leads to a new distance function called deep relative trust and a descent lemma for neural networks. Since the…
Canonical distances such as Euclidean distance often fail to capture the appropriate relationships between items, subsequently leading to subpar inference and prediction. Many algorithms have been proposed for automated learning of suitable…
All known algorithms for the Fr\'echet distance between curves proceed in two steps: first, they construct an efficient oracle for the decision version; second, they use this oracle to find the optimum from a finite set of critical values.…
Several researchers proposed using non-Euclidean metrics on point sets in Euclidean space for clustering noisy data. Almost always, a distance function is desired that recognizes the closeness of the points in the same cluster, even if the…