Related papers: Characterizing how 'distributional' NLP corpora di…
This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…
What distributions arise as the distribution of the distance between two typical points in some measured metric space? This seems to be a surprisingly subtle problem. We conjecture that every distribution with a density function whose…
Out-of-Distribution (OoD) detection aims to justify whether a given sample is from the training distribution of the classifier-under-protection, i.e., In-Distribution (InD), or from OoD. Diffusion Models (DMs) are recently utilized in OoD…
Energy statistics are estimators of the energy distance that depend on the distances between observations. The idea behind energy statistics is to consider a statistical potential energy that would parallel Newton's gravitational potential…
Non-deterministic measurements are common in real-world scenarios: the performance of a stochastic optimization algorithm or the total reward of a reinforcement learning agent in a chaotic environment are just two examples in which…
In the statistical literature, as well as in artificial intelligence and machine learning, measures of discrepancy between two probability distributions are largely used to develop measures of goodness-of-fit. We concentrate on quadratic…
Maximum Mean Discrepancy (MMD) has been widely used in the areas of machine learning and statistics to quantify the distance between two distributions in the $p$-dimensional Euclidean space. The asymptotic property of the sample MMD has…
We consider a distributed detection problem where measurements at each sensor follow a general parametric distribution. The network does not have a central processing unit or fusion center (FC). Thus, each node takes some measurements, does…
The Wasserstein distance is a powerful metric based on the theory of optimal transport. It gives a natural measure of the distance between two distributions with a wide range of applications. In contrast to a number of the common…
Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we…
Metrics for rigorously defining a distance between two events have been used to study the properties of the dataspace manifold of particle collider physics. The probability distribution of pairwise distances on this dataspace is unique with…
The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…
A novel nonparametric clustering algorithm is proposed using the interpoint distances between the members of the data to reveal the inherent clustering structure existing in the given set of data, where we apply the classical nonparametric…
In this paper, the statistical properties of Newton s method algorithm output in a specific case have been studied. The relative frequency density of this sample converges to a well-defined function, prompting us to explore its…
Comparing the representations learned by different neural networks has recently emerged as a key tool to understand various architectures and ultimately optimize them. In this work, we introduce GULP, a family of distance measures between…
We derive a hierarchy of equations which allow a general $n$-body distribution function to be measured by test-particle insertion of between $1$ and $n$ particles, and successfully apply it to measure the pair and three-body distribution…
Clustering is a fundamental approach to understanding data patterns, wherein the intuitive Euclidean distance space is commonly adopted. However, this is not the case for implicit cluster distributions reflected by qualitative attribute…
Optimal transport and its related problems, including optimal partial transport, have proven to be valuable tools in machine learning for computing meaningful distances between probability or positive measures. This success has led to a…
The spatial distributions of cities fall into two groups: one is the simple distribution with characteristic scale (e.g. exponential distribution), and the other is the complex distribution without characteristic scale (e.g. power-law…
The degree distribution is one of the most fundamental graph properties of interest for real-world graphs. It has been widely observed in numerous domains that graphs typically have a tailed or scale-free degree distribution. While the…