Related papers: Bounded Statistics
This paper studies a novel approach for approximating the behavior of compartmental spreading processes. In contrast to prior work, the methods developed describe a dynamics which bound the exact moment dynamics, without explicitly…
We derive the sampling probability density function (pdf) of an ideal localized random electromagnetic field, its amplitude and intensity in an electromagnetic environment that is quasi-statically time-varying statistically homogeneous or…
Scientific explanation often requires inferring maximally predictive features from a given data set. Unfortunately, the collection of minimal maximally predictive features for most stochastic processes is uncountably infinite. In such…
The concept of image similarity is ambiguous, and images can be similar in one context and not in another. This ambiguity motivates the creation of metrics for specific contexts. This work explores the ability of deep perceptual similarity…
The following work is written in easy language for college level students. It shows how the first digit probabilities of a group of continuous real-valued functions can be calculated. Thus, examples explaining how the probabilities are…
We consider the estimation of densities in multiple subpopulations, where the available sample size in each subpopulation greatly varies. This problem occurs in epidemiology, for example, where different diseases may share similar…
We describe a new method for summarizing similarities and differences in a pair of related documents using a graph representation for text. Concepts denoted by words, phrases, and proper names in the document are represented positionally as…
This book deals with functions allowing to express the dissimilarity (discrepancy) between two data fields or ''divergence functions'' with the aim of applications to linear inverse problems. Most of the divergences found in the litterature…
The inclusion of semantic information in any similarity measures improves the efficiency of the similarity measure and provides human interpretable results for further analysis. The similarity calculation method that focuses on features…
In this exploratory article, we draw attention to the common formal ground among various estimators such as the belief functions of evidence theory and their relatives, approximation quality of rough set theory, and contextual probability.…
Existing methods to measure sentence similarity are faced with two challenges: (1) labeled datasets are usually limited in size, making them insufficient to train supervised neural models; (2) there is a training-test gap for unsupervised…
We introduce and study the computational problem of determining statistical similarity between probability distributions. For distributions $P$ and $Q$ over a finite sample space, their statistical similarity is defined as…
We study the frequentist properties of confidence intervals computed by the method known to statisticians as the Profile Likelihood. It is seen that the coverage of these intervals is surprisingly good over a wide range of possible…
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…
Several methods have been proposed for classifying long textual documents using Transformers. However, there is a lack of consensus on a benchmark to enable a fair comparison among different approaches. In this paper, we provide a…
Modern analysis on parton distribution functions (PDFs) requires calculations of the log-likelihood functions from thousands of experimental data points, and scans of multi-dimensional parameter space with tens of degrees of freedom. In…
The probability density function (PDF) of a random variable associated with the solution of a partial differential equation (PDE) with random parameters is approximated using a truncated series expansion. The random PDE is solved using two…
For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the…
Similarity measures play a central role in various data science application domains for a wide assortment of tasks. This guide describes a comprehensive set of prevalent similarity measures to serve both non-experts and professional.…
While spherical data arises in many contexts, including in directional statistics, the current tools for density estimation and population comparison on spheres are quite limited. Popular approaches for comparing populations (on Euclidean…