Related papers: Distance Covariance, Independence, and Pairwise Di…
High dimensional time series datasets are becoming increasingly common in various fields such as economics, finance, meteorology, and neuroscience. Given this ubiquity of time series data, it is surprising that very few works on variable…
The statistics of records in sequences of independent, identically distributed random variables is a classic subject of study. One of the earliest results concerns the stochastic independence of record events. Recently, records statistics…
The Davis--Kahan theorem is used in the analysis of many statistical procedures to bound the distance between subspaces spanned by population eigenvectors and their sample versions. It relies on an eigenvalue separation condition between…
Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of…
Cosine similarity is a popular distance measure that measures the similarity between two vectors in the inner product space. It is widely used in many data classification algorithms like K-Nearest Neighbors, Clustering etc. This study…
Real-world data typically contain a large number of features that are often heterogeneous in nature, relevance, and also units of measure. When assessing the similarity between data points, one can build various distance measures using…
A framework for quantifying dependence between random vectors is introduced. With the notion of a collapsing function, random vectors are summarized by single random variables, called collapsed random variables in the framework. Using this…
The correlation distance quantifies the statistical independence of two classical or quantum systems, via the distance from their joint state to the product of the marginal states. Tight lower bounds are given for the mutual information…
Detecting dependence between two random variables is a fundamental problem. Although the Pearson correlation is effective for capturing linear dependency, it can be entirely powerless for detecting nonlinear and/or heteroscedastic patterns.…
Measuring and quantifying dependencies between random variables (RV's) can give critical insights into a data-set. Typical questions are: `Do underlying relationships exist?', `Are some variables redundant?', and `Is some target variable…
Defining a distance in a mixed setting requires the quantification of observed differences of variables of different types and of variables that are measured on different scales. There exist several proposals for mixed variable distances,…
Performance estimation under covariate shift is a crucial component of safe AI model deployment, especially for sensitive use-cases. Recently, several solutions were proposed to tackle this problem, most leveraging model predictions or…
We develop the information-theoretical concepts required to study the statistical dependencies among three variables. Some of such dependencies are pure triple interactions, in the sense that they cannot be explained in terms of a…
Motivated by the importance of measuring the association between the response and predictors in high dimensional data, In this article, we propose a new mean variance test of independence between a categorical random variable and a…
Is it possible to define a coefficient of correlation which is (a) as simple as the classical coefficients like Pearson's correlation or Spearman's correlation, and yet (b) consistently estimates some simple and interpretable measure of the…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
The quotient correlation is defined here as an alternative to Pearson's correlation that is more intuitive and flexible in cases where the tail behavior of data is important. It measures nonlinear dependence where the regular correlation…
Distance queries are a basic tool in data analysis. They are used for detection and localization of change for the purpose of anomaly detection, monitoring, or planning. Distance queries are particularly useful when data sets such as…
Log-Euclidean distances are commonly used to quantify the similarity between positive definite matrices using geometric considerations. This paper analyzes the behavior of this distance when it is used to measure closeness between…
One of the most popular class of tests for independence between two random variables is the general class of rank statistics which are invariant under permutations. This class contains Spearman's coefficient of rank correlation statistic,…