Related papers: Measuring Dependence with Matrix-based Entropy Fun…

The monotonic dependence of the outputs of a neural network on some of its inputs is a crucial inductive bias in many scenarios where domain knowledge dictates such behavior. This is especially important for interpretability and fairness…

In this article, we show that the recently introduced ordinal pattern dependence fits into the axiomatic framework of general multivariate dependence measures, i.e., measures of dependence between two multivariate random objects.…

Statistically sound pattern discovery harnesses the rigour of statistical hypothesis testing to overcome many of the issues that have hampered standard data mining approaches to pattern discovery. Most importantly, application of…

When two variables depend on the same or similar underlying network, their shared network dependence structure can lead to spurious associations. While statistical associations between two variables sampled from interconnected subjects are…

The ability to remove unwanted dependencies from data is crucial in various domains, including fairness, robust learning, and privacy protection. In this work, we propose an encoder-based approach that learns a representation independent of…

Since its inception, the neural estimation of mutual information (MI) has demonstrated the empirical success of modeling expected dependency between high-dimensional random variables. However, MI is an aggregate statistic and cannot be used…

The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…

We study the problem of learning feature representations from a pair of random variables, where we focus on the representations that are induced by their dependence. We provide sufficient and necessary conditions for such dependence induced…

We explore fairness from a statistical perspective by selectively utilizing either conditional distance covariance or distance covariance statistics as measures to assess the independence between predictions and sensitive attributes. We…

Data plays a pivotal role in the groundbreaking advancements in artificial intelligence. The quantitative analysis of data significantly contributes to model training, enhancing both the efficiency and quality of data utilization. However,…

Deep learning methods have proved highly effective for classification and image recognition problems. In this paper, we ask whether this success can be transferred to hypothesis testing: if a neural network can distinguish, for example, an…

Multiplex graphs, characterised by their layered structure, exhibit informative interdependencies within layers that are crucial for understanding complex network dynamics. Quantifying the interaction and shared information among these…

Data-driven decision-making has drawn scrutiny from policy makers due to fears of potential discrimination, and a growing literature has begun to develop fair statistical techniques. However, these techniques are often specialized to one…

Attribute reduction is a basic issue in knowledge representation and data mining. Rough sets provide a theoretical foundation for the issue. Matroids generalized from matrices have been widely used in many fields, particularly greedy…

A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…

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…

We develop inference procedures robust to general forms of weak dependence. The procedures utilize test statistics constructed by resampling in a manner that does not depend on the unknown correlation structure of the data. We prove that…

Deep artificial neural networks show high predictive performance in many fields, but they do not afford statistical inferences and their black-box operations are too complicated for humans to comprehend. Because positing that a relationship…

The interactions between three or more random variables are often nontrivial, poorly understood, and yet, are paramount for future advances in fields such as network information theory, neuroscience, genetics and many others. In this work,…

Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is…