Related papers: Equitability, interval estimation, and statistical…
A measure of dependence is said to be equitable if it gives similar scores to equally noisy relationships of different types. Equitability is important in data exploration when the goal is to identify a relatively small set of strongest…
In exploratory data analysis, we are often interested in identifying promising pairwise associations for further analysis while filtering out weaker, less interesting ones. This can be accomplished by computing a measure of dependence on…
The maximal information coefficient (MIC) is a tool for finding the strongest pairwise relationships in a data set with many variables (Reshef et al., 2011). MIC is useful because it gives similar scores to equally noisy relationships of…
Measuring dependence between two random variables is very important, and critical in many applied areas such as variable selection, brain network analysis. However, we do not know what kind of functional relationship is between two…
Given a high-dimensional data set we often wish to find the strongest relationships within it. A common strategy is to evaluate a measure of dependence on every variable pair and retain the highest-scoring pairs for follow-up. This strategy…
Reshef et al. recently proposed a new statistical measure, the "maximal information coefficient" (MIC), for quantifying arbitrary dependencies between pairs of stochastic quantities. MIC is based on mutual information, a fundamental…
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…
The comparison of a parameter in $k$ populations is a classical problem in statistics. Testing for the equality of means or variances are typical examples. Most procedures designed to deal with this problem assume that $k$ is fixed and that…
In this paper, we propose standard statistical tools as a solution to commonly highlighted problems in the explainability literature. Indeed, leveraging statistical estimators allows for a proper definition of explanations, enabling…
In this paper, a robust non-parametric measure of statistical dependence, or correlation, between two random variables is presented. The proposed coefficient is a permutation-like statistic that quantifies how much the observed sample S_n :…
Experimental research on behavior and cognition frequently rests on stimulus or subject selection where not all characteristics can be fully controlled, even when attempting strict matching. For example, when contrasting patients to…
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 inference with a small labeled sample, a large unlabeled sample, and high-quality predictions from an external model. We link prediction-powered inference with empirical likelihood by stacking supervised estimating equations based…
When two variables are related by a known function, the coefficient of determination (denoted $R^2$) measures the proportion of the total variance in the observations that is explained by that function. This quantifies the strength of the…
Experiments often yield non-identically distributed data for statistical analysis. Tests of hypothesis under such set-ups are generally performed using the likelihood ratio test, which is non-robust with respect to outliers and model…
Empirical analyses on income and wealth inequality and those in other fields in economics and finance often face the difficulty that the data is heterogeneous, heavy-tailed or correlated in some unknown fashion. The paper focuses on…
In Science, Reshef et al. (2011) proposed the concept of equitability for measures of dependence between two random variables. To this end, they proposed a novel measure, the maximal information coefficient (MIC). Recently a PNAS paper…
We consider the problem of fitting a relationship (e.g. a potential scientific law) to data involving multiple variables. Ordinary (least squares) regression is not suitable for this because the estimated relationship will differ according…
We consider basic conceptual questions concerning the relationship between statistical estimation and causal inference. Firstly, we show how to translate causal inference problems into an abstract statistical formalism without requiring any…
Statistical techniques are used in all branches of science to determine the feasibility of quantitative hypotheses. One of the most basic applications of statistical techniques in comparative analysis is the test of equality of two…