Related papers: The Generalized Mean Information Coefficient
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…
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…
The maximal information coefficient (MIC), which measures the amount of dependence between two variables, is able to detect both linear and non-linear associations. However, computational cost grows rapidly as a function of the dataset…
The Maximal Information Coefficient (MIC) of Reshef et al. (Science, 2011) is a statistic for measuring dependence between variable pairs in large datasets. In this note, we prove that MIC is a consistent estimator of the corresponding…
The proposal of Reshef et al. (2011) is an interesting new approach for discovering non-linear dependencies among pairs of measurements in exploratory data mining. However, it has a potentially serious drawback. The authors laud the fact…
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…
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…
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…
Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we…
Quantifying the dependence between high-dimensional random variables is central to statistical learning and inference. Two classical methods are canonical correlation analysis (CCA), which identifies maximally correlated projected versions…
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 powerful statistic to identify dependencies between variables. However, it may be applied to sensitive data, and publishing it could leak private information. As a solution, we present…
Through computer simulations, we research several different measures of dependence, including Pearson's and Spearman's correlation coefficients, the maximal correlation, the distance correlation, a function of the mutual information called…
Mutual information (MI) is one of the most general ways to measure relationships between random variables, but estimating this quantity for complex systems is challenging. Denoising diffusion models have recently set a new bar for density…
We propose a new sparse estimation method, termed MIC (Minimum approximated Information Criterion), for generalized linear models (GLM) in fixed dimensions. What is essentially involved in MIC is the approximation of the $\ell_0$-norm with…
The ability to compress observational data and accurately estimate physical parameters relies heavily on informative summary statistics. In this paper, we introduce the use of mutual information (MI) as a means of evaluating the quality of…
Mutual information (MI) is a fundamental quantity in information theory and machine learning. However, direct estimation of MI is intractable, even if the true joint probability density for the variables of interest is known, as it involves…
Data analysis in modern science using extensive experimental and observational facilities, such as a gravitational wave detector, is essential in the search for novel scientific discoveries. Accordingly, various techniques and mathematical…
Recent development in computing, sensing and crowd-sourced data have resulted in an explosion in the availability of quantitative information. The possibilities of analyzing this so-called Big Data to inform research and the decision-making…
Estimating the strength of dependency between two variables is fundamental for exploratory analysis and many other applications in data mining. For example: non-linear dependencies between two continuous variables can be explored with the…