Related papers: A Rank Minrelation - Majrelation Coefficient
This article presents several alternatives to Pearson's correlation coefficient and many examples. In the samples where the rank in a discrete variable counts more than the variable values, the mixtures that we propose of Pearson's and…
Symmetry arises often when learning from high dimensional data. For example, data sets consisting of point clouds, graphs, and unordered sets appear routinely in contemporary applications, and exhibit rich underlying symmetries.…
Recently, Chatterjee has introduced a new coefficient of correlation which has several natural properties. In particular, the coefficient attains its maximal value if and only if one variable is a measurable function of the other variable.…
A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the…
This work is motivated by a hand-collected data set from one of the largest Internet portals in Korea. This data set records the top 30 most frequently discussed stocks on its on-line message board. The frequencies are considered to measure…
Chatterjee (2021)'s ingenious approach to estimating a measure of dependence first proposed by Dette et al. (2013) based on simple rank statistics has quickly caught attention. This measure of dependence has the unusual property of being…
Latent variable models are well-known to suffer from rank deficiencies, causing problems with convergence and stability. Such problems are compounded in the "reduced-group split-ballot multitrait-multimethod model", which omits a set of…
A new class of general exponential ranking models is introduced which we label angle-based models for ranking data. A consensus score vector is assumed, which assigns scores to a set of items, where the scores reflect a consensus view of…
The relationship between statistical dependency and causality lies at the heart of all statistical approaches to causal inference. Recent results in the ChaLearn cause-effect pair challenge have shown that causal directionality can be…
Not a matter of serious contention, Pearson's correlation coefficient is still the most important statistical association measure. Restricted to just two variables, this measure sometimes doesn't live up to users' needs and expectations.…
For independent random variables $(X_i)_{1\leq i\leq n}$, we consider the maximal correlation coefficient $R=R(\min_{i:1\leq i\leq m}X_i,\min_{j:\ell+1\leq j\leq n}X_j)$. If $X_1,X_2,\ldots,X_n$ are identically distributed with the same…
In this paper, we propose a novel Euclidean-distance-based coefficient, named differential distance correlation, to measure the strength of dependence between a random variable $ Y \in \mathbb{R} $ and a random vector $ \boldsymbol{X} \in…
We describe a method that infers whether statistical dependences between two observed variables X and Y are due to a "direct" causal link or only due to a connecting causal path that contains an unobserved variable of low complexity, e.g.,…
High-dimensional mixed data as a combination of both continuous and ordinal variables are widely seen in many research areas such as genomic studies and survey data analysis. Estimating the underlying correlation among mixed data is hence…
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…
Existing metrics in competing risks survival analysis such as concordance and accuracy do not evaluate a model's ability to jointly predict the event type and the event time. To address these limitations, we propose a new metric, which we…
Data in the form of ranking lists are frequently encountered, and combining ranking results from different sources can potentially generate a better ranking list and help understand behaviors of the rankers. Of interest here are the rank…
The multimodal relevance metric is usually borrowed from the embedding ability of pretrained contrastive learning models for bimodal data, which is used to evaluate the correlation between cross-modal data (e.g., CLIP). However, the…
Under the null hypothesis, the marginal probability of the positive response is symmetric at any specified correlated coefficient, and the discordance probability is also symmetric to the positive response probability. The marginal…
In this paper, a class of statistics named ART (the alternant recursive topology statistics) is proposed to measure the properties of correlation between two variables. A wide range of bi-variable correlations both linear and nonlinear can…