New estimators reduce computation for Kendall's tau and conditional Kendall's tau matrices under structural assumptions.
problem Efficient estimation of Kendall's tau and conditional Kendall's tau matrices for large dimensions.
method Averaging pairwise estimates over blocks or conditional estimates, exploiting structural assumptions.
result Improved estimators with reduced computational cost and similar error level.
Kendall transformation converts continuous data into categorical vectors for robust information theory.
problem Handling small number of observations and preserving ranking in continuous data.
method Kendall transformation converts ordered features into categorical vectors of pairwise order relations.
result Kendall transformation makes information theory methods applicable to continuous data robustly.
Python tools for 3D shape analysis on Kendall's space.
problem Lack of practical utilities for advanced 3D shape analysis.
method Developed Python tools for 3D shape analysis on Kendall's 3D Shape Space.
result Efficient, accessible software solutions for researchers.
We propose new positive definite kernels for permutations. First we introduce a weighted version of the Kendall kernel, which allows to weight unequally the contributions of different item pairs in the permutations depending on their ranks. Like the Kendall kernel, we show that the weighted version is invariant to rela…
Improved portfolio optimization using Kendall-like correlation coefficients.
problem Accurate estimation of eigenvectors in data-poor regimes for portfolio optimization.
method Developed generalized correlation coefficients based on Kendall's rank correlation.
result Markowitz portfolios with lower out-of-sample risk using these coefficients.
A new algorithm for parallel transport on shape spaces is presented and compared to existing methods.
problem Statistical analysis of shape data, especially in time series and optimization.
method Pole ladder algorithm for parallel transport on Kendall shape spaces, compared to integration methods.
result The pole ladder algorithm is a more efficient method for parallel transport.
We show how the problem of estimating conditional Kendall's tau can be rewritten as a classification task. Conditional Kendall's tau is a conditional dependence parameter that is a characteristic of a given pair of random variables. The goal is to predict whether the pair is concordant (value of 1) or discordant (val…
New method reconstructs 3D shapes from 2D images using Kendall's shape space.
problem Reconstruct 3D shapes from 2D images, especially for rare specimens.
method Kendall's shape space approach with prior information.
result More robust and plausible shapes compared to previous methods.
This paper proposes a new class of copulas which characterize the set of all twice continuously differentiable copulas. We show that our proposed new class of copulas is a new generalized copula family that include not only asymmetric copulas but also all smooth copula families available in the current literature. Spea…
New tests for conditional copulas based on decision trees.
problem Testing constancy of conditional dependence structure given conditioning events.
method Data-driven decision trees to maximize differences in conditional Kendall's tau.
result Asymptotic distributions of test statistics under the null hypothesis.
Epilepsy is an important public health issue. An appropriate epileptiform discharge pattern detection of this neurological disease is a typical problem in biomedical engineering. In this paper, a new method is proposed for spike-and-wave discharge pattern detection based on Kendall's Tau-b coefficient. The proposed app…
Copula Discrepancy benchmarks sample dependence structure against known families.
problem Benchmarking sample dependence structure against known families.
method Copula Discrepancy (CD) statistic comparing target Kendall's tau with fitted parameter.
result CD reliably separates on-target and off-target copulas.
Permutation-valued features arise in a variety of applications, either in a direct way when preferences are elicited over a collection of items, or an indirect way in which numerical ratings are converted to a ranking. To date, there has been relatively limited study of regression, classification, and testing problems …
Kernel methods have had great success in Statistics and Machine Learning. Despite their growing popularity, however, less effort has been drawn towards developing kernel based classification methods on Riemannian manifolds due to difficulty in dealing with non-Euclidean geometry. In this paper, motivated by the extrins…
Hierarchical geodesic model for analyzing shapes on manifolds.
problem Analyzing temporal observations on manifold-valued data.
method Adapted functional-based metric for efficiency; variational time discretization of geodesics.
result Performed hypothesis tests and estimated mean trends in longitudinal analysis.
In this paper we extend the concept of Competitivity Graph to compare series of rankings with ties ({\em partial rankings}). We extend the usual method used to compute Kendall's coefficient for two partial rankings to the concept of evolutive Kendall's coefficient for a series of partial rankings. The theoretical frame…
High-dimensional data models, often with low sample size, abound in many interdisciplinary studies, genomics and large biological systems being most noteworthy. The conventional assumption of multinormality or linearity of regression may not be plausible for such models which are likely to be statistically complex due …
Correlation matrices play a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson's sample correlation matrix. Although Pearson's sample correlation matrix enjoys various good prop…
This paper studies the extreme dependencies between energy, agriculture and metal commodity markets, with a focus on local co-movements, allowing the identification of asymmetries and changing trend in the degree of co-movements. More precisely, starting from a non-parametric mixture copula, we use a novel copula-based…
We study the adaptive estimation of copula correlation matrix Σ for the semi-parametric elliptical copula model. In this context, the correlations are connected to Kendall's tau through a sine function transformation. Hence, a natural estimate for Σ is the plug-in estimator Σ^ with Kendall's tau statistic. We …
Study measures uncertainty in MST identification across different correlation networks.
problem Uncertainty in MST identification across various correlation-based market networks.
method Developed a framework using random variable networks (RVN) to measure uncertainty of MST identification.
result FDR is the most appropriate measure for MST identification reliability.
We introduce a new family of minmax rank aggregation problems under two distance measures, the Kendall τ and the Spearman footrule. As the problems are NP-hard, we proceed to describe a number of constant-approximation algorithms for solving them. We conclude with illustrative applications of the aggregation methods on…
Framework clusters noisy MTS with robust fuzzy clustering, improving accuracy over existing methods.
problem Challenges in clustering multivariate time series due to non-stationary dependencies, noise, and state boundaries.
method Spectral fuzzy clustering using Kendall's tau-based canonical coherence for frequency-specific monotonic relationships.
result Framework outperforms existing methods in clustering noisy, high-dimensional MTS.
Proposes Isometric Graph Neural Networks to preserve graph distances.
problem Lack of faithful distance representation in graph neural networks.
method Introduces a new technique to modify GNNs' input space and loss function.
result Significant improvement in reflecting graph distances, as measured by KT.
Study eigenvalue estimates on Kähler and quaternion Kähler manifolds.
problem Estimating first eigenvalues in Kähler and quaternion Kähler manifolds.
method Using Kendall-Cranston coupling to analyze eigenvalues.
result Eigenvalue estimates in terms of dimension, diameter, and curvature.
Correlation matrices are omnipresent in multivariate data analysis. When the number d of variables is large, the sample estimates of correlation matrices are typically noisy and conceal underlying dependence patterns. We consider the case when the variables can be grouped into K clusters with exchangeable dependence; t…
In this paper we develop the theory of parametric polynomial regression in Riemannian manifolds and Lie groups. We show application of Riemannian polynomial regression to shape analysis in Kendall shape space. Results are presented, showing the power of polynomial regression on the classic rat skull growth data of Book…
We construct short retractions of a CAT(1) space to its small convex subsets. This construction provides an alternative geometric description of an analytic tool introduced by Wilfrid Kendall. Our construction uses a tractrix flow which can be defined as a gradient flow for a family of functions of certain type. In an …
We formulate a supervised learning problem, referred to as continuous ranking, where a continuous real-valued label Y is assigned to an observable r.v. X taking its values in a feature space X and the goal is to order all possible observations x in X by means of a scoring function $s:\mathcal{X}…
Standardizes weighted ranking correlation coefficients to maintain zero expected value.
problem Measuring correlation between weighted rankings of items.
method Develops a standardization function g(·) that transforms coefficients to zero expected value under randomness.
result A general standardization function g(Γ) that preserves the domain [-1,1] and reduces to the identity for coefficients already satisfying zero-expected-value property.
Network analysis reveals changing cryptocurrency market leaders.
problem Understanding evolving cryptocurrency market leaders and their influence.
method Hourly-resolution data and Kendall's Tau correlation for network analysis.
result Pearson's correlation underestimates market dynamics; FTT and FTX were key during the 2021 bull run.
A new class of bivariate distributions is introduced that extends the Generalized Marshall-Olkin distributions of Li and Pellerey (2011). Their dependence structure is studied through the analysis of the copula functions that they induce. These copulas, that include as special cases the Generalized Marshall-Olkin copul…
New method for summarizing ranking distributions using consensus ranking distributions.
problem Summarizing ranking distributions efficiently and accurately.
method Introducing consensus ranking distributions and a top-down tree-structured statistical algorithm.
result Optimal distortion can be expressed as a function of pairwise probabilities, enabling efficient learning methods.
IGNIS uses neural networks to estimate copula parameters robustly.
problem Pathological properties of Archimedean copulas make traditional estimators brittle.
method Unified neural estimation framework with multi-input architecture and softplus output layer.
result Accurate and stable estimates for real-world datasets.
We review the main "omnibus procedures" for goodness-of-fit testing for copulas: tests based on the empirical copula process, on probability integral transformations, on Kendall's dependence function, etc, and some corresponding reductions of dimension techniques. The problems of finding asymptotic distribution-free te…
We propose a semiparametric approach, named nonparanormal skeptic, for estimating high dimensional undirected graphical models. In terms of modeling, we consider the nonparanormal family proposed by Liu et al (2009). In terms of estimation, we exploit nonparametric rank-based correlation coefficient estimators includin…
An investigation is presented of how a comprehensive choice of five most important measures of concordance (namely Spearman's rho, Kendall's tau, Gini's gamma, Blomqvist's beta, and their weaker counterpart Spearman's footrule) relate to non-exchangeability, i.e., asymmetry on copulas. Besides these results, the method…
We study the problem of non-explosion of diffusion processes on a manifold with time-dependent Riemannian metric. In particular we obtain that Brownian motion cannot explode in finite time if the metric evolves under backwards Ricci flow. Our result makes it possible to remove the assumption of non-explosion in the pat…
This paper uses rank correlation methods to construct MSTs from financial returns, finding them more stable and robust.
problem Stability and robustness of MSTs constructed from financial correlation matrices.
method Pearson, Spearman, and Kendall's τ rank correlation methods applied to daily financial returns. result Rank MSTs are more stable and robust than MSTs constructed using Pearson correlation.
New analysis shows interpretability doesn't guarantee steering utility in LLMs.
problem Does higher interpretability lead to better steering utility in large language models?
method Trained 90 SAEs across three LLMs, evaluated interpretability and steering utility, used Kendall's rank coefficients for analysis.
result Interpretability is only weakly associated with steering utility, and features selected by Delta Token Confidence improve steering performance.
We relate the existence problem of harmonic maps into S2 to the convex geometry of S2. On one hand, this allows us to construct new examples of harmonic maps of degree 0 from compact surfaces of arbitrary genus into S2. On the other hand, we produce new example of regions that do not contain closed geodesics (…
Copula is a powerful tool to model multivariate data. We propose the modelling of intraday financial returns of multiple assets through copula. The problem originates due to the asynchronous nature of intraday financial data. We propose a consistent estimator of the correlation coefficient in case of Elliptical copula …
An investigation is presented of how a comprehensive choice of four most important measures of concordance (namely Spearman's rho, Kendall's tau, Spearman's footrule, and Gini's gamma) relate to the fifth one, i.e., the Blomqvist's beta. In order to work out these results we present a novel method of estimating the val…
We introduce a new method for estimating the parameter of the bivariate Clayton copulas within the framework of Algorithmic Inference. The method consists of a variant of the standard boot-strapping procedure for inferring random parameters, which we expressly devise to bypass the two pitfalls of this specific instance…
The optimal ranking score between precision and recall is rarely F1 and can be found using specific methods.
problem Finding a meaningful and optimal compromise between precision and recall scores.
method Established a shortest path between precision- and recall-induced rankings, framed the problem as an optimization problem, and provided theoretical tools to find the optimal β.
result F1 and its skew-insensitive version are not optimal tradeoffs between precision and recall scores.
We formulate coherence modeling as a regression task and propose two novel methods to combine techniques from our setup with pairwise approaches. The first of our methods is a model that we call "first-next," which operates similarly to selection sorting but conditions decision-making on information about already-sorte…
This paper presents performance analysis of hybrid model comprise of concordance and Genetic Programming (GP) to forecast financial market with some existing models. This scheme can be used for in depth analysis of stock market. Different measures of concordances such as Kendalls Tau, Ginis Mean Difference, Spearmans R…
Stochastic Schwarz lemma on Kähler manifolds via couplings.
problem Develop a new Schwarz lemma for Kähler manifolds.
method Probabilistic approach using Markovian couplings.
result Improved gradient estimates for harmonic functions.