New measure detects direct causal influences and captures strong dependencies.
problem Shortcomings of existing dependency measures in detecting direct causal influences and group selection.
method Inspired by Dobrushin's coefficients, the measure uses conditional distribution properties.
result Advantages over related measures in detecting dependencies and causal influences.
New measures quantify mutual dependence between multiple random vectors.
problem Measuring mutual dependence between multiple random vectors.
method Proposes three measures based on generalized distance covariance.
result Empirical and simplified empirical measures effectively test mutual independence.
New multivariate dependency measure using Gaussian kernel and copula.
problem Measuring dependency between multivariate distributions.
method Gaussian kernel distance to uniform copula, normalization, nonparametric estimate.
result Proposed measure satisfies desirable properties and is compared with existing measures.
New measures capture tail dependence and non-exchangeability in financial data.
problem Underestimation of tail dependence and inability to capture non-exchangeable tail dependence.
method Tail copulas and novel tail dependence measures (MTCM, ATCM) are proposed.
result Captures non-exchangeable tail dependence and provides analytical forms for various copulas.
In data science, it is often required to estimate dependencies between different data sources. These dependencies are typically calculated using Pearson's correlation, distance correlation, and/or mutual information. However, none of these measures satisfy all the Granger's axioms for an "ideal measure". One such ideal…
This research evaluates measures of dependence for financial time-series data.
problem Accurately preparing time series data and selecting an appropriate measure of dependence is challenging.
method Review and establishment of a comprehensive analysis framework for shaping time-series data and evaluating measures of dependence.
result A method, framework, and example for selecting and evaluating a suitable measure of dependence are presented.
A new measure of dependence for various data types.
problem Measuring dependence in multivariate, functional, and structured data.
method Combines local normalization with RKHS flexibility.
result Validates the measure's properties and competitive performance.
We present a general construction for dependent random measures based on thinning Poisson processes on an augmented space. The framework is not restricted to dependent versions of a specific nonparametric model, but can be applied to all models that can be represented using completely random measures. Several existing …
Proposes a new dependency function for measuring non-linear relationships.
problem Need for a general-purpose measure of dependency between random variables.
method Revision of ideal properties and proposal of a new dependency function.
result Proposes a new dependency function that meets all desired properties.
New measures quantify dependence between variables without distribution estimation.
problem Measuring dependence between variables in arbitrary dimensions.
method Proposed matrix-based normalized total correlation and dual total correlation measures.
result Measures are differentiable and statistically more powerful than existing methods.
Paper proposes universally consistent K-sample tests using any dependence measure.
problem Testing whether K groups of data points are drawn from the same distribution.
method Demonstrates the use of any dependence measure for K-sample testing.
result Achieves universally consistent K-sample testing using distance correlation and Hilbert-Schmidt independence criterion.
New tail dependence measures for stock indices.
problem Measuring tail dependence between financial variables.
method Introducing a new stochastic order and studying monotone tail dependence measures.
result Advantage of new tail dependence measures over classical ones.
The paper proposes a framework to adjust dependency measure estimates for chance.
problem Challenges in interpreting and ranking dependency measures on finite samples.
method Simple adjustments to improve interpretability and accuracy of dependency measures.
result Improves interpretability and accuracy of dependency measures, demonstrated on MIC and random forests.
Improved clustering in mixture models using dependent random measures with independent increments.
problem Improving clustering in mixture models with dependent structures.
method Normalized dependent random measures with independent increments applied to mixture models.
result Superior performance in clustering with appropriate mixing weights and cluster number inference.
The study measures systemic risk using common and tail dependence factors.
problem Measuring systemic risk accurately during economic downturns.
method Modeling systemic risk with a common factor for market-wide shocks and a tail dependence factor for extreme events.
result Measures including a tail dependence factor offer better forecasting of financial stress than measures based solely on a common factor.
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 covariates, which requires the dependence measure to be equitable. That is, it gives sim…
Measures dependence between two systems using Bayesian model comparison.
problem Quantifying dependence between two systems in a dataset.
method Bayesian model comparison of independence and dependence models.
result Dependence measure quantifies evidence for dependence in data.
We introduce a new functional measure of tail dependence for weakly dependent (asymptotically independent) random vectors, termed weak tail dependence function. The new measure is defined at the level of copulas and we compute it for several copula families such as the Gaussian copula, copulas of a class of Gaussian mi…
In this paper we introduce a new multivariate dependence measure based on comonotonicity by means of product moment which motivated by the recent papers of Koch and Schepper (ASTIN Bulletin 41 (2011) 191-213) and Dhaene et al. (Journal of Computational and Applied Mathematics 263 (2014) 78-87). Some differences and rel…
Paper introduces MTCM to measure multivariate tail dependence.
problem Classical TDC fails to capture non-exchangeable features of multivariate tail dependence.
method Extends bivariate tail copula measure to multivariate case.
result MTCM reveals off-diagonal stress directions and differences in extremal dependence.
Global sensitivity analysis with variance-based measures suffers from several theoretical and practical limitations, since they focus only on the variance of the output and handle multivariate variables in a limited way. In this paper, we introduce a new class of sensitivity indices based on dependence measures which o…
New measure assesses predictive dependence between continuous variables, capturing non-functional relationships.
problem Quantifying the joint dependence between continuous random variables.
method Introduces a novel, fully non-parametric measure bounded [0,1] that assesses predictive accuracy loss.
result The measure captures a wide range of relationships, including non-functional ones, and is interpretable.
Improves ICA via novel mutual dependence measures.
problem Improving Independent Component Analysis (ICA) for better component independence.
method Combines distance-based and kernel-based mutual dependence measures, introduces Latin hypercube sampling and Bayesian optimization for initialization.
result MDMICA outperforms other methods in terms of mutual independence of estimated components, especially when the ICA model is misspecified.
Paper introduces quantile coherency to measure dependence in economic time series.
problem Measuring general dependence structures in economic time series.
method Defined quantile coherency estimators and discussed their asymptotic properties.
result Demonstrated the usefulness of quantile coherency in assessing time series models.
This paper improves the robustness of risk estimation for financial positions.
problem Ensuring robustness of risk measures in the presence of data noise.
method Proposes a quantitative approach using the Fortet-Mourier metric to quantify the variation of true probability measures.
result Derives explicit error bounds for discrepancies between laws of estimators based on true and perturbed data.
New findings show Shannon information measures fail to accurately assess multivariate dependencies.
problem Accurately measuring information flow in complex systems.
method Demonstrated that Shannon information measures fail to distinguish between dyadic and polyadic relationships.
result Shannon information measures are inadequate for discovering meaningful dependency structures in joint probability distributions.
This paper presents theory for Normalized Random Measures (NRMs), Normalized Generalized Gammas (NGGs), a particular kind of NRM, and Dependent Hierarchical NRMs which allow networks of dependent NRMs to be analysed. These have been used, for instance, for time-dependent topic modelling. In this paper, we first introdu…
Study heat flows on time-dependent metric measure spaces, proving properties related to super-Ricci flows.
problem Characterize heat flows and their properties on time-dependent metric measure spaces.
method Prove existence, uniqueness, and regularity of heat equations and their duals on time-dependent metric measure spaces.
result Equivalence of dynamic convexity of Boltzmann entropy, monotonicity of Wasserstein distances, gradient estimates, and Bochner inequality.
Modeling financial institution dependence structures for systemic risk.
problem Understanding and measuring systemic risk in financial systems.
method Dynamic model of dependence structure using Markov structures of joint credit migrations.
result Different Markov structures with distinct dependence structures lead to varying systemic instability.
We proposed a new statistical dependency measure called Copula Dependency Coefficient(CDC) for two sets of variables based on copula. It is robust to outliers, easy to implement, powerful and appropriate to high-dimensional variables. These properties are important in many applications. Experimental results show that C…
We develop dependent hierarchical normalized random measures and apply them to dynamic topic modeling. The dependency arises via superposition, subsampling and point transition on the underlying Poisson processes of these measures. The measures used include normalised generalised Gamma processes that demonstrate power …
New measures detect asymmetries, non-linearity in stock returns.
problem Detecting asymmetries and non-linearity in stock returns.
method Proposed non-linear, local, invariant dependence measures; nonparametric estimator proven.
result Measures show tail asymmetry, non-linearity, risk buildup during market distress.
We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The second, simultaneously applies the distortion on the survival function of the su…
This paper presents a new methodology for clustering multivariate time series leveraging optimal transport between copulas. Copulas are used to encode both (i) intra-dependence of a multivariate time series, and (ii) inter-dependence between two time series. Then, optimal copula transport allows us to define two distan…
Methodology to measure non-linear correlations using copulas and clustering.
problem Measuring pairwise correlations between variables in datasets.
method Copulas for encoding dependence, optimal transport for geometry, clustering for summarizing patterns.
result Novel dependence coefficient parameterized by clusters centers.
Reframed GES uses a neural conditional dependence measure for consistent causal structure learning.
problem Identifying causal structure in nonparametric settings.
method Reframed GES algorithm with a neural conditional dependence measure.
result Optimality and consistency of the reframed GES algorithm under standard assumptions.
New algorithms reduce regret in online MDPs by adapting to data and variance.
problem Adapting to both adversarial and stochastic environments in online MDPs.
method Develops algorithms based on global optimization and policy optimization, using optimistic follow-the-regularized-leader with log-barrier regularization.
result Achieves refined data-dependent and variance-dependent regret bounds.
We simplify information measure computation using learned features.
problem Computing information measures from raw data is computationally expensive.
method Developed a separable design for computing information measures from learned feature representations.
result A variety of information measures can be computed efficiently through learned feature representations.
Study introduces a new copula-based measure for financial asset cointegration.
problem Traditional correlation coefficient's limitations in measuring financial asset relationships.
method Utilizes copulas to measure dependence among financial asset returns.
result Enhanced stability and informativeness in measuring financial asset relationships.
New method measures model risk in dynamic settings with uncertain state processes.
problem Lack of non-parametric approach for dynamic model risk quantification.
method Generalizes relative-entropic approach to dynamic case under f-divergence. result Unified treatment for worst-case risk and f-divergence budget. Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding conditional independence test is developed with the asymptotic null distribution …
We investigate the relative information content of six measures of dependence between two random variables X and Y for large or extreme events for several models of interest for financial time series. The six measures of dependence are respectively the linear correlation ρv+ and Spearman's rho ρs(v) conditio…
New metrics for assessing neural network dependability.
problem Need for metrics to measure NN dependability.
method Proposed metrics for NN robustness, interpretability, completeness, correctness.
result Efficiently computable metrics for NN dependability.
Paper proposes a new method to evaluate joint risk under uncertainty.
problem Evaluating joint risk of multiple insurance risks under dependence uncertainty.
method Axiomatic approach to scalar and vector-valued distortion joint risk measures.
result Established a new scalar distortion joint risk measure with positive homogeneity.
Paper introduces DCoVaR for aggregate risk models, outperforming existing methods.
problem Lack of coherent risk measures for aggregate risk models.
method Proposes Dependent Conditional Value-at-Risk (DCoVaR) for a target loss dependent on another random loss.
result DCoVaR outperforms MCoVaR and CCoVaR in numerical simulations and empirical studies.
The paper shows vector-valued risk measures ignore dependence structures.
problem Defining capital allocation rules for random vectors with dependence.
method Defined vector-valued risk measures by axioms and showed their properties.
result Vector-valued risk measures ignore dependence structures, unlike set-valued measures.
Introduces preference-robust decision making for risk models.
problem Ambiguity in risk functionals.
method Constructs ambiguity sets on distortion functions using Wasserstein distance and Bregman divergences.
result Derives closed-form expressions for worst- and best-case distortion risk measures.
Bell's theorem shows quantum correlations can't be explained by classical causal models, even with some measurement dependence.
problem Quantum correlations violate classical causal models.
method Using causal networks, the study bounds the level of measurement dependence and derives nonlinear Bell inequalities.
result Quantum correlations can't be explained by classical causal models even with some measurement dependence.