Related papers: On the minimum information checkerboard copulas un…
We propose to use precise estimators of mutual information (MI) to find least dependent components in a linearly mixed signal. On the one hand this seems to lead to better blind source separation than with any other presently available…
We correct claims about lower bounds on mutual information (MI) between real-valued random variables made in A. Kraskov {\it et al.}, Phys. Rev. E {\bf 69}, 066138 (2004). We show that non-trivial lower bounds on MI in terms of linear…
We study the problem of choosing the copula when the marginal distributions of a random vector are not all continuous. Inspired by four motivating examples including simulation from copulas, stress scenarios, co-risk measures, and…
We provide a set of copulas that can be interpreted as having the negative extreme dependence. This set of copulas is interesting because it coincides with countermonotonic copula for a bivariate case, and more importantly, is shown to be…
Estimation of mutual information between random variables has become crucial in a range of fields, from physics to neuroscience to finance. Estimating information accurately over a wide range of conditions relies on the development of…
Ordinal classification has been widely applied in many high-stakes applications, e.g., medical imaging and diagnosis, where reliable uncertainty quantification (UQ) is essential for decision making. Conformal prediction (CP) is a general UQ…
Many types of bounded data defined on the unit interval arise naturally as ratios of the form $X/(X + Y)$. In the existing literature, the main statistical models proposed for this type of bounded data typically based on the assumption that…
The goal of rank fusion in information retrieval (IR) is to deliver a single output list from multiple search results. Improving performance by combining the outputs of various IR systems is a challenging task. A central point is the fact…
We propose a novel estimator of the mutual information between two ordinal vectors $x$ and $y$. Our approach is inductive (as opposed to deductive) in that it depends on the data generating distribution solely through some nonparametric…
We establish the limiting spectral distribution of Kendall's correlation matrices in the moderate high-dimensional regime where the dimension grows slower than the sample size. Our framework allows observations to be independent but not…
Linear constraints for a matrix polytope with no fractional vertex are investigated as intersecting research among permutation codes, rank modulations, and linear programming methods. By focusing the discussion to the block structure of…
We study the adaptive estimation of copula correlation matrix $\Sigma$ 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…
A framework for quantifying dependence between random vectors is introduced. With the notion of a collapsing function, random vectors are summarized by single random variables, called collapsed random variables in the framework. Using this…
Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Sklar's theorem, "the fundamental theorem of copulas", makes a clear distinction between the continuous case…
Copula models have been widely used to model the dependence between continuous random variables, but modeling count data via copulas has recently become popular in the statistics literature. Spearman's rho is an appropriate and effective…
We propose Conformal Mixed-Integer Constraint Learning (C-MICL), a novel framework that provides probabilistic feasibility guarantees for data-driven constraints in optimization problems. While standard Mixed-Integer Constraint Learning…
One of the main goals in non-life insurance is to estimate the claims reserve distribution. A generalized time series model, that allows for modeling the conditional mean and variance of the claim amounts, is proposed for the claims…
Thanks to their ability to capture complex dependence structures, copulas are frequently used to glue random variables into a joint model with arbitrary marginal distributions. More recently, they have been applied to solve statistical…
Effective feature selection is critical for robust and interpretable predictive modeling in medicine, especially when risk factors matter most in extreme patient strata. Many standard selectors emphasize average associations and can miss…
We apply two variations of the principle of Minimum Cross Entropy (the Kullback information measure) to fit parameterized probability density models to observed data densities. For an array beamforming problem with P incident narrowband…