Related papers: On the minimum information checkerboard copulas un…
Simplicial-simplicial regression refers to the regression setting where both the responses and predictor variables lie within the simplex space, i.e. they are compositional. For this setting, constrained least squares, where the regression…
This paper presents methods that quantify the structure of statistical interactions within a given data set, and was first used in \cite{Tapia2018}. It establishes new results on the k-multivariate mutual-informations (I_k) inspired by the…
Continuation refers to the operation by which the cumulative distribution function of a discontinuous random vector is made continuous through multilinear interpolation. The copula that results from the application of this technique to the…
Quantification of microbial interactions from 16S rRNA and meta-genomic sequencing data is difficult due to their sparse nature, as well as the fact that the data only provides measures of relative abundance. In this paper, we propose using…
We derive information-theoretic converses (i.e., lower bounds) for the minimum time required by any algorithm for distributed function computation over a network of point-to-point channels with finite capacity, where each node of the…
This paper introduces a nonparametric copula-based index for detecting the strength and monotonicity structure of linear and nonlinear statistical dependence between pairs of random variables or stochastic signals. Our index, termed Copula…
We consider the problem of finite-time identification of linear dynamical systems from $T$ samples of a single trajectory. Recent results have predominantly focused on the setup where either no structural assumption is made on the system…
Statistical modelling of covariate distributions allows to generate virtual populations or to impute missing values in a covariate dataset. Covariate distributions typically have non-Gaussian margins and show nonlinear correlation…
The Information Bottleneck (IB) is a conceptual method for extracting the most compact, yet informative, representation of a set of variables, with respect to the target. It generalizes the notion of minimal sufficient statistics from…
To characterize the Kullback-Leibler divergence and Fisher information in general parametrized hidden Markov models, in this paper, we first show that the log likelihood and its derivatives can be represented as an additive functional of a…
We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…
We show that moment inequalities in a wide variety of economic applications have a particular linear conditional structure. We use this structure to construct uniformly valid confidence sets that remain computationally tractable even in…
Copulas are popular as models for multivariate dependence because they allow the marginal densities and the joint dependence to be modeled separately. However, they usually require that the transformation from uniform marginals to the…
The Kullback-Leibler (KL) divergence is a foundational measure for comparing probability distributions. Yet in multivariate settings, its single value often obscures the underlying reasons for divergence, conflating mismatches in individual…
Classical estimators, the cornerstones of statistical inference, face insurmountable challenges when applied to important emerging classes of Archimedean copulas. These models exhibit pathological properties, including numerically unstable…
For the estimation of cumulative link models for ordinal data, the bias-reducing adjusted score equations in \citet{firth:93} are obtained, whose solution ensures an estimator with smaller asymptotic bias than the maximum likelihood…
Dependence strucuture estimation is one of the important problems in machine learning domain and has many applications in different scientific areas. In this paper, a theoretical framework for such estimation based on copula and copula…
This paper is concerned with modeling the dependence structure of two (or more) time-series in the presence of a (possible multivariate) covariate which may include past values of the time series. We assume that the covariate influences…
Conformal prediction builds marginally valid prediction intervals that cover the unknown outcome of a randomly drawn test point with a prescribed probability. However, in practice, data-driven methods are often used to identify specific…
Copula-based models provide a great deal of flexibility in modelling multivariate distributions, allowing for the specifications of models for the marginal distributions separately from the dependence structure (copula) that links them to…