Related papers: Copula Entropy: Theory and Applications
When scholars study joint distributions of multiple variables, copulas are useful. However, if the variables are not linearly correlated with each other yet are still not independent, most of conventional copulas are not up to the task.…
We consider the minimum error entropy (MEE) criterion and an empirical risk minimization learning algorithm in a regression setting. A learning theory approach is presented for this MEE algorithm and explicit error bounds are provided in…
The coincidence method of measuring the entropy of a system, proposed some time ago by Ma, is generalized to include systems out of equilibrium. It is suggested that the method can be adapted to analyze multiparticle states produced in…
This text discusses several popular explanatory methods that go beyond the error measurements and plots traditionally used to assess machine learning models. Some of the explanatory methods are accepted tools of the trade while others are…
We propose a formal expansion of the transfer entropy to put in evidence irreducible sets of variables which provide information for the future state of each assigned target. Multiplets characterized by a large contribution to the expansion…
Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…
We study a simple statistic for benchmarking how well a sample preserves a known bivariate dependence structure. Given a target copula family (Clayton or Gumbel) and parameter $\theta_P$, the Copula Discrepancy (CD) compares the target…
An approach is proposed to determine structural shift in time-series assuming non-linear dependence of lagged values of dependent variable. Copulas are used to model non-linear dependence of time series components.
A dependence measure for arbitrary type pairs of random variables is proposed and analyzed, which in the particular case where both random variables are continuous turns out to be a concordance measure. Also, a sample version of the…
We formulate a unified definition of the statistical effective temperature (SET) for finite-dimensional classical and quantum systems using dimension-dependent indices of purity derived from the eigenvalue spectrum. This spectral approach…
Structural equation models (SEMs) are fundamental to causal mediation pathway discovery. However, traditional SEM approaches often rely on \emph{ad hoc} model specifications when handling complex data structures such as mixed data types or…
In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These…
This study investigates entropy's potential for analyzing scientific research patterns across disciplines. Originating from thermodynamics, entropy now measures uncertainty and diversity in information systems. We examine Shannon Entropy,…
Copula modelling has in the past decade become a standard tool in many areas of applied statistics. However, a largely neglected aspect concerns the design of related experiments. Particularly the issue of whether the estimation of copula…
Conformal Prediction (CP) is a powerful framework for constructing prediction sets with guaranteed coverage. However, recent studies have shown that integrating confidence calibration with CP can lead to a degradation in efficiency. In this…
Notions of topological free entropy and of free capacity are introduced in the $C^*$-algebra context. Basic properties, basic problems and connections to potential theory and random matrix theory are discussed.
We introduce Causal Program Dependence Analysis (CPDA), a dynamic dependence analysis that applies causal inference to model the strength of program dependence relations in a continuous space. CPDA observes the association between program…
This paper describes an entropy equation, but one that should be used for measuring energy and not information. In relation to the human brain therefore, both of these quantities can be used to represent the stored information. The human…
Correspondence analysis (CA) is a multivariate statistical tool used to visualize and interpret data dependencies by finding maximally correlated embeddings of pairs of random variables. CA has found applications in fields ranging from…
This paper proposes a regression tree procedure to estimate conditional copulas. The associated algorithm determines classes of observations based on covariate values and fits a simple parametric copula model on each class. The association…