Related papers: Cumulative Information Generating Function and Gen…
Numerous entropy-type characteristics (functionals) generalizing R\'enyi entropy are widely used in mathematical statistics, physics, information theory, and signal processing for characterizing uncertainty in probability distributions and…
Estimating the mutual information from samples from a joint distribution is a challenging problem in both science and engineering. In this work, we realize a variational bound that generalizes both discriminative and generative approaches.…
When one tries to take into account the non-trivial vacuum structure of Quantum Field Theory, the standard functional-integral tools such as generating functionals or transitional amplitudes, are often quite inadequate for such purposes.…
Growing dimensionality of data calls for beyond-pairwise interactions quantification. Measures of multidimensional interactions quantification are hindered, among others, by two issues: 1. Interpretation difficulties, 2. the curse of…
This paper introduces a unified theoretical perspective that views deep generative models as probability transformation functions. Despite the apparent differences in architecture and training methodologies among various types of generative…
Conditional Mutual Information (CMI) is a measure of conditional dependence between random variables X and Y, given another random variable Z. It can be used to quantify conditional dependence among variables in many data-driven inference…
Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…
We introduce innovative inference procedures for analyzing time series data. Our methodology enables density approximation and composite hypothesis testing based on Whittle's estimator, a widely applied M-estimator in the frequency domain.…
In this paper, we study the properties of the weighted entropy generating function (WEGF). We also introduce the weighted residual entropy generating function (WREGF) and establish some characterization results based on its connections with…
We propose a summary measure defined as the expected value of a random variable over disjoint subsets of its support that are specified by a given grid of proportions, and consider its use in a regression modeling framework. The obtained…
We introduce a new category of multivariate conditional generative models and demonstrate its performance and versatility in probabilistic time series forecasting and simulation. Specifically, the output of quantile regression networks is…
Machine Learning (ML)-based unfolding methods have enabled high-dimensional and unbinned differential cross section measurements. While a suite of such methods has been proposed, most focus exclusively on the challenge of statistically…
Quantiles, expectiles and extremiles can be seen as concepts defined via an optimization problem, where this optimization problem is driven by two important ingredients: the loss function as well as a distributional weight function. This…
The aim of this paper is to introduce a risk measure that extends the Gini-type measures of risk and variability, the Extended Gini Shortfall, by taking risk aversion into consideration. Our risk measure is coherent and catches variability,…
Recently a class of generalized information measures was defined on sets of items parametrized by submodular functions. In this paper, we propose and study various notions of independence between sets with respect to such information…
The diffusion probabilistic generative models are widely used to generate high-quality data. Though they can synthetic data that does not exist in the training set, the rationale behind such generalization is still unexplored. In this…
Transfer entropy provides a general tool for analyzing the magnitudes and directions---but not the \emph{kinds}---of information transfer in a system. We extend transfer entropy in two complementary ways. First, we distinguish…
We solve a functional equation connected to the algebraic characterization of generalized information functions. To prove the symmetry of the solution, we study a related system of functional equations, which involves two homographies.…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…
We propose a GAN design which models multiple distributions effectively and discovers their commonalities and particularities. Each data distribution is modeled with a mixture of $K$ generator distributions. As the generators are partially…