arXiv research

HNet detects significant associations in mixed data types efficiently.

We introduce a new class of identifiable DAG models where the conditional distribution of each node given its parents belongs to a family of generalized hypergeometric distributions (GHD). A family of generalized hypergeometric distributions includes a lot of discrete distributions such as the binomial, Beta-binomial, …

Study spherical Fourier transform on hypergeometric type harmonic manifolds.

A new class of harmonic Hadamard manifolds, those spaces called of hypergeometric type, is defined in terms of Gauss hypergeometric equations. Spherical Fourier transform defined on a harmonic Hadamard manifold of hypergeometric type admits an inversion formula. A characterization of harmonic Hadamard manifold being of…

We give a new proof of the rearrangement lemma that works for all dimensions and all heat coefficients in the study of modular geometry on noncommutative tori. The building blocks of the spectral functions are landed in a hypergeometric family knowns as Lauricella functions of type $D$. We investigate the differential …

Harmonic manifolds of hypergeometric type have entropy bounds related to real hyperbolic spaces.

We show that all the currently known non-arithmetic lattices in ${\rm PU}(2,1)$ are monodromy groups of higher hypergeometric functions.

Proposes a differentiable hypergeometric distribution for learning group importance.

Estimates unknown population sizes using the hypergeometric distribution.

We extend projectively equivariant quantization and symbol calculus to symbols of pseudo-differential operators. An explicit expression in terms of hypergeometric functions with noncommutative arguments is given. Some examples are worked out, one of them yielding a quantum length element on $S^3$.

This paper establishes certain existence and classification results for solutions to $SU(n)$ Toda systems with three singular sources at 0, 1, and $\infty$. First, we determine the necessary conditions for such an $SU(n)$ Toda system to be related to an $n$th order hypergeometric equation. Then, we construct solutions …

We investigate the pricing of financial options under the 2-hypergeometric stochastic volatility model. This is an analytically tractable model that reproduces the volatility smile and skew effects observed in empirical market data. Using a regular perturbation method from asymptotic analysis of partial differential eq…

Study of line congruences for Appell's rank-4 hypergeometric functions.

The aim of this text is to establish some relations between Markov chains in Dirichlet Environments on directed graphs and certain hypergeometric integrals associated with a particular arrangement of hyperplanes. We deduce from these relations and the computation of the connexion obtained by moving one hyperplane of th…

We first show that hypergeometric functions appear naturally as spectral functions when applying pseudo-differential calculus to decipher heat kernel asymptotic in the situation where the symbol algebra is noncommutative. Such observation leads to a unified (works for arbitrary dimension) method of computing the modula…

We derive a factorization of the Alexander polynomial of the 4-strand Turk's head knot using hypergeometric representations.

We present a global representation for surfaces in 3-dimensional hyperbolic space with constant mean curvature 1 (CMC-1 surfaces) in terms of holomorphic spinors. This is a modification of Bryant's representation. It is used to derive explicit formulas in hypergeometric functions for CMC-1 surfaces of genus 0 with thre…

New groups discovered with unique properties in a specific space.

Paper proves BGW tau-function can be represented as Q-polynomials.

In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a hypergraph exactly corresponds to the graphical model given by the dual hypergraph. …

The n-dimensional hypergeometric integrals associated with a hypersphere arrangement are formulated by the pairing of n-dimensional twisted cohomology and its dual. Under the condition of general position there are stated some results which concern an explicit representation of the standard form by a special (NBC) basi…

We propose Graphical Generative Adversarial Networks (Graphical-GAN) to model structured data. Graphical-GAN conjoins the power of Bayesian networks on compactly representing the dependency structures among random variables and that of generative adversarial networks on learning expressive dependency functions. We intr…

Graphical normalizing flows use Bayesian networks to improve normalizing flows' interpretability and performance.

Constructs explicit nontrivial cycles in Habiro cohomology of smooth varieties.

We propose a general modeling and inference framework that composes probabilistic graphical models with deep learning methods and combines their respective strengths. Our model family augments graphical structure in latent variables with neural network observation models. For inference, we extend variational autoencode…

Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly…

The aim of this chapter is twofold. In the first part we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures. In particular we will develop Markov networks (also known as Markov random field…

Deep networks can approximate score functions in high-dimensional graphical models efficiently.

rags2ridges simplifies graphical modeling of high-dimensional data.

Paper introduces MGLasso for multiscale graph inference in clustering and network analysis.

Bayesian method for estimating functional graphical models from neuroimaging data.

Explicit computation of Kontsevich weights for symplectic Poisson structures.

In the genus one case, we make explicit some constructions of Veech on flat surfaces and generalize some geometric results of Thurston about moduli spaces of flat spheres as well as some equivalent ones but of an analytico-cohomological nature of Deligne-Mostow, which concern the monodromy of Appell-Lauricella hypergeo…

This paper develops a nonparametric model for complex network data.

Graphical notation simplifies tensor operations and decompositions.

In this paper we develop a methodology to analyze and compare multiple global networks. We focus our analysis on the relation between human migration and trade. First, we identify the subset of products for which the presence of a community of migrants significantly increases trade intensity. To assure comparability ac…

New quasi-Einstein metrics found on a sphere.

A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit computationally convenient factorization properties and have long been a valuable tool for t…

We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, including Bayesian networks …

New method aggregates nodes in sparse graphical models.

Paper compares two methods for inferring network structures in presence of latent confounders.

This work presents an exact solution to the generalized Heston model, where the model parameters are assumed to have linear time dependence The solution for the model in expressed in terms of confluent hypergeometric functions.

In many applications, multivariate samples may harbor previously unrecognized heterogeneity at the level of conditional independence or network structure. For example, in cancer biology, disease subtypes may differ with respect to subtype-specific interplay between molecular components. Then, both subtype discovery and…

Profile graphical models represent multivariate dependence under varying risk factors.

New neural network approach for optimizing latent variable models.

As the second part of the sequel, we investigate the variation of rearrangement operators (more precisely, the spectral functions behind) arising in the study of modular geometry on noncommutative (two) tori. We initiate a systematic approach by introducing transformations corresponding to basic operations in calculus,…

Neural network method estimates covariate-dependent graphical models with statistical guarantees.

New results connect RBMs to neural networks, improving learning efficiency.