Related papers: On a method to construct exponential families by r…

In his article "Transcending Classical Invariant Theory" (J.A.M.S., 1989, Vol 2), Roger Howe established a correspondence between representations of a dual pair of reductive groups. This correspondence is known as Howe's correspondence or…

We start from a study of the density-potential relation for classical homeoids in terms of an asymptotic expansion for small deviations from spherical symmetry. We then show that such expansion is a useful device that allows us to construct…

Deep generative models are commonly used for generating images and text. Interpretability of these models is one important pursuit, other than the generation quality. Variational auto-encoder (VAE) with Gaussian distribution as prior has…

We present a probabilistic generative model and efficient algorithm to model reciprocity in directed networks. Unlike other methods that address this problem such as exponential random graphs, it assigns latent variables as community…

Bayes' rule describes how to infer posterior beliefs about latent variables given observations, and inference is a critical step in learning algorithms for latent variable models (LVMs). Although there are exact algorithms for inference and…

Let $G$ be a group and $q$ a non-negative integer. We denote by $\nu^q(G)$ a certain extension of the $q$-tensor square $G \otimes^q G$ by $G \times G$. In this paper we derive a polycyclic presentation for $G \otimes^q G$, when $G$ is…

We describe birational representations of discrete groups generated by involutions, having their origin in the theory of exactly solvable vertex-models in lattice statistical mechanics. These involutions correspond respectively to two kinds…

We show a higher order integrability theorem for distributions generated by a family of vector fields under a horizontal regularity assumption on their coefficients. We use as chart a class of almost exponential maps which we discuss in…

We introduce Exponential Family Discriminant Analysis (EFDA), a unified generative framework that extends classical Linear Discriminant Analysis (LDA) beyond the Gaussian setting to any member of the exponential family. Under the assumption…

For the simple Lie algebra $g = sl(n,C)$ we we find a set of generators and relations for the classical family algebra $(End(g)\otimes S(g))^G$ as an algebra over the ring $I(g)$. From these we can then determine a $I(g)$-linear basis of…

Hypergraphs are powerful mathematical structures that can model complex, high-order relationships in various domains, including social networks, bioinformatics, and recommender systems. However, generating realistic and diverse hypergraphs…

Variational Autoencoders (VAEs) are expressive latent variable models that can be used to learn complex probability distributions from training data. However, the quality of the resulting model crucially relies on the expressiveness of the…

Generation of photo-realistic images, semantic editing and representation learning are a few of many potential applications of high resolution generative models. Recent progress in GANs have established them as an excellent choice for such…

Consider the undirected graph $G_n=(V_n, E_n)$ where $V_n = (Z/nZ)^2$ and $E_n$ contains an edge from $(x,y)$ to $(x+1,y)$, $(x,y+1)$, $(x+y,y)$, and $(x,y+x)$ for every $(x,y) \in V_n$. Gabber and Galil, following Margulis, gave an…

This paper investigates the distribution of integral points on projective varieties via two distinct methods: the Ru-Vojta theorem and our higher-dimensional generalization of the Huang-Levin-Xiao inequalities. These approaches operate…

We present a comprehensive survey of the advancements and techniques in the field of tractable probabilistic generative modeling, primarily focusing on Probabilistic Circuits (PCs). We provide a unified perspective on the inherent…

Recently, a very attractive logistic regression inference method for exponential family Gibbs spatial point processes was introduced. We combined it with the technique of quadratic tangential variational approximation and derived a new…

Given a reference model that includes all the available variables, projection predictive inference replaces its posterior with a constrained projection including only a subset of all variables. We extend projection predictive inference to…

Using the Generalized Maximium Entropy Principle based on the nonextensive q entropy a new family of random matrix ensembles is generated. This family unifies previous extensions of Random Matrix Theory and gives rise to an orthogonal…

Many fundamental questions in theoretical computer science are naturally expressed as special cases of the following problem: Let $G$ be a complex reductive group, let $V$ be a $G$-module, and let $v,w$ be elements of $V$. Determine if $w$…