Related papers: Binary Cumulant Varieties
We use covariants of binary sextics to describe the structure of modules of scalar-valued or vector-valued Siegel modular forms of degree 2 with character, over the ring of scalar-valued Siegel modular forms of even weight. For a modular…
There is a classical geometric construction which uses a binary quadratic form to define an involution on the space of binary d-ics. We give a complete characterization of a general class of such involutions which are definable using…
Forecasting with longitudinal data has been rarely studied. Most of the available studies are for continuous response and all of them are for univariate response. In this study, we consider forecasting multivariate longitudinal binary data.…
We investigate the representation of hierarchical models in terms of marginals of other hierarchical models with smaller interactions. We focus on binary variables and marginals of pairwise interaction models whose hidden variables are…
A new family of polynomials, called cumulant polynomial sequence, and its extensions to the multivariate case is introduced relied on a purely symbolic combinatorial method. The coefficients of these polynomials are cumulants, but depending…
Making predictions in an unseen environment given data from multiple training environments is a challenging task. We approach this problem from an invariance perspective, focusing on binary classification to shed light on general nonlinear…
In $\mathbb R^d$, it is well-known that cumulants provide an alternative to moments that can achieve the same goals with numerous benefits such as lower variance estimators. In this paper we extend cumulants to reproducing kernel Hilbert…
A new orthogonal decomposition for bivariate probability densities embedded in Bayes Hilbert spaces is derived. It allows one to represent a density into independent and interactive parts, the former being built as the product of revised…
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…
We derive a closed form description of the convex hull of mixed-integer bilinear covering set with bounds on the integer variables. This convex hull description is determined by considering some orthogonal disjunctive sets defined in a…
We use classical invariant theory to construct invariants of complex graded Gorenstein algebras of finite vector space dimension. As a consequence, we obtain a way of extracting certain numerical invariants of quasi-homogeneous isolated…
We discuss in this paper combinatorial aspects of boundary loop models, that is models of self-avoiding loops on a strip where loops get different weights depending on whether they touch the left, the right, both or no boundary. These…
We study the problem of characterizing linear preserver subgroups of algebraic varieties, with a particular emphasis on secant varieties and other varieties of tensors. We introduce a number of techniques built on different geometric…
Binary classification is a common statistical learning problem in which a model is estimated on a set of covariates for some outcome indicating the membership of one of two classes. In the literature, there exists a distinction between hard…
In this paper, we focus on the variable selection techniques for a class of semiparametric spatial regression models which allow one to study the effects of explanatory variables in the presence of the spatial information. The spatial…
Many problems in high-dimensional statistics appear to have a statistical-computational gap: a range of values of the signal-to-noise ratio where inference is information-theoretically possible, but (conjecturally) computationally…
The work is devoted to the variety of $2$-dimensional algebras over an algebraically closed field. Firstly, we classify such algebras modulo isomorphism. Then we describe the degenerations and the closures of principal algebra series in the…
We consider a discrete latent variable model for two-way data arrays, which allows one to simultaneously produce clusters along one of the data dimensions (e.g. exchangeable observational units or features) and contiguous groups, or…
This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…
Using a binary representation for basis elements of an algebra combined with a framework of multiplier and index functions, a connection has been established between the structure of a large class of algebras and the XOR componentwise…