Related papers: Algebraic geometry of discrete interventional mode…

We construct and study noncommutative deformations of toric varieties by combining techniques from toric geometry, isospectral deformations, and noncommutative geometry in braided monoidal categories. Our approach utilizes the same fan…

Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…

A well-studied challenge that arises in the structure learning problem of causal directed acyclic graphs (DAG) is that using observational data, one can only learn the graph up to a "Markov equivalence class" (MEC). The remaining undirected…

Information geometry has offered a way to formally study the efficacy of scientific models by quantifying the impact of model parameters on the predicted effects. However, there has been little formal investigation of causation in this…

In this position paper, we promote the study of function spaces parameterized by machine learning models through the lens of algebraic geometry. To this end, we focus on algebraic models, such as neural networks with polynomial activations,…

We study the homology of an explicit finite-index subgroup of the automorphism group of a partially commutative group, in the case when its defining graph is a tree. More concretely, we give a lower bound on the first Betti number of this…

We consider spatial discretizations by the finite section method of the restricted group algebra of a finitely generated discrete group, which is represented as a concrete operator algebra via its left-regular representation. Special…

Using both observational and experimental data, a causal discovery process can identify the causal relationships between variables. A unique adaptive intervention design paradigm is presented in this work, where causal directed acyclic…

The investigation of directed acyclic graphs (DAGs) encoding the same Markov property, that is the same conditional independence relations of multivariate observational distributions, has a long tradition; many algorithms exist for model…

We study dynamical systems arising from word maps on simple groups. We develop a geometric method based on the classical trace map for investigating periodic points of such systems. These results lead to a new approach to the search of…

Fair machine learning aims to prevent discrimination against individuals or sub-populations based on sensitive attributes such as gender and race. In recent years, causal inference methods have been increasingly used in fair machine…

In this paper we investigate undirected discrete graphical tree models when all the variables in the system are binary, where leaves represent the observable variables and where all the inner nodes are unobserved. A novel approach based on…

Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background…

In this article, gentle algebras are realised as tiling algebras, which are associated to partial triangulations of unpunctured surfaces with marked points on the boundary. This notion of tiling algebras generalise the notion of Jacobian…

Background: Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, with the goal to gain a better understanding of the system. The…

Tropical algebraic geometry is the geometry of the tropical semiring $(\mathbb{R},\min,+)$. Its objects are polyhedral cell complexes which behave like complex algebraic varieties. We give an introduction to this theory, with an emphasis on…

It is often noted that many of the basic concepts of differential geometry, such as the definition of connection, are purely algebraic in nature. Here, we review and extend existing work on fully algebraic formulations of differential…

The increasing availability of interventional data offers new opportunities for causal discovery, with gene perturbation studies providing a prominent example. Such data are typically count-valued and subject to substantial measurement…

Understanding the deep representations of complex networks is an important step of building interpretable and trustworthy machine learning applications in the age of internet. Global surrogate models that approximate the predictions of a…

The aim of this paper is to study the behavior of Hodge-theoretic (intersection homology) genera and their associated characteristic classes under proper morphisms of complex algebraic varieties. We obtain formulae that relate (parametrized…