Related papers: Algebraic geometry of discrete interventional mode…
The invariance properties of interventional distributions relative to the observational distribution, and how these properties allow us to refine Markov equivalence classes (MECs) of DAGs, is central to causal DAG discovery algorithms that…
We outline a representation for discrete multivariate distributions in terms of interventional potential functions that are globally normalized. This representation can be used to model the effects of interventions, and the independence…
Causal interactions among a group of variables are often modeled by a single causal graph. In some domains, however, these interactions are best described by multiple co-existing causal graphs, e.g., in dynamical systems or genomics. This…
In many application areas---lending, education, and online recommenders, for example---fairness and equity concerns emerge when a machine learning system interacts with a dynamically changing environment to produce both immediate and…
We consider the problem of learning causal Directed Acyclic Graphs (DAGs) using combinations of observational and interventional experimental data. Current methods tailored to this setting assume that interventions either destroy…
Coloured probability tree models are statistical models coding conditional independence between events depicted in a tree graph. They are more general than the very important class of context-specific Bayesian networks. In this paper, we…
We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [Berstel et al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely studied…
In this work we study several types of diagonal-effect models for two-way contingency tables in the framework of Algebraic Statistics. We use both toric models and mixture models to encode the different behavior of the diagonal cells. We…
Probabilistic inference in graphical models is the task of computing marginal and conditional densities of interest from a factorized representation of a joint probability distribution. Inference algorithms such as variable elimination and…
In this paper, we study a class of toric ideals obtained by using some geometric data of ADE trees which are the minimal resolution graphs of rational surface singularities. We compute explicit Gr\"obner bases for these toric ideals that…
A growing body of work has begun to study intervention design for efficient structure learning of causal directed acyclic graphs (DAGs). A typical setting is a causally sufficient setting, i.e. a system with no latent confounders, selection…
We present a graphical approach to deriving inequality constraints for directed acyclic graph (DAG) models, where some variables are unobserved. In particular we show that the observed distribution of a discrete model is always restricted…
This paper presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are…
We build and investigate a pure gauge theory on arbitrary discrete groups. A systematic approach to the construction of the differential calculus is presented. We discuss the metric properties of the models and introduce the action…
Describing the causal relations governing a system is a fundamental task in many scientific fields, ideally addressed by experimental studies. However, obtaining data under intervention scenarios may not always be feasible, while…
The purpose of this paper is fourfold. The first is to develop the theory of tropical differential algebraic geometry from scratch; the second is to present the tropical fundamental theorem for differential algebraic geometry, and show how…
This chapter of the forthcoming Handbook of Graphical Models contains an overview of basic theorems and techniques from algebraic geometry and how they can be applied to the study of conditional independence and graphical models. It also…
This paper considers inference of causal structure in a class of graphical models called "conditional DAGs". These are directed acyclic graph (DAG) models with two kinds of variables, primary and secondary. The secondary variables are used…
The 2-matrix model has been introduced to study Ising model on random surfaces. Since then, the link between matrix models and combinatorics of discrete surfaces has strongly tightened. This manuscript aims to investigate these deep links…
New biological assays like Perturb-seq link highly parallel CRISPR interventions to a high-dimensional transcriptomic readout, providing insight into gene regulatory networks. Causal gene regulatory networks can be represented by directed…