Modeling Discrete Interventional Data using Directed Cyclic Graphical Models

TL;DR

This paper introduces a novel directed cyclic graphical model for discrete interventional data, enabling modeling of intervention effects, inference, and learning through convex optimization, with applications demonstrated on simulated and biological data.

Contribution

It presents a new representation for discrete multivariate distributions with cycles, along with convex methods for parameter and structure learning.

Findings

Effective modeling of intervention effects in cyclic graphs

Convex optimization approach for parameter estimation

Successful application to biological and simulated data

Abstract

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 properties encoded in this model can be represented as a directed graph that allows cycles. In addition to discussing inference and sampling with this representation, we give an exponential family parametrization that allows parameter estimation to be stated as a convex optimization problem; we also give a convex relaxation of the task of simultaneous parameter and structure learning using group l1-regularization. The model is evaluated on simulated data and intracellular flow cytometry data.