A Proposal on Discovering Causal Structures inTechnical Systems by Means of Interventions

Causal Discovery has become an area of high interest for researchers. It haslead to great advances in medicine, in the social sciences and in genetics. Butup til now, it is hardly used to identify causal relations in technical systems.This paper presents the basic building blocks for in-depth research. This paperreviews established causal discovery methods and causal models. In contrast toexisting surveys of this domain, we focus on the causal discovery methods usinginterventions. Based thereon, we propose the idea of a promising interventionaldiscovery approach for technical systems. It takes advantage of not only direct,but also indirect causal relationships, which might improve the learning processof causal structures

Penalized Estimation of Directed Acyclic Graphs From Discrete Data

Bayesian networks, with structure given by a directed acyclic graph (DAG), are a popular class of graphical models. However, learning Bayesian networks from discrete or categorical data is particularly challenging, due to the large parameter space and the difficulty in searching for a sparse structure. In this article, we develop a maximum penalized likelihood method to tackle this problem. Instead of the commonly used multinomial distribution, we model the conditional distribution of a node given its parents by multi-logit regression, in which an edge is parameterized by a set of coefficient vectors with dummy variables encoding the levels of a node. To obtain a sparse DAG, a group norm penalty is employed, and a blockwise coordinate descent algorithm is developed to maximize the penalized likelihood subject to the acyclicity constraint of a DAG. When interventional data are available, our method constructs a causal network, in which a directed edge represents a causal relation. We apply our method to various simulated and real data sets. The results show that our method is very competitive, compared to many existing methods, in DAG estimation from both interventional and high-dimensional observational data.Comment: To appear in Statistics and Computin

FED-CD: Federated Causal Discovery from Interventional and Observational Data

Causal discovery, the inference of causal relations from data, is a core task of fundamental importance in all scientific domains, and several new machine learning methods for addressing the causal discovery problem have been proposed recently. However, existing machine learning methods for causal discovery typically require that the data used for inference is pooled and available in a centralized location. In many domains of high practical importance, such as in healthcare, data is only available at local data-generating entities (e.g. hospitals in the healthcare context), and cannot be shared across entities due to, among others, privacy and regulatory reasons. In this work, we address the problem of inferring causal structure - in the form of a directed acyclic graph (DAG) - from a distributed data set that contains both observational and interventional data in a privacy-preserving manner by exchanging updates instead of samples. To this end, we introduce a new federated framework, FED-CD, that enables the discovery of global causal structures both when the set of intervened covariates is the same across decentralized entities, and when the set of intervened covariates are potentially disjoint. We perform a comprehensive experimental evaluation on synthetic data that demonstrates that FED-CD enables effective aggregation of decentralized data for causal discovery without direct sample sharing, even when the contributing distributed data sets cover disjoint sets of interventions. Effective methods for causal discovery in distributed data sets could significantly advance scientific discovery and knowledge sharing in important settings, for instance, healthcare, in which sharing of data across local sites is difficult or prohibited