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Distributed Learning of Generalized Linear Causal Networks

Qiaoling Ye, Arash A. Amini, Qing Zhou

TL;DR

This work tackles scalable causal discovery from distributed data by introducing DARLS, a method that combines simulated annealing over topological sorts with a distributed, DANE-like optimization to maximize a regularized likelihood across all data. By employing generalized linear DAGs (GLDAGs), the authors achieve identifiability for continuous models and provide rigorous convergence and consistency guarantees for the distributed estimator. Empirically, DARLS shows state-of-the-art or competitive structure learning accuracy on simulated distributed data and achieves superior predictive likelihood on a real ChIP-Seq protein–DNA binding dataset, illustrating practical gains in distributed settings. The approach advances scalable causal inference with theoretical guarantees and demonstrated applicability to complex biological networks and large-scale distributed data environments.

Abstract

We consider the task of learning causal structures from data stored on multiple machines, and propose a novel structure learning method called distributed annealing on regularized likelihood score (DARLS) to solve this problem. We model causal structures by a directed acyclic graph that is parameterized with generalized linear models, so that our method is applicable to various types of data. To obtain a high-scoring causal graph, DARLS simulates an annealing process to search over the space of topological sorts, where the optimal graphical structure compatible with a sort is found by a distributed optimization method. This distributed optimization relies on multiple rounds of communication between local and central machines to estimate the optimal structure. We establish its convergence to a global optimizer of the overall score that is computed on all data across local machines. To the best of our knowledge, DARLS is the first distributed method for learning causal graphs with such theoretical guarantees. Through extensive simulation studies, DARLS has shown competing performance against existing methods on distributed data, and achieved comparable structure learning accuracy and test-data likelihood with competing methods applied to pooled data across all local machines. In a real-world application for modeling protein-DNA binding networks with distributed ChIP-Sequencing data, DARLS also exhibits higher predictive power than other methods, demonstrating a great advantage in estimating causal networks from distributed data.

Distributed Learning of Generalized Linear Causal Networks

TL;DR

This work tackles scalable causal discovery from distributed data by introducing DARLS, a method that combines simulated annealing over topological sorts with a distributed, DANE-like optimization to maximize a regularized likelihood across all data. By employing generalized linear DAGs (GLDAGs), the authors achieve identifiability for continuous models and provide rigorous convergence and consistency guarantees for the distributed estimator. Empirically, DARLS shows state-of-the-art or competitive structure learning accuracy on simulated distributed data and achieves superior predictive likelihood on a real ChIP-Seq protein–DNA binding dataset, illustrating practical gains in distributed settings. The approach advances scalable causal inference with theoretical guarantees and demonstrated applicability to complex biological networks and large-scale distributed data environments.

Abstract

We consider the task of learning causal structures from data stored on multiple machines, and propose a novel structure learning method called distributed annealing on regularized likelihood score (DARLS) to solve this problem. We model causal structures by a directed acyclic graph that is parameterized with generalized linear models, so that our method is applicable to various types of data. To obtain a high-scoring causal graph, DARLS simulates an annealing process to search over the space of topological sorts, where the optimal graphical structure compatible with a sort is found by a distributed optimization method. This distributed optimization relies on multiple rounds of communication between local and central machines to estimate the optimal structure. We establish its convergence to a global optimizer of the overall score that is computed on all data across local machines. To the best of our knowledge, DARLS is the first distributed method for learning causal graphs with such theoretical guarantees. Through extensive simulation studies, DARLS has shown competing performance against existing methods on distributed data, and achieved comparable structure learning accuracy and test-data likelihood with competing methods applied to pooled data across all local machines. In a real-world application for modeling protein-DNA binding networks with distributed ChIP-Sequencing data, DARLS also exhibits higher predictive power than other methods, demonstrating a great advantage in estimating causal networks from distributed data.
Paper Structure (16 sections, 3 theorems, 19 equations, 3 figures, 3 tables, 3 algorithms)

This paper contains 16 sections, 3 theorems, 19 equations, 3 figures, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Generalized linear DAG models
  3. Distributed DAG learning
  4. Global objective function and annealing
  5. Local objective functions and distributed optimization
  6. Tuning parameter selection and structure estimation
  7. Theoretical guarantees
  8. Distributed estimate convergence
  9. Consistency
  10. Results on simulated data
  11. Methods
  12. Accuracy metrics
  13. GLDAG data
  14. Other data generation models
  15. Real data application
  16. ...and 1 more sections

Key Result

Proposition 1

Suppose the joint distribution $L(X)$ is defined by the log-pdf $L(x; \beta)$ with a DAG $\mathcal{G}_0$ according to eq:glm-sem-log-pdf such that $\beta_{ij} \neq 0$ if and only if $i \in \text{PA}_j$ in $\mathcal{G}_0$. If $L(x; \beta)$ is second-order differentiable with respect to $x$ and the fi

Figures (3)

  • Figure 1: SHD comparison between DARLS and the best competing method using combined or distributed data. For each graph, the box plots from left to right report the results for the best competing method on combined data (best-combined), DARLS on combined combined, DARLS on distributed data and the best competing method on distributed data (best-distributed).
  • Figure 2: Accuracy and computation time comparison for $f(\pi)$. computation time comparison, with mean and standard deviations plotted, is performed over 20 datasets generated from Insurance.
  • Figure 3: DAG (left) and the converted CPDAG (right) learned by DARLS.

Theorems & Definitions (5)

  • Definition 1: Identifiability
  • Proposition 1
  • Theorem 1
  • Theorem 2
  • Remark 1