• Corpus ID: 53217974

DAGs with NO TEARS: Continuous Optimization for Structure Learning

@inproceedings{Zheng2018DAGsWN,
title={DAGs with NO TEARS: Continuous Optimization for Structure Learning},
author={Xun Zheng and Bryon Aragam and Pradeep Ravikumar and Eric P. Xing},
booktitle={Neural Information Processing Systems},
year={2018}
}
• Published in
Neural Information Processing…
4 March 2018
• Computer Science
Estimating the structure of directed acyclic graphs (DAGs, also known as {Bayesian networks}) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. [] Key Method This is achieved by a novel characterization of acyclicity that is not only smooth but also exact. The resulting problem can be efficiently solved by standard numerical algorithms, which also makes implementation effortless. The proposed method outperforms existing ones…
328 Citations

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References

SHOWING 1-10 OF 63 REFERENCES

Penalized estimation of directed acyclic graphs from discrete data

• Computer Science
Stat. Comput.
• 2019
A maximum penalized likelihood method to tackle Bayesian networks from discrete or categorical data, which model the conditional distribution of a node given its parents by multi-logit regression instead of the commonly used multinomial distribution.

A Simple Approach for Finding the Globally Optimal Bayesian Network Structure

• Computer Science
UAI
• 2006
It is shown that it is possible to learn the best Bayesian network structure with over 30 variables, which covers many practically interesting cases and offers a possibility for efficient exploration of the best networks consistent with different variable orderings.

Ordering-Based Search: A Simple and Effective Algorithm for Learning Bayesian Networks

• Computer Science
UAI
• 2005
It is shown that ordering-based search outperforms the standard baseline, and is competitive with recent algorithms that are much harder to implement.

0-PENALIZED MAXIMUM LIKELIHOOD FOR SPARSE DIRECTED ACYCLIC GRAPHS BY SARA

It is shown that the 0-penalized maximum likelihood estimator of a DAG has about the same number of edges as the minimal-edge I-MAP (a DAG with minimal number of edge representing the distribution), and that it converges in Frobenius norm.

Optimal Structure Identification With Greedy Search

This paper proves the so-called "Meek Conjecture", which shows that if a DAG H is an independence map of another DAG G, then there exists a finite sequence of edge additions and covered edge reversals in G such that H remains anindependence map of G and after all modifications G =H.

Learning Sparse Causal Gaussian Networks With Experimental Intervention: Regularization and Coordinate Descent

• Computer Science
• 2013
An L 1-penalized likelihood approach to estimate the structure of causal Gaussian networks is developed and it is established that model selection consistency for causalGaussian networks can be achieved with the adaptive lasso penalty and sufficient experimental interventions.

Bayesian network learning with cutting planes

The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered and it is shown that this is a particularly fast method for exact BN learning.

Finding optimal Bayesian networks by dynamic programming

• Computer Science, Mathematics
• 2005
This paper describes a “merely” exponential space/time algorithm for finding a Bayesian network that corresponds to a global maxima of a decomposable scoring function, such as BDeu or BIC.

Learning Graphical Model Structure Using L1-Regularization Paths

• Computer Science
AAAI
• 2007
This paper shows how the decomposability of the MDL score, plus the ability to quickly compute entire regularization paths, allows us to efficiently pick the optimal regularization parameter on a per-node basis.

Learning Bayesian networks with ancestral constraints

• Computer Science
NIPS
• 2016
This work considers the problem of learning Bayesian networks optimally, when subject to background knowledge in the form of ancestral constraints, and demonstrates that the approach can be orders-of-magnitude more efficient than alternative frameworks, such as those based on integer linear programming.