arXiv subjects

Ignavier Ng

Publications and source records attributed to Ignavier Ng.

39 records · Page 3Linked to original sources

arXiv2021

On the Role of Sparsity and DAG Constraints for Learning Linear DAGs

Learning graphical structures based on Directed Acyclic Graphs (DAGs) is a challenging problem, partly owing to the large search space of possible graphs. A recent line of work formulates the structure learning problem as a continuous constrained optimization task using the least squares objective and an algebraic characterization of DAGs. However, the formulation requires a hard DAG constraint and may lead to optimization difficulties. In this paper, we study the asymptotic role of the sparsity and DAG constraints for learning DAG models in the linear Gaussian and non-Gaussian cases, and investigate their usefulness in the finite sample regime. Based on the theoretical results, we formulate a likelihood-based score function, and show that one only has to apply soft sparsity and DAG constraints to learn a DAG equivalent to the ground truth DAG. This leads to an unconstrained optimization problem that is much easier to solve. Using gradient-based optimization and GPU acceleration, our procedure can easily handle thousands of nodes while retaining a high accuracy. Extensive experiments validate the effectiveness of our proposed method and show that the DAG-penalized likelihood objective is indeed favorable over the least squares one with the hard DAG constraint.

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arXiv2020

Causal Discovery with Reinforcement Learning

Discovering causal structure among a set of variables is a fundamental problem in many empirical sciences. Traditional score-based casual discovery methods rely on various local heuristics to search for a Directed Acyclic Graph (DAG) according to a predefined score function. While these methods, e.g., greedy equivalence search, may have attractive results with infinite samples and certain model assumptions, they are usually less satisfactory in practice due to finite data and possible violation of assumptions. Motivated by recent advances in neural combinatorial optimization, we propose to use Reinforcement Learning (RL) to search for the DAG with the best scoring. Our encoder-decoder model takes observable data as input and generates graph adjacency matrices that are used to compute rewards. The reward incorporates both the predefined score function and two penalty terms for enforcing acyclicity. In contrast with typical RL applications where the goal is to learn a policy, we use RL as a search strategy and our final output would be the graph, among all graphs generated during training, that achieves the best reward. We conduct experiments on both synthetic and real datasets, and show that the proposed approach not only has an improved search ability but also allows a flexible score function under the acyclicity constraint.

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arXiv2019

A Graph Autoencoder Approach to Causal Structure Learning

Causal structure learning has been a challenging task in the past decades and several mainstream approaches such as constraint- and score-based methods have been studied with theoretical guarantees. Recently, a new approach has transformed the combinatorial structure learning problem into a continuous one and then solved it using gradient-based optimization methods. Following the recent state-of-the-arts, we propose a new gradient-based method to learn causal structures from observational data. The proposed method generalizes the recent gradient-based methods to a graph autoencoder framework that allows nonlinear structural equation models and is easily applicable to vector-valued variables. We demonstrate that on synthetic datasets, our proposed method outperforms other gradient-based methods significantly, especially on large causal graphs. We further investigate the scalability and efficiency of our method, and observe a near linear training time when scaling up the graph size.

cs.LG↗