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Multi-agent dynamical systems refer to scenarios where multiple units (aka agents) interact with each other and evolve collectively over time. For instance, people’s health conditions are mutually influenced. Receiving vaccinations not only strengthens the longterm health status of one unit but also provides protection for those in their immediate surroundings. To make informed decisions in multi-agent dynamical systems, such as determining the optimal vaccine distribution plan, it is essential for decision-makers to estimate the continuous-time counterfactual outcomes. However, existing studies of causal inference over time rely on the assumption that units are mutually independent, which is not valid for multi-agent dynamical systems. In this paper, we aim to bridge this gap and study how to estimate counterfactual outcomes in multi-agent dynamical systems. Causal inference in a multi-agent dynamical system has unique challenges: 1) Confounders are timevarying and are present in both individual unit covariates and those of other units; 2) Units are affected by not only their own but also others’ treatments; 3) The treatments are naturally dynamic, such as receiving vaccines and boosters in a seasonal manner. To this end, we model a multi-agent dynamical system as a graph and propose a novel model called CF-GODE (CounterFactual Graph Ordinary Differential Equations). CF-GODE is a causal model that estimates continuous-time counterfactual outcomes in the presence of inter-dependencies between units. To facilitate continuous-time estimation,we propose Treatment-Induced GraphODE, a novel ordinary differential equation based on graph neural networks (GNNs), which can incorporate dynamical treatments as additional inputs to predict potential outcomes over time. To remove confounding bias, we propose two domain adversarial learning based objectives that learn balanced continuous representation trajectories, which are not predictive of treatments and interference. We further provide theoretical justification to prove their effectiveness. Experiments on two semi-synthetic datasets confirm that CF-GODE outperforms baselines on counterfactual estimation. We also provide extensive analyses to understand how our model works.
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Network Synthetic Interventions: A Causal Framework for Panel Data Under Network Interference
We propose a generalization of the synthetic controls and synthetic interventions methodology to incorporate network interference. We consider the estimation of unit-specific potential outcomes from panel data in the presence of spillover across units and unobserved confounding. Key to our approach is a novel latent factor model that takes into account network interference and generalizes the factor models typically used in panel data settings. We propose an estimator, Network Synthetic Interventions (NSI), and show that it consistently estimates the mean outcomes for a unit under an arbitrary set of counterfactual treatments for the network. We further establish that the estimator is asymptotically normal. We furnish two validity tests for whether the NSI estimator reliably generalizes to produce accurate counterfactual estimates. We provide a novel graph-based experiment design that guarantees the NSI estimator produces accurate counterfactual estimates, and also analyze the sample complexity of the proposed design. We conclude with simulations that corroborate our theoretical findings.
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- Award ID(s):
- 2022448
- PAR ID:
- 10525305
- Publisher / Repository:
- https://arxiv.org/pdf/2210.11355
- Date Published:
- Format(s):
- Medium: X
- Institution:
- Massachusetts Institute of Technology
- Sponsoring Org:
- National Science Foundation
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