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Independent-Set Design of Experiments for Estimating Treatment and Spillover Effects under Network Interference
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Proposes an independent-set experimental design that splits network units into an independent set (analyzed) and an auxiliary set (used to control interference), with a greedy lower bound on set size and estimators for direct, spillover, and total effects.
Problem
Causal inference under network interference on sparse, connected networks, where treatment assignments and interference exposures are entangled and spillover variance collapses under conventional randomization.
Approach
Partition units into an independent set (no edges among them) whose treatments are randomized and an auxiliary set whose assignments are optimized so the interference received by the independent set matches a target or is spread to extremes, enabling separate control of treatment and interference on the independent set.
Key results
- On 50 Erdos-Renyi graphs (n=60, p=0.1), IS design achieves lower bias and variance than CR, Full, graph cluster and ego-clusters for spillover effect estimation across gamma=5,10,15,20.
- Across ER, Barabasi-Albert and small-world settings (2,000 runs each), IS has the lowest bias and variance for spillover estimation and for direct effect estimation (e.g., direct effect variance on small-world n=50: 0.029 vs 0.877 for Full).
- Theory: the greedy algorithm yields an independent set of size at least (log s / s) n with high probability on Erdos-Renyi graphs with average degree s.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use the independent-set design rather than conventional designs | average spillover effect estimation · Erdos-Renyi, Barabasi-Albert, and small-world graphs | Bias: 0.598 -> 0.398 | Helped |
| use the independent-set design rather than conventional designs | average spillover effect estimation · Erdos-Renyi, Barabasi-Albert, and small-world graphs | Variance: 0.468 -> 0.242 | Helped |
| use the independent-set design rather than conventional designs | average direct effect estimation · Erdos-Renyi, Barabasi-Albert, and small-world graphs | Bias: 0.262 -> 0.117 | Helped |
| use the independent-set design rather than conventional designs | average direct effect estimation · Erdos-Renyi, Barabasi-Albert, and small-world graphs | Variance: 0.035 -> 0.009 | Helped |
Surprising findings
- Table of sample size comparison claims the greedy independent set (log s/s)n is larger than ego-cluster count n/(s+1) by a factor of log s, while the table lists the independent set size as (n log s)/s.
Limitations
- Estimation restricted to the independent set, reducing effective sample size.
- Optimizing auxiliary assignments can be computationally expensive.
- Performance on misspecified observed networks is unknown.
Experimental setup
Datasets: simulated Erdos-Renyi graphs Barabasi-Albert graphs small-world graphs
Benchmarks: simulated networks with linear potential outcome model
Metrics: bias variance
Baselines: Completely randomized design on independent set (CR) Completely randomized design on full graph (Full) Ego-clusters Graph cluster randomization
Builds on: randomized saturation design ego-clusters design graph cluster randomization Rubin potential outcomes
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