We propose a new method to estimate structural parameters in multi-way networks while controlling for rich structures of fixed effects. The method is based on a series of classification tasks and is agnostic to both the number and structure of fixed effects. In contrast to full maximum likelihood approaches, our estimator does not suffer from the incidental parameter problem. For sparsely connected networks, it is also computationally faster than PPML. We provide empirical evidence that our estimator yields more reliable confidence intervals than PPML and its bias-correction strategies. These improvements hold even under model misspecification and are more pronounced in sparse settings. While PPML remains competitive in dense, low-dimensional data, our approach offers a robust alternative for multi-way models that scales efficiently with sparsity. The method is applied to study the causal effect of a policy reform on spatial accessibility to health care in France.

翻译：我们提出了一种新方法，用于在控制丰富固定效应结构的同时估计多向网络中的结构参数。该方法基于一系列分类任务，且对固定效应的数量和结构均保持不可知性。与完全最大似然方法相比，我们的估计量不受伴随参数问题的影响。对于稀疏连接网络，其计算速度也快于PPML。我们提供的经验证据表明，与PPML及其偏差校正策略相比，我们的估计量能产生更可靠的置信区间。这些改进即使在模型设定错误的情况下依然成立，且在稀疏设置中更为显著。尽管PPML在稠密、低维数据中仍具竞争力，但我们的方法为多向模型提供了一种稳健的替代方案，并能随稀疏性高效扩展。该方法被应用于研究法国一项政策改革对医疗保健空间可达性的因果效应。