We present generalized balancing weights, Neural Balancing Weights (NBW), to estimate the causal effects for an arbitrary mixture of discrete and continuous interventions. The weights were obtained by directly estimating the density ratio between the source and balanced distributions by optimizing the variational representation of $f$-divergence. For this, we selected $\alpha$-divergence since it has good properties for optimization: It has an estimator whose sample complexity is independent of it's ground truth value and unbiased mini-batch gradients and is advantageous for the vanishing gradient problem. In addition, we provide a method for checking the balance of the distribution changed by the weights. If the balancing is imperfect, the weights can be improved by adding new balancing weights. Our method can be conveniently implemented with any present deep-learning libraries, and weights can be used in most state-of-the-art supervised algorithms. The code for our method is available online.

翻译：我们提出广义平衡权重——神经平衡权重（NBW），用于估计任意离散与连续干预混合场景下的因果效应。这些权重通过优化$f$-散度的变分表示，直接估计源分布与平衡分布之间的密度比得到。为此，我们选择$\alpha$-散度，因其具有优良的优化性质：其估计器的样本复杂度与真实值无关，支持无偏小批量梯度，并能有效缓解梯度消失问题。此外，我们提供了一种检查权重改变后分布平衡性的方法。若平衡不完美，可通过添加新的平衡权重进行改进。本方法可便捷地应用于现有深度学习库，且权重适用于绝大多数前沿监督学习算法。相关代码已在线公开。