Moment restrictions and their conditional counterparts emerge in many areas
of machine learning and statistics ranging from causal inference to
reinforcement learning. Estimators for these tasks, generally called methods of
moments, include the prominent generalized method of moments (GMM) which has
recently gained attention in causal inference. GMM is a special case of the
broader family of empirical likelihood estimators which are based on
approximating a population distribution by means of minimizing a
$\varphi$-divergence to an empirical distribution. However, the use of
$\varphi$-divergences effectively limits the candidate distributions to
reweightings of the data samples. We lift this long-standing limitation and
provide a method of moments that goes beyond data reweighting. This is achieved
by defining an empirical likelihood estimator based on maximum mean discrepancy
which we term the kernel method of moments (KMM). We provide a variant of our
estimator for conditional moment restrictions and show that it is
asymptotically first-order optimal for such problems. Finally, we show that our
method achieves competitive performance on several conditional moment
restriction tasks.

提出了一种去除了原有约束的方法的方法，称之为核矩法，并将其用于条件矩限制问题上并取得一定的实验结果。