Several interesting generative learning algorithms involve a complex
probability distribution over many random variables, involving intractable
normalization constants or latent variable normalization. Some of them may even
not have an analytic expression for the unnormalized probability function and
no tractable approximation. This makes it difficult to estimate the quality of
these models, once they have been trained, or to monitor their quality (e.g.
for early stopping) while training. A previously proposed method is based on
constructing a non-parametric density estimator of the model's probability
function from samples generated by the model. We revisit this idea, propose a
more efficient estimator, and prove that it provides a lower bound on the true
test log-likelihood, and an unbiased estimator as the number of generated
samples goes to infinity, although one that incorporates the effect of poor
mixing. We further propose a biased variant of the estimator that can be used
reliably with a finite number of samples for the purpose of model comparison.

研究提出了一种更高效的密度估计方法，从而解决了一些复杂的生成学习算法中难以估计模型质量的问题，并证明其提供了真实测试对数似然的下界和无偏估计，同时还提出了一种偏差估计的变体，可以在有限的样本数下可靠地用于模型比较。