论文标题
离散生成模型的适当损失
Proper losses for discrete generative models
论文作者
论文摘要
我们启动适当损失的研究，以评估离散环境中的生成模型。与传统的适当损失不同，我们同时将生成模型和目标分布视为黑盒，仅假定能够绘制I.I.D.的能力。样品。如果最小化预期损失的生成分布等于目标分布，我们将损失定义为黑框。使用统计估计理论中的技术，我们给出了黑框的一般结构和表征：它们必须采用多项式形式，并且来自模型和目标分布的绘制数必须超过多项式的程度。表征排除了一种损失，其期望是目标分布与模型之间的跨凝结。但是，通过将构造扩展到诸如Poisson采样等任意抽样方案，我们表明可以构建这种损失。
We initiate the study of proper losses for evaluating generative models in the discrete setting. Unlike traditional proper losses, we treat both the generative model and the target distribution as black-boxes, only assuming ability to draw i.i.d. samples. We define a loss to be black-box proper if the generative distribution that minimizes expected loss is equal to the target distribution. Using techniques from statistical estimation theory, we give a general construction and characterization of black-box proper losses: they must take a polynomial form, and the number of draws from the model and target distribution must exceed the degree of the polynomial. The characterization rules out a loss whose expectation is the cross-entropy between the target distribution and the model. By extending the construction to arbitrary sampling schemes such as Poisson sampling, however, we show that one can construct such a loss.
