In this paper, we discuss the problem of estimating the minimum error reachable by a regression model given a dataset, prior to learning. More specifically, we extend the Gamma Test estimates of the variance of the noise from the continuous case to the binary case. We give some heuristics for further possible extensions of the theory in the continuous case with the Lp-norm and conclude with some applications and simulations. From the point of view of machine learning, the result is relevant because it gives conditions under which there is no need to learn the model in order to predict the best possible performance.

中文翻译：

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将 Gamma 检验统计扩展到二元变量和一些应用

在本文中，我们讨论了在学习之前估计给定数据集的回归模型可达到的最小误差的问题。更具体地说，我们将噪声方差的 Gamma 测试估计从连续情况扩展到二元情况。我们给出了一些启发式方法，以便在连续情况下进一步扩展该理论大号p-规范并以一些应用程序和模拟结束。从机器学习的角度来看，结果是相关的，因为它给出了无需学习模型即可预测最佳性能的条件。