It is well known in machine learning that models trained on a training set generated by a probability distribution function perform far worse on test sets generated by a different probability distribution function. In the limit, it is feasible that a continuum of probability distribution functions might have generated the observed test set data; a desirable property of a learned model in that case is its ability to describe most of the probability distribution functions from the continuum equally well. This requirement naturally leads to sampling methods from the continuum of probability distribution functions that lead to the construction of optimal training sets. We study the sequential prediction of Ornstein-Uhlenbeck processes that form a parametric family. We find empirically that a simple deep network trained on optimally constructed training sets using the methods described in this letter can be robust to changes in the test set distribution.

中文翻译：

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参数族的最优采样：对机器学习的影响

在机器学习中众所周知，在由概率分布函数生成的训练集上训练的模型在由不同概率分布函数生成的测试集上的表现要差得多。在极限情况下，概率分布函数的连续统可能已经生成了观察到的测试集数据；在这种情况下，学习模型的一个理想特性是它能够同样好地描述来自连续体的大多数概率分布函数。这一要求自然会导致从概率分布函数的连续统中产生采样方法，从而构建最佳训练集。我们研究形成参数族的 Ornstein-Uhlenbeck 过程的顺序预测。