论文标题
贝叶斯机器科学家，以帮助解决挑战性科学问题
A Bayesian machine scientist to aid in the solution of challenging scientific problems
论文作者
论文摘要
封闭形式，可解释的数学模型对促进我们对世界的理解发挥了重要作用。随着数据革命，我们现在可能可以揭示从物理学到社会科学的许多系统的新模型。但是，要处理越来越多的数据，我们需要能够自动从数据中提取这些模型的“机器科学家”。在这里，我们介绍了一位贝叶斯机器科学家，该科学家在模型上使用明确的近似值建立了模型的合理性，并通过从大量的数学表达式中学习来确定其对模型的先前期望。它使用马尔可夫链蒙特卡洛探索了模型的空间。我们表明，这种方法可以发现合成和真实数据的准确模型，并提供了与现有方法和其他非参数方法的样本外预测更准确的预测。
Closed-form, interpretable mathematical models have been instrumental for advancing our understanding of the world; with the data revolution, we may now be in a position to uncover new such models for many systems from physics to the social sciences. However, to deal with increasing amounts of data, we need "machine scientists" that are able to extract these models automatically from data. Here, we introduce a Bayesian machine scientist, which establishes the plausibility of models using explicit approximations to the exact marginal posterior over models and establishes its prior expectations about models by learning from a large empirical corpus of mathematical expressions. It explores the space of models using Markov chain Monte Carlo. We show that this approach uncovers accurate models for synthetic and real data and provides out-of-sample predictions that are more accurate than those of existing approaches and of other nonparametric methods.
