论文标题

先前信息和计算能力在机器学习中的作用

The role of prior information and computational power in Machine Learning

论文作者

Marcondes, Diego, Simonis, Adilson, Barrera, Junior

论文摘要

储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。

Science consists on conceiving hypotheses, confronting them with empirical evidence, and keeping only hypotheses which have not yet been falsified. Under deductive reasoning they are conceived in view of a theory and confronted with empirical evidence in an attempt to falsify it, and under inductive reasoning they are conceived based on observation, confronted with empirical evidence and a theory is established based on the not falsified hypotheses. When the hypotheses testing can be performed with quantitative data, the confrontation can be achieved with Machine Learning methods, whose quality is highly dependent on the hypotheses' complexity, hence on the proper insertion of prior information into the set of hypotheses seeking to decrease its complexity without loosing good hypotheses. However, Machine Learning tools have been applied under the pragmatic view of instrumentalism, which is concerned only with the performance of the methods and not with the understanding of their behavior, leading to methods which are not fully understood. In this context, we discuss how prior information and computational power can be employed to solve a learning problem, but while prior information and a careful design of the hypotheses space has as advantage the interpretability of the results, employing high computational power has the advantage of a higher performance. We discuss why learning methods which combine both should work better from an understanding and performance perspective, arguing in favor of basic theoretical research on Machine Learning, in special about how properties of classifiers may be identified in parameters of modern learning models.

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