Hefny Ahmed, Downey Carlton, Gordon Geoffrey J
Carnegie Mellon University, Pittsburgh, PA 15213.
Adv Neural Inf Process Syst. 2015;28:1954-1962.
Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be difficult to use and extend in practice: e.g., they can make it difficult to incorporate prior information such as sparsity or structure. To address this problem, we present a new view of dynamical system learning: we show how to learn dynamical systems by solving a sequence of ordinary supervised learning problems, thereby allowing users to incorporate prior knowledge via standard techniques such as regularization. Many existing spectral methods are special cases of this new framework, using linear regression as the supervised learner. We demonstrate the effectiveness of our framework by showing examples where nonlinear regression or lasso let us learn better state representations than plain linear regression does; the correctness of these instances follows directly from our general analysis.
最近，人们对用于学习动力系统的谱方法产生了浓厚兴趣。这些方法很受欢迎，因为它们通常在计算效率和统计效率之间提供了良好的权衡。不幸的是，它们在实践中可能难以使用和扩展：例如，它们可能使得纳入诸如稀疏性或结构等先验信息变得困难。为了解决这个问题，我们提出了一种动力系统学习的新观点：我们展示了如何通过解决一系列普通的监督学习问题来学习动力系统，从而允许用户通过诸如正则化等标准技术纳入先验知识。许多现有的谱方法都是这个新框架的特殊情况，使用线性回归作为监督学习器。我们通过展示一些示例来证明我们框架的有效性，在这些示例中，非线性回归或套索回归让我们能够学习到比普通线性回归更好的状态表示；这些实例的正确性直接源于我们的一般分析。
