基于子模块度的连续和离散模型联合选择
Joint Continuous and Discrete Model Selection via Submodularity
摘要：
在机器学习的模型选择问题中，对具有有意义结构的性能良好的模型的期望通常通过正则化最优化问题来表达。然而，在许多情况下，有意义的结构被指定在一些离散空间，导致困难的非凸最优化问题。在本文中，我们连接的模型选择问题与结构促进正则化次模函数最小化连续和离散的参数。特别是，我们利用理论的次模函数，以确定一类这些问题，可以准确和有效地解决与不可知的组合离散和连续优化例程。我们展示了如何简单的连续或离散约束也可以处理某些问题类，并将这些想法扩展到一个强大的优化框架。我们还展示了这个类之外的一些问题如何可以嵌入到类中，进一步扩展了我们的框架可以容纳的问题类。最后，我们数值验证我们的理论结果与几个概念验证的例子与合成和真实世界的数据，比较国家的最先进的算法。
英文摘要：
In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is specified in some discrete space, leading to difficult nonconvex optimization problems. In this paper, we connect the model selection problem with structure-promoting regularizers to submodular function minimization with continuous and discrete arguments. In particular, we leverage the theory of submodular functions to identify a class of these problems that can be solved exactly and efficiently with an agnostic combination of discrete and continuous optimization routines. We show how simple continuous or discrete constraints can also be handled for certain problem classes and extend these ideas to a robust optimization framework. We also show how some problems outside of this class can be embedded within the class, further extending the class of problems our framework can accommodate. Finally, we numerically validate our theoretical results with several proof-of-concept examples with synthetic and real-world data, comparing against state-of-the-art algorithms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
