基于一阶逻辑约束的多任务核学习方法
Multitask Kernel-based Learning with First-Order Logic Constraints
AI总结：
本文提出一种通用框架，将一阶逻辑约束集成到核机器中，用于多任务学习，通过两阶段优化处理非凸惩罚项，以联合学习多个谓词。
摘要：
在本文中，我们提出一个通用框架，将监督和无监督示例与以一组一阶逻辑子句形式表达的背景知识集成到核机器中。具体而言，我们考虑一种多任务学习方案，其中定义在一组对象上的多个谓词需要从示例中联合学习，同时对其值的可接受配置强制执行一组FOL约束。这些谓词定义在特征空间上（输入对象在该空间中表示），并且可以预先已知或通过适当的基于核的学习器近似。我们提出了一种通用方法，将FOL子句转换为连续实现，该实现能够处理由基于核的谓词计算出的输出。学习问题被表述为半监督任务，需要在原始空间中优化一个损失函数，该函数结合了监督示例上的拟合损失度量、正则化项以及一个惩罚项，该惩罚项对监督和无监督示例都强制执行约束。不幸的是，惩罚项不是凸的，它可能阻碍优化过程。然而，通过使用两阶段学习方案可以避免较差的解，在该方案中首先学习监督示例，然后强制执行约束。
英文摘要：
In this paper we propose a general framework to integrate supervised and unsupervised examples with background knowledge expressed by a collection of first-order logic clauses into kernel machines. In particular, we consider a multi-task learning scheme where multiple predicates defined on a set of objects are to be jointly learned from examples, enforcing a set of FOL constraints on the admissible configurations of their values. The predicates are defined on the feature spaces, in which the input objects are represented, and can be either known a priori or approximated by an appropriate kernel-based learner. A general approach is presented to convert the FOL clauses into a continuous implementation that can deal with the outputs computed by the kernel-based predicates. The learning problem is formulated as a semi-supervised task that requires the optimization in the primal of a loss function that combines a fitting loss measure on the supervised examples, a regularization term, and a penalty term that enforces the constraints on both the supervised and unsupervised examples. Unfortunately, the penalty term is not convex and it can hinder the optimization process. However, it is possible to avoid poor solutions by using a two stage learning schema, in which the supervised examples are learned first and then the constraints are enforced.
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。
