Better than Trees: Applying Semilattices to Balance the Accuracy and Complexity of Machine Learning Models

Balancing the accuracy and the complexity of models is a well established and ongoing challenge. Models can be misleading if they are not accurate, but models may be incomprehensible if their accuracy depends upon their being complex. In this paper, semilattices are examined as an option for balancing the accuracy and the complexity of machine learning models. This is done with a type of machine learning that is based on semilattices: algebraic machine learning. Unlike trees, semilattices can include connections between elements that are in different hierarchies. Trees are a subclass of semilattices. Hence, semilattices have higher expressive potential than trees. The explanation provided here encompasses diagrammatic semilattices, algebraic semilattices, and interrelationships between them. Machine learning based on semilattices is explained with the practical example of urban food access landscapes, comprising food deserts, food oases, and food swamps. This explanation describes how to formulate an algebraic machine learning model. Overall, it is argued that semilattices are better for balancing the accuracy and complexity of models than trees, and it is explained how algebraic semilattices can be the basis for machine learning models.