24 research outputs found
Learning Interpretable Rules for Multi-label Classification
Multi-label classification (MLC) is a supervised learning problem in which,
contrary to standard multiclass classification, an instance can be associated
with several class labels simultaneously. In this chapter, we advocate a
rule-based approach to multi-label classification. Rule learning algorithms are
often employed when one is not only interested in accurate predictions, but
also requires an interpretable theory that can be understood, analyzed, and
qualitatively evaluated by domain experts. Ideally, by revealing patterns and
regularities contained in the data, a rule-based theory yields new insights in
the application domain. Recently, several authors have started to investigate
how rule-based models can be used for modeling multi-label data. Discussing
this task in detail, we highlight some of the problems that make rule learning
considerably more challenging for MLC than for conventional classification.
While mainly focusing on our own previous work, we also provide a short
overview of related work in this area.Comment: Preprint version. To appear in: Explainable and Interpretable Models
in Computer Vision and Machine Learning. The Springer Series on Challenges in
Machine Learning. Springer (2018). See
http://www.ke.tu-darmstadt.de/bibtex/publications/show/3077 for further
informatio
On the algebra of quasi-shuffles
For any commutative algebra R the shuffle product on the tensor module T(R) can be deformed to a new product. It is called the quasi-shuffle algebra, or stuffle algebra, and denoted T q (R). We show that if R is the polynomial algebra, then T q (R) is free for some algebraic structure called Commutative TriDendriform (CTD-algebras). This result is part of a structure theorem for CTD-bialgebras which are associative as coalgebras and whose primitive part is commutative. In other words, there is a good triple of operads (As, CTD, Com) analogous to (Com, As, Lie). In the last part we give a similar interpretation of the quasi-shuffle algebra in the noncommutative setting