Fine-grained Generalization Analysis of Structured Output Prediction
This provides a solid theoretical foundation for learning in large-scale structured output prediction problems, which is incremental but important for domains like NLP and computer vision.
The paper tackles the problem of vacuous generalization bounds in structured output prediction by developing new high-probability bounds with logarithmic dependency on label set size and expectation bounds with no dependency, significantly improving over existing square-root bounds.
In machine learning we often encounter structured output prediction problems (SOPPs), i.e. problems where the output space admits a rich internal structure. Application domains where SOPPs naturally occur include natural language processing, speech recognition, and computer vision. Typical SOPPs have an extremely large label set, which grows exponentially as a function of the size of the output. Existing generalization analysis implies generalization bounds with at least a square-root dependency on the cardinality $d$ of the label set, which can be vacuous in practice. In this paper, we significantly improve the state of the art by developing novel high-probability bounds with a logarithmic dependency on $d$. Moreover, we leverage the lens of algorithmic stability to develop generalization bounds in expectation without any dependency on $d$. Our results therefore build a solid theoretical foundation for learning in large-scale SOPPs. Furthermore, we extend our results to learning with weakly dependent data.