A PAC-Bayesian Perspective on Structured Prediction with Implicit Loss Embeddings

TL;DR

This paper introduces a PAC-Bayesian approach to structured prediction with implicit loss embeddings, providing new theoretical bounds and algorithms for better risk management in complex prediction tasks.

Contribution

It offers a novel PAC-Bayesian perspective on ILE structured prediction, deriving generalization bounds and developing new learning algorithms.

Findings

Derived two generalization bounds for ILE predictors

Implemented and analyzed two new learning algorithms

Provided insights into the behavior of PAC-Bayes ILE predictors

Abstract

Many practical machine learning tasks can be framed as Structured prediction problems, where several output variables are predicted and considered interdependent. Recent theoretical advances in structured prediction have focused on obtaining fast rates convergence guarantees, especially in the Implicit Loss Embedding (ILE) framework. PAC-Bayes has gained interest recently for its capacity of producing tight risk bounds for predictor distributions. This work proposes a novel PAC-Bayes perspective on the ILE Structured prediction framework. We present two generalization bounds, on the risk and excess risk, which yield insights into the behavior of ILE predictors. Two learning algorithms are derived from these bounds. The algorithms are implemented and their behavior analyzed, with source code available at \url{https://github.com/theophilec/PAC-Bayes-ILE-Structured-Prediction}.