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

Théophile Cantelobre (1, 2, 3) , Benjamin Guedj (4, 5, 6, 2, 3) , María Pérez-Ortiz (4, 5, 3) , John Shawe-Taylor (4, 5, 3)

1 Mines Paris - PSL (École nationale supérieure des mines de Paris)
2 MODAL - MOdel for Data Analysis and Learning
3 Inria-London - The Inria London Programme
4 UCL - University College of London [London]
5 UCL-CS - Department of Computer science [University College of London]
6 Inria-CWI - Inria-CWI

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 https://github.com/theophilec/ PAC-Bayes-ILE-Structured-Prediction.

Mots clés: Statistical learning theory; PAC-Bayes theory; Structured output prediction; Implicit Loss Embeddings; Generalization bounds

Domaines: Apprentissage [cs.LG]; Machine Learning [stat.ML]; Théorie [stat.TH]

Théophile Cantelobre, Benjamin Guedj, María Pérez-Ortiz, John Shawe-Taylor. A PAC-Bayesian Perspective on Structured Prediction with Implicit Loss Embeddings. 2020. ⟨hal-03046401⟩