A General Framework for Consistent Structured Prediction with Implicit Loss Embeddings

2020/02/13 by Carlo Ciliberto, Lorenzo Rosasco, Ciliberto, Carlo +3 · 4 citations
Computer Science · #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Machine Learning and Data Classification #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2002.05424

openalex publication_date 2020/02/13 · openalex created_date 2020/02/24 · openalex updated_date 2026/07/28

Abstract

We propose and analyze a novel theoretical and algorithmic framework for structured prediction. While so far the term has referred to discrete output spaces, here we consider more general settings, such as manifolds or spaces of probability measures. We define structured prediction as a problem where the output space lacks a vectorial structure. We identify and study a large class of loss functions that implicitly defines a suitable geometry on the problem. The latter is the key to develop an algorithmic framework amenable to a sharp statistical analysis and yielding efficient computations. When dealing with output spaces with infinite cardinality, a suitable implicit formulation of the estimator is shown to be crucial.

Citations

• Learning with a Wasserstein Loss
• A Consistent Regularization Approach for Structured Prediction
• On Structured Prediction Theory with Calibrated Convex Surrogate Losses
• A Structured Prediction Approach for Label Ranking
• Learning with SGD and Random Features
• Leveraging Low-Rank Relations Between Surrogate Tasks in Structured\n Prediction
• Structured Prediction with Projection Oracles

Cited by

• Non-Stationary Online Structured Prediction with Surrogate Losses
• Towards Size-invariant Salient Object Detection: A Generic Evaluation and Optimization Approach
• A Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning
• Establishing Linear Surrogate Regret Bounds for Convex Smooth Losses via Convolutional Fenchel-Young Losses

Related

• A Consistent Regularization Approach for Structured Prediction
• Learning Output Embeddings in Structured Prediction
• Manifold Structured Prediction
• Structured Prediction with Projection Oracles
• Structured Prediction in Online Learning