A General Framework for Consistent Structured Prediction with Implicit Loss Embeddings
This work addresses a foundational gap in structured prediction for researchers in machine learning, extending it beyond discrete outputs to more general settings.
The authors tackled the problem of structured prediction in non-vectorial output spaces like manifolds or probability measures, proposing a framework that uses implicit loss embeddings to define geometry, enabling sharp statistical analysis and efficient computations.
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.