DeepAI AI Chat
Log In Sign Up

A General Framework for Consistent Structured Prediction with Implicit Loss Embeddings

by   Carlo Ciliberto, et al.

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.


page 1

page 2

page 3

page 4


Manifold Structured Prediction

Structured prediction provides a general framework to deal with supervis...

Structured Prediction with Projection Oracles

We propose in this paper a general framework for deriving loss functions...

Output Space Search for Structured Prediction

We consider a framework for structured prediction based on search in the...

Learning Output Embeddings in Structured Prediction

A powerful and flexible approach to structured prediction consists in em...

Localized Structured Prediction

Key to structured prediction is exploiting the problem structure to simp...

A Consistent Regularization Approach for Structured Prediction

We propose and analyze a regularization approach for structured predicti...

Approximation and Structured Prediction with Sparse Wasserstein Barycenters

We develop a general theoretical and algorithmic framework for sparse ap...