A General Framework for Consistent Structured Prediction with Implicit Loss Embeddings
arXiv:2002.05424
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.
53 pages
References in corpus (12)
- Learning with a Wasserstein Loss
- Generalization Properties of Learning with Random Features
- Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distance
- A Consistent Regularization Approach for Structured Prediction
- Learning with SGD and Random Features
- Structured Prediction Theory Based on Factor Graph Complexity
- A Generalized Kernel Approach to Structured Output Learning
- A Structured Prediction Approach for Label Ranking
- Structured Prediction with Projection Oracles
- On Structured Prediction Theory with Calibrated Convex Surrogate Losses
- Leveraging Low-Rank Relations Between Surrogate Tasks in Structured Prediction
- Geometric Losses for Distributional Learning
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- Sketch In, Sketch Out: Accelerating both Learning and Inference for Structured Prediction with Kernels
- Structured Prediction with Partial Labelling through the Infimum Loss
- Learning Output Embeddings in Structured Prediction