mlsanityData to 14 Oct 2026

A General Framework for Consistent Structured Prediction with Implicit Loss Embeddings

arXiv 2002.05424 ↗First posted 13 Feb 2020stat.ML cs.LG math.STcited by 35

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Abstract (arXiv)

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.

Key facts. Cited by 35 papers in the map (data through 14 Oct 2026). First posted on arXiv 13 Feb 2020.

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Citing papers per year: 2021: 5; 2022: 4; 2023: 8; 2024: 12; 2025: 5; 2026: 1.

35 papers.

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  1. 2023Sharp Spectral Rates for Koopman Operator Learningcited by 36
  2. 2024A Universal Growth Rate for Learning with Smooth Surrogate Lossescited by 24
  3. 2021PSD Representations for Effective Probability Modelscited by 23
  4. 2022Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenterscited by 22
  5. 2023Towards Optimal Sobolev Norm Rates for the Vector-Valued Regularized Least-Squares Algorithmcited by 22
  6. 2024AUCSeg: AUC-oriented Pixel-level Long-tail Semantic Segmentationcited by 18
  7. 2023Estimating Koopman operators with sketching to provably learn large scale dynamical systemscited by 15
  8. 2024Size-invariance Matters: Rethinking Metrics and Losses for Imbalanced Multi-object Salient Object Detectioncited by 14
  9. 2024Optimal Rates for Vector-Valued Spectral Regularization Learning Algorithmscited by 12
  10. 2021Fast rates in structured predictioncited by 11
  11. 2024Nonparametric Instrumental Regression via Kernel Methods is Minimax Optimalcited by 8
  12. 2024Online Structured Prediction with Fenchel--Young Losses and Improved Surrogate Regret for Online Multiclass Classification with Logistic Losscited by 7
23 more
  1. 2024Operator World Models for Reinforcement Learningcited by 7
  2. 2022Fast Kernel Methods for Generic Lipschitz Losses via p-Sparsified Sketchescited by 5
  3. 2022Vector-Valued Least-Squares Regression under Output Regularity Assumptionscited by 5
  4. 2023Sketch In, Sketch Out: Accelerating both Learning and Inference for Structured Prediction with Kernelscited by 5
  5. 2024Overcoming Saturation in Density Ratio Estimation by Iterated Regularizationcited by 5
  6. 2021Disambiguation of weak supervision with exponential convergence ratescited by 4
  7. 2023A randomized algorithm to solve reduced rank operator regressioncited by 4
  8. 2022Active Labeling: Streaming Stochastic Gradientscited by 3
  9. 2024Proper losses regret at least 1/2-ordercited by 3
  10. 2024Generalization Bounds of Surrogate Policies for Combinatorial Optimization Problemscited by 3
  11. 2024Deep Sketched Output Kernel Regression for Structured Predictioncited by 2
  12. 2024Structured Prediction in Online Learningcited by 2
  13. 2025Establishing Linear Surrogate Regret Bounds for Convex Smooth Losses via Convolutional Fenchel-Young Lossescited by 2
  14. 2021Beyond Tikhonov: Faster Learning with Self-Concordant Losses via Iterative Regularizationcited by 1
  15. 2023A Structured Prediction Approach for Robot Imitation Learningcited by 1
  16. 2023Exploiting Edge Features in Graphs with Fused Network Gromov-Wasserstein Distancecited by 1
  17. 2025Bandit and Delayed Feedback in Online Structured Predictioncited by 1
  18. 2025A Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learningcited by 1
  19. 2021Structured Prediction for CRiSP Inverse Kinematics Learning with Misspecified Robot Modelscited by 0
  20. 2023On Certified Generalization in Structured Predictioncited by 0
  21. 2025Towards Size-invariant Salient Object Detection: A Generic Evaluation and Optimization Approachcited by 0
  22. 2025Non-Stationary Online Structured Prediction with Surrogate Lossescited by 0
  23. 2026Beyond Surrogates: A Quantitative Analysis for Inter-Metric Relationshipscited by 0