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Merge pull request #27 from hi-paris/gaetanbrison-patch-4
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gaetanbrison authored May 14, 2024
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Expand Up @@ -8,7 +8,7 @@ Structured prediction or structured (output) learning is an umbrella term for su

Similar to commonly used supervised learning techniques, structured prediction models are typically trained by means of observed data in which the true prediction value is used to adjust model parameters. Due to the complexity of the model and the interrelations of predicted variables the process of prediction using a trained model and of training itself is often computationally infeasible and approximate inference and learning methods are used.

![sp]([https://raw.githubusercontent.com/mlfoundations/open_clip/main/docs/CLIP.png](https://i.postimg.cc/nVvFxCky/Screenshot-2024-05-14-at-10-04-42.png))
![sp](https://i.postimg.cc/nVvFxCky/Screenshot-2024-05-14-at-10-04-42.png)

A powerful and flexible approach to structured prediction consists in embedding the structured objects to be predicted into a feature space of possibly infinite dimension by means of output kernels, and then, solving a regression problem in this output space. A prediction in the original space is computed by solving a pre-image problem. In such an approach, the embedding, linked to the target loss, is defined prior to the learning phase. In this work, we propose to jointly learn a finite approximation of the output embedding and the regression function into the new feature space. For that purpose, we leverage a priori information on the outputs and also unexploited unsupervised output data, which are both often available in structured prediction problems. We prove that the resulting structured predictor is a consistent estimator, and derive an excess risk bound. Moreover, the novel structured prediction tool enjoys a significantly smaller computational complexity than former output kernel methods. The approach empirically tested on various structured prediction problems reveals to be versatile and able to handle large datasets.

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