Key to structured prediction is exploiting the problem's structure to simplify the learning process. A major challenge arises when data exhibit a local structure (i.e., are made ``by parts'') that can be leveraged to better approximate the relation between (parts of) the input and (parts of) the output. Recent literature on signal processing, and in particular computer vision, shows that capturing these aspects is indeed essential to achieve state-of-the-art performance. However, in this context algorithms are typically derived on a case-by-case basis. In this work we propose the first theoretical framework to deal with part-based data from a general perspective and study a novel method within the setting of statistical learning theory. Our analysis is novel in that it explicitly quantifies the benefits of leveraging the part-based structure of a problem on the learning rates of the proposed estimator.

The model is learned by breaking the structure into parts and performing kernel ridge regression on the parts. They show elaborate convergence rate analysis in the estimation. The theoretical analysis is the strong part of this paper. In a lot of computer vision and NLP applications the latest research is about capturing long range dependencies. The correlation in Figure 1 is highly concentrated at the central patch because it's the average of many different images, but on individual images the correlation patten can be very different.

The authors propose a general theoretical framework for structured prediction that deals with cases where the data exhibits a local structure, so that the inputs and outputs can be decomposed into parts. The reviewers deemed the theoretical contributions to be of original and of a high quality. The author response addressed the perceived weaknesses, in particular in the empirical evaluation, in a satisfcatory way.

Key to structured prediction is exploiting the problem's structure to simplify the learning process. A major challenge arises when data exhibit a local structure (i.e., are made by parts'') that can be leveraged to better approximate the relation between (parts of) the input and (parts of) the output. Recent literature on signal processing, and in particular computer vision, shows that capturing these aspects is indeed essential to achieve state-of-the-art performance. However, in this context algorithms are typically derived on a case-by-case basis. In this work we propose the first theoretical framework to deal with part-based data from a general perspective and study a novel method within the setting of statistical learning theory.

Key to structured prediction is exploiting the problem's structure to simplify the learning process. A major challenge arises when data exhibit a local structure (i.e., are made by parts'') that can be leveraged to better approximate the relation between (parts of) the input and (parts of) the output. Recent literature on signal processing, and in particular computer vision, shows that capturing these aspects is indeed essential to achieve state-of-the-art performance. However, in this context algorithms are typically derived on a case-by-case basis. In this work we propose the first theoretical framework to deal with part-based data from a general perspective and study a novel method within the setting of statistical learning theory.