A Generalized Kernel Approach to Structured Output Learning

By Hachem Kadri, Mohammad Ghavamzadeh, Philippe Preux. 2012

38 citations recorded by the source corpus.

We study the problem of structured output learning from a regression perspective. We first provide a general formulation of the kernel dependency estimation (KDE) approach to this problem using operator-valued kernels. Our formulation overcomes the two main limitations of the original KDE approach, namely the decoupling between outputs in the image space and the inability to use a joint feature space. We then propose a covariance-based operator-valued kernel that allows us to take into account the structure of the kernel feature space. This kernel operates on the output space and only encodes the interactions between the outputs without any reference to the input space. To address this issue, we introduce a variant of our KDE method based on the conditional covariance operator that in addition to the correlation between the outputs takes into account the effects of the input variables. Finally, we evaluate the performance of our KDE approach on three structured output problems, and compare it to the state-of-the-art kernel-based structured output regression methods.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

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Citations in the corpus

Learning Theory for Distribution Regression (2014, background): “, 2016), or structured output prediction (Brouard et al., 2011; Kadri et al., 2013) fall under the same umbrella: they can be naturally phrased as learning vectorvalued functions (Micchelli and Pontil, 2005).”
Operator-valued Kernels for Learning from Functional Response Data (2015, background): “…in other machine learning problems such as collaborative filtering (Abernethy et al., 2009) and structured output prediction (Brouard et al., 2011; Kadri et al., 2013b) by building operator-valued kernels that can capture not only the functional information of responses, but also other types of…”
Input Output Kernel Regression (2016, background): “The interested reader may want to refer to Honeine and Richard (2011) or Kadri et al. (2013) to beneﬁt from existing pre-image algorithms to solve structured output learning tasks.”
A Consistent Regularization Approach for Structured Prediction (2016, methodology): “As a consequence, approaches in [12, 13, 14] are not consistent in the general case.”