Sparse conditional copula models for structured output regression

作者：Kim Minyoung^*

来源：Pattern Recognition, 2016, 60: 761-769.

DOI：10.1016/j.patcog.2016.03.027

• Multiple output regression
• Sparse inverse covariance estimation
• Copula models
• Gaussian random fields

We deal with the multiple output regression task where the central theme is to capture the sparse output correlation among the output variables. Sparse inverse covariance learning of linear Gaussian conditional models has been recently studied, shown to achieve superb prediction performance. However, it can fail when the underlying true input-output process is non-Gaussian and/or non-linear. We introduce a novel sparse conditional copula model to represent the joint density of the output variables. By incorporating a Gaussian copula function, yet modeling univariate marginal densities by (non-Gaussian) mixtures of experts, we achieve high flexibility in representation that admits non-linear and non-Gaussian densities. We then propose a sparse learning method for this copula-based model that effectively imposes sparsity in the conditional dependency among output variables. The learning optimization is efficient as it can be decomposed into gradient-descent marginal density estimation and the sparse inverse covariance learning for the copula function. Improved performance of the proposed approach is demonstrated on several interesting image/vision tasks with high dimensions.

• 出版日期2016-12