Timezone: »
Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of regions and region-specific models. This paper proposes novel convex region-specific linear models, which we refer to as partition-wise linear models. Our key ideas are 1) assigning linear models not to regions but to partitions (region-specifiers) and representing region-specific linear models by linear combinations of partition-specific models, and 2) optimizing regions via partition selection from a large number of given partition candidates by means of convex structured regularizations. In addition to providing initialization-free globally-optimal solutions, our convex formulation makes it possible to derive a generalization bound and to use such advanced optimization techniques as proximal methods and decomposition of the proximal maps for sparsity-inducing regularizations. Experimental results demonstrate that our partition-wise linear models perform better than or are at least competitive with state-of-the-art region-specific or locally linear models.
Author Information
Hidekazu Oiwa (The University of Tokyo)
Ryohei Fujimaki (NEC Data Science Research Laboratories)
More from the Same Authors
-
2017 Poster: Scalable Model Selection for Belief Networks »
Zhao Song · Yusuke Muraoka · Ryohei Fujimaki · Lawrence Carin -
2016 Poster: Large-Scale Price Optimization via Network Flow »
Shinji Ito · Ryohei Fujimaki -
2016 Oral: Large-Scale Price Optimization via Network Flow »
Shinji Ito · Ryohei Fujimaki -
2014 Poster: Exclusive Feature Learning on Arbitrary Structures via $\ell_{1,2}$-norm »
Deguang Kong · Ryohei Fujimaki · Ji Liu · Feiping Nie · Chris Ding -
2013 Poster: Factorized Asymptotic Bayesian Inference for Latent Feature Models »
Kohei Hayashi · Ryohei Fujimaki