Strongly Hierarchical Factorization Machines and ANOVA Kernel Regression
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High-order parametric models that include terms for feature interactions are applied to various data min- ing tasks, where ground truth depends on interactions of features. However, with sparse data, the high- dimensional parameters for feature interactions often face three issues: expensive computation, difficulty in parameter estimation and lack of structure. Previous work has proposed approaches which can partially re- solve the three issues. In particular, models with fac- torized parameters (e.g. Factorization Machines) and sparse learning algorithms (e.g. FTRL-Proximal) can tackle the first two issues but fail to address the third. Regarding to unstructured parameters, constraints or complicated regularization terms are applied such that hierarchical structures can be imposed. However, these methods make the optimization problem more challeng- ing. In this work, we propose Strongly Hierarchical Factorization Machines and ANOVA kernel regression where all the three issues can be addressed without making the optimization problem more difficult. Ex- perimental results show the proposed models signifi- cantly outperform the state-of-the-art in two data min- ing tasks: cold-start user response time prediction and stock volatility prediction.
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