Generalized Additive Model Selection

By Alexandra Chouldechova, Trevor J. Hastie. 2015

91 citations recorded by the source corpus.

We introduce GAMSEL (Generalized Additive Model Selection), a penalized likelihood approach for fitting sparse generalized additive models in high dimension. Our method interpolates between null, linear and additive models by allowing the effect of each variable to be estimated as being either zero, linear, or a low-complexity curve, as determined by the data. We present a blockwise coordinate descent procedure for efficiently optimizing the penalized likelihood objective over a dense grid of the tuning parameter, producing a regularization path of additive models. We demonstrate the performance of our method on both real and simulated data examples, and compare it with existing techniques for additive model selection.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Generalized Sparse Additive Models (2019, background): “There are also a number of other proposals that do not quite fall in the GSAM framework [Chouldechova and Hastie, 2015, Fan et al., 2012, Yin et al., 2012].”
Sparse Partially Linear Additive Models (2014, methodology): “After posting the initial draft of this article online, we learned of a similar method being developed independently and concurrently to ours (Chouldechova and Hastie 2015); their approach to the GPLAM problem also makes use of an overlapping group lasso penalty, but uses a different form of…”
Optimization Models for Machine Learning: A Survey (2019, background): “Alternatively, [67] proposes to fit a constrained version of GAMs by solving a conic programming problem.”
Hierarchical Sparse Modeling: A Choice of Two Group Lasso Formulations (2015, background): “…2016), covariance matrix estimation (Levina, Rothman and Zhu, 2008, Rothman, Levina and Zhu, 2010, Bien, Bunea and Xiao, 2016), additive models (Lou et al., 2016, Chouldechova and Hastie, 2015), time series models (Nicholson, Bien and Matteson, 2014), and multiple kernel learning (Bach, 2008).”
COGAM: Measuring and Moderating Cognitive Load in Machine Learning Model Explanations (2020, background): “GAMSEL [10] and SPLAM [38] have formulated new optimization objectives to induce sparsity and partial linearity to find one GAM solution that has the best accuracy.”