Fused Lasso Additive Model

By Ashley Petersen, Daniela M. Witten, Noah R. Simon. 2014

76 citations recorded by the source corpus.

We consider the problem of predicting an outcome variable using p covariates that are measured on n independent observations, in a setting in which additive, flexible, and interpretable fits are desired. We propose the fused lasso additive model (FLAM), in which each additive function is estimated to be piecewise constant with a small number of adaptively chosen knots. FLAM is the solution to a convex optimization problem, for which a simple algorithm with guaranteed convergence to a global optimum is provided. FLAM is shown to be consistent in high dimensions, and an unbiased estimator of its degrees of freedom is proposed. We evaluate the performance of FLAM in a simulation study and on two datasets. Supplemental materials are available online, and the R package flam is available on CRAN.

Subfields: Statistics and Probability, Optimization & Training

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Citations in the corpus

Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges (2021, methodology): “…functions are estimated by splines, many works apply convex regularizers (e.g., `1) to control both smoothness and sparsity (Lin et al., 2006; Ravikumar et al., 2009; Meier et al., 2009; Yin and Yu, 2017; Petersen et al., 2016; Lou et al., 2016; Sadhanala et al., 2019; Haris et al., 2019).”
Generalized Sparse Additive Models (2019, methodology): “Theorem 1 improves upon the slow rates established by Petersen et al. [2016] of the order log( np ) /n ; Theorem 2 establishes fast rates by solving the problem which Sadhanala and Tibshirani [2018] characterized as “... still an open problem”.”
Convex-constrained Sparse Additive Modeling and Its Extensions (2017, methodology): “The class of bounded variation functions motivates the development of the fused lasso additive model (FLAM), in which each component function fj is estimated to be piecewise constant with a small number of adaptively chosen knots (Petersen et al., 2016).”
Additive models with trend filtering (2017, background): “Petersen et al. (2016) studied the estimator in (44) when k = 0, i.”
Sparse Partially Linear Additive Models (2014, methodology): “Also, Petersen, Witten, and Simon (2016) in a recent preprint propose a method that combines feature selection and nonlinear, piecewise-constant modeling using a fused-lasso penalty.”
Penalized Estimation in Additive Regression with High-Dimensional Data (2017, methodology): “Previously, only the slower rate, {log(np)/n}1/2, was obtained for in-sample prediction in additive regression with the bounded variation space V1 by Petersen et al. (2016).”
Wavelet regression and additive models for irregularly spaced data (2019, unknown): “For sparse additive waveMesh ( λ 2 6 = 0 ), the problem can be solved by solving (9) with λ 2 = 0 following by a soft-scaling operation [Petersen et al., 2016, Lemma 7.1].”