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.

中文翻译：

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融合套索相加模型


我们考虑使用在 n 个独立观测值上测量的 p 个协变量来预测结果变量的问题，其中需要附加的、灵活的和可解释的拟合。我们提出了融合套索加性模型（FLAM），其中每个加性函数被估计为具有少量自适应选择的结的分段常数。 FLAM 是凸优化问题的解决方案，为此提供了一种保证收敛到全局最优的简单算法。 FLAM 在高维度上被证明是一致的，并且提出了其自由度的无偏估计器。我们在模拟研究和两个数据集上评估 FLAM 的性能。补充材料可在线获取，R 包 Flam 可在 CRAN 上获取。