Outcomes of the Equivalence of Adaptive Ridge with Least Absolute Shrinkage
Outcomes of the Equivalence of Adaptive Ridge with Least Absolute Shrinkage
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发表时间：
1998-12
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通讯作者：
Yves Grandvalet;S. Canu
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作者：
Yves Grandvalet;S. Canu
自适应岭是岭回归的一种特殊形式，它平衡了模型中每个参数的二次惩罚。它被证明是等效的套索（最小绝对收缩和选择算子），在这个意义上，这两个程序产生相同的估计。因此，Lasso可以被视为一个特殊的二次惩罚器。从这个观察，我们得到一个不动点算法来计算Lasso解决方案。类比也提供了一个新的超参数，有效地调整模型的复杂性。最后，我们提出了一系列可能的扩展套索执行稀疏回归核平滑，添加剂建模和神经网络训练。
Adaptive Ridge is a special form of Ridge regression, balancing the quadratic penalization on each parameter of the model. It was shown to be equivalent to Lasso (least absolute shrinkage and selection operator), in the sense that both procedures produce the same estimate. Lasso can thus be viewed as a particular quadratic penalizer. From this observation, we derive a fixed point algorithm to compute the Lasso solution. The analogy provides also a new hyper-parameter for tuning effectively the model complexity. We finally present a series of possible extensions of lasso performing sparse regression in kernel smoothing, additive modeling and neural net training.