On the Consistency of Feature Selection With Lasso for Non-linear Targets
On the Consistency of Feature Selection With Lasso for Non-linear Targets
复制标题
非线性目标Lasso特征选择的一致性研究
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Soumya Ray
中科院分区：
文献类型：
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作者：
Yue Zhang;Weihong Guo;Soumya Ray
特征选择中的一个重要问题是，给定足够的数据，选择策略是否能恢复“真实”的特征集。我们在流行的最小绝对收缩和选择算子（Lasso）特征选择策略的背景下研究了这个问题。特别地，我们考虑了模型被错误指定的情况，使得学习到的模型是线性的，而潜在的实际目标是非线性的。令人惊讶的是，我们证明了在一定条件下，Lasso仍然能够在这种情况下恢复正确的特征。我们还进行了数值研究，以经验验证理论结果，并探讨了证明成立的条件的必要性。
An important question in feature selection is whether a selection strategy recovers the "true" set of features, given enough data. We study this question in the context of the popular Least Absolute Shrinkage and Selection Operator (Lasso) feature selection strategy. In particular, we consider the scenario when the model is misspecified so that the learned model is linear while the underlying real target is nonlinear. Surprisingly, we prove that under certain conditions, Lasso is still able to recover the correct features in this case. We also carry out numerical studies to empirically verify the theoretical results and explore the necessity of the conditions under which the proof holds.