有限集最优模型精确路径的线性时间动态规划
Linear time dynamic programming for the exact path of optimal models selected from a finite set
摘要：
许多学习算法都是根据寻找模型参数来制定的，这些参数使数据拟合损失函数加上正则化器最小化。当正则化涉及l0伪范数时，得到的正则化路径由有限的模型集组成。现有的计算正则化路径中断点的最快算法在模型数量上是二次的，因此它对高维问题的扩展性很差。我们提供了新的形式证明，动态规划算法可以用来计算断点在线性时间。对变点检测问题的实验结果表明，相对于网格搜索和以前的二次时间算法，该算法提高了精度和速度。
英文摘要：
Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l0 pseudo-norm, the resulting regularization path consists of a finite set of models. The fastest existing algorithm for computing the breakpoints in the regularization path is quadratic in the number of models, so it scales poorly to high dimensional problems. We provide new formal proofs that a dynamic programming algorithm can be used to compute the breakpoints in linear time. Empirical results on changepoint detection problems demonstrate the improved accuracy and speed relative to grid search and the previous quadratic time algorithm.
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