A Tunable Loss Function for Binary Classification
A Tunable Loss Function for Binary Classification
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DOI：
10.1109/isit.2019.8849796
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发表时间：
2019-02
期刊：
影响因子：
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通讯作者：
Tyler Sypherd;Mario Díaz;L. Sankar;P. Kairouz
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文献类型：
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作者：
Tyler Sypherd;Mario Díaz;L. Sankar;P. Kairouz
我们提出了α-Loss，α∈[1，∞]，一个可调的二进制分类损失函数，它连接了原木损失(α=1)和0-1损失(α=∞)。我们证明了α损失具有等价的基于边际的形式，并且是分类校准的，这是理想但难处理的0-1损失的好的替代损失函数的两个理想性质。对于基于Logistic回归的分类，我们通过利用经验风险函数的李普希兹效应以及最近关于经验风险函数的景观特征的最新结果，提供了经验风险临界点的α损失的经验风险与预期风险之间的差异的上界。最后，对于Logistic回归，我们证明了α=2时的α损失要好于LOG损失。
We present α-loss, α ∈ [1, ∞], a tunable loss function for binary classification that bridges log-loss (α = 1) and 0-1 loss (α = ∞). We prove that α-loss has an equivalent margin-based form and is classification-calibrated, two desirable properties for a good surrogate loss function for the ideal yet intractable 0-1 loss. For logistic regression-based classification, we provide an upper bound on the difference between the empirical and expected risk for α-loss at the critical points of the empirical risk by exploiting its Lipschitzianity along with recent results on the landscape features of empirical risk functions. Finally, we show that α-loss with α = 2 performs better than log-loss on MNIST for logistic regression.