Han Xintian, Goldstein Mark, Puli Aahlad, Wies Thomas, Perotte Adler J, Ranganath Rajesh
NYU.
Columbia University.
Adv Neural Inf Process Syst. 2021 Dec;34:2160-2172.
Deep models trained through maximum likelihood have achieved state-of-the-art results for survival analysis. Despite this training scheme, practitioners evaluate models under other criteria, such as binary classification losses at a chosen set of time horizons, e.g. Brier score (BS) and Bernoulli log likelihood (BLL). Models trained with maximum likelihood may have poor BS or BLL since maximum likelihood does not directly optimize these criteria. Directly optimizing criteria like BS requires inverse-weighting by the censoring distribution. However, estimating the censoring model under these metrics requires inverse-weighting by the failure distribution. The objective for each model requires the other, but neither are known. To resolve this dilemma, we introduce . In these games, objectives for each model are built from re-weighted estimates featuring the other model, where the latter is held fixed during training. When the loss is proper, we show that the games always have the true failure and censoring distributions as a stationary point. This means models in the game do not leave the correct distributions once reached. We construct one case where this stationary point is unique. We show that these games optimize BS on simulations and then apply these principles on real world cancer and critically-ill patient data.
通过最大似然法训练的深度模型在生存分析中取得了领先成果。尽管采用了这种训练方案，但从业者会根据其他标准评估模型，例如在选定的一组时间范围内的二元分类损失，例如布里尔评分（BS）和伯努利对数似然（BLL）。由于最大似然法并不直接优化这些标准，因此用最大似然法训练的模型可能具有较差的BS或BLL。直接优化诸如BS之类的标准需要按删失分布进行逆加权。然而，在这些指标下估计删失模型需要按失败分布进行逆加权。每个模型的目标都需要另一个模型的信息，但两者均未知。为了解决这一困境，我们引入了……在这些博弈中，每个模型的目标都是基于以另一个模型为特征的重新加权估计构建的，其中后者在训练期间保持固定。当损失是恰当的时候，我们表明这些博弈总是以真实的失败和删失分布作为一个稳定点。这意味着博弈中的模型一旦达到就不会偏离正确的分布。我们构建了一个这种稳定点唯一的案例。我们表明这些博弈在模拟中优化了BS，然后将这些原理应用于真实世界的癌症和重症患者数据。
