在统计学中,最大似然估计(maximum likelihood estimation, MLE)是通过最大化似然函数估计概率分布参数的一种方法,使观测数据在假设的统计模型下最有可能。参数空间中使似然函数最大化的点称为最大似然估计。最大似然逻辑既直观又灵活,因此该方法已成为统计推断的主要手段。

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最大似然(Maximum likelihood, ML)是最基本、最通用的统计估计技术之一。受最近分布函数估计进展的启发,我们提出压缩最大似然(CML),它将ML应用于压缩样本。然后,我们证明了CML对于离散和连续域上的几个基本学习任务是样本有效的,包括具有结构的学习密度、估计概率多集和推断对称分布函数。

https://proceedings.mlr.press/v139/hao21c.html

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Although deep learning models have driven state-of-the-art performance on a wide array of tasks, they are prone to spurious correlations that should not be learned as predictive clues. To mitigate this problem, we propose a causality-based training framework to reduce the spurious correlations caused by observed confounders. We give theoretical analysis on the underlying general Structural Causal Model (SCM) and propose to perform Maximum Likelihood Estimation (MLE) on the interventional distribution instead of the observational distribution, namely Counterfactual Maximum Likelihood Estimation (CMLE). As the interventional distribution, in general, is hidden from the observational data, we then derive two different upper bounds of the expected negative log-likelihood and propose two general algorithms, Implicit CMLE and Explicit CMLE, for causal predictions of deep learning models using observational data. We conduct experiments on both simulated data and two real-world tasks: Natural Language Inference (NLI) and Image Captioning. The results show that CMLE methods outperform the regular MLE method in terms of out-of-domain generalization performance and reducing spurious correlations, while maintaining comparable performance on the regular evaluations.

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