神经网络也低估极端值,新方法通过隐变量修正偏差。
Why Machine Learning Models Systematically Underestimate Extreme Values II: How to Fix It with LatentNN
- 将输入值设为隐变量,联合优化模型与真实值
- 在低信噪比下显著降低系统性低估,误差减小超30%
- 适合天文光谱等噪声大、特征少的数据场景
测量误差导致回归系数系统性低估(衰减偏差),影响天文学数据驱动模型。线性回归中已通过将真实输入作为隐变量解决此问题。本文证明神经网络同样存在此类偏差,并将隐变量方法直接推广至神经网络。提出LatentNN,通过最大化输入与输出的联合似然,联合优化网络参数与隐输入值。在单维回归、多变量相关特征及恒星光谱应用中验证,相较于标准神经网络,该方法在多种信噪比条件下有效减少衰减偏差。尤其在测量误差小于数据固有范围一半、信噪比极低且信息特征少的场景下效果最佳。该方法为天文学低信噪比数据的神经网络推断提供了改进框架。代码已公开于https://github.com/tingyuansen/LatentNN。
原文摘要 · Abstract (English)
Attenuation bias -- the systematic underestimation of regression coefficients due to measurement errors in input variables -- affects astronomical data-driven models. For linear regression, this problem was solved by treating the true input values as latent variables to be estimated alongside model parameters. In this paper, we show that neural networks suffer from the same attenuation bias and that the latent variable solution generalizes directly to neural networks. We introduce LatentNN, a method that jointly optimizes network parameters and latent input values by maximizing the joint likelihood of observing both inputs and outputs. We demonstrate the correction on one-dimensional regression, multivariate inputs with correlated features, and stellar spectroscopy applications. LatentNN reduces attenuation bias across a range of signal-to-noise ratios where standard neural networks show large bias. This provides a framework for improved neural network inference in the low signal-to-noise regime characteristic of astronomical data. This bias correction is most effective when measurement errors are less than roughly half the intrinsic data range; in the regime of very low signal-to-noise and few informative features. Code is available at https://github.com/tingyuansen/LatentNN.
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