论文标题
关于因果位置尺度噪声模型的可识别性和估计
On the Identifiability and Estimation of Causal Location-Scale Noise Models
论文作者
论文摘要
我们研究了位置尺度或异质噪声模型（LSNMS）的类别，其中可以将$ y $ $ y $编写为$ x $的函数，而噪声源$ n $独立于$ x $，可以用正函数$ g $缩放，即$ g $，即$ y = y = f（x） + g（x） + g（x） + g（x）n $。尽管模型类具有一般性，但我们表明在某些病理病例中可以识别因果方向。为了从经验验证这些理论发现，我们提出了两个基于（非线性）特征图的估计值的估计值，另一个基于神经网络。两者都将$ y $的条件分布构成给定$ x $的条件分布，作为由其自然参数进行参数的高斯参数。当正确指定特征图时，我们证明我们的估计器是共同凹的，并且是因果效应识别任务的一致估计器。尽管神经网络无法继承这些保证，但它可以符合任意复杂性的功能，并在基准中达到最先进的性能。
We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect $Y$ can be written as a function of the cause $X$ and a noise source $N$ independent of $X$, which may be scaled by a positive function $g$ over the cause, i.e., $Y = f(X) + g(X)N$. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of $Y$ given $X$ as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.
