Causal Inference with Noisy and Missing Covariates via Matrix Factorization
Causal Inference with Noisy and Missing Covariates via Matrix Factorization
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发表时间：
2018-06
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通讯作者：
Nathan Kallus;Xiaojie Mao;Madeleine Udell
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作者：
Nathan Kallus;Xiaojie Mao;Madeleine Udell
在观察性研究中有效的因果推断通常需要控制混杂因素。然而，在实践中，混杂因素的测量可能会有噪声，并可能导致对因果影响的有偏见的估计。我们表明，我们可以减少测量噪声引起的偏差，使用大量的潜在混杂噪声的噪声测量。我们提出使用矩阵因式分解从有噪声的协变量中推断混杂因素，这是一个灵活和原则性的框架，它适应缺失值，适应广泛的数据类型，并可以增加许多因果推理方法。利用指数族矩阵补全预处理，我们对诱导平均处理效应估计的误差进行了界，并证明了它在线性回归设置下是一致的。我们用合成数据和真实的临床数据在数值实验中证明了所提出的方法的有效性。
Valid causal inference in observational studies often requires controlling for confounders. However, in practice measurements of confounders may be noisy, and can lead to biased estimates of causal effects. We show that we can reduce the bias caused by measurement noise using a large number of noisy measurements of the underlying confounders. We propose the use of matrix factorization to infer the confounders from noisy covariates, a flexible and principled framework that adapts to missing values, accommodates a wide variety of data types, and can augment many causal inference methods. We bound the error for the induced average treatment effect estimator and show it is consistent in a linear regression setting, using Exponential Family Matrix Completion preprocessing. We demonstrate the effectiveness of the proposed procedure in numerical experiments with both synthetic data and real clinical data.