mRSC: Multidimensional Robust Synthetic Control
mRSC: Multidimensional Robust Synthetic Control
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mRSC：多维鲁棒综合控制
DOI：
10.1145/3309697.3331507
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Shen, Dennis
中科院分区：
文献类型：
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作者：
Amjad, Muhammad Jehangir;Misra, Vishal;Shah, Devavrat;Shen, Dennis
在评估政策的影响时（例如，枪支控制）对感兴趣的度量（例如，犯罪率），进行随机对照试验可能不可能或不可行。在只有观测数据的情况下，综合控制方法[2-4]提供了一种流行的数据驱动方法，通过结合“类似”替代品或单位（称为“供体”）的测量结果来估计“综合”或“虚拟”控制。最近，提出了鲁棒综合控制（RSC）[7]作为SC的推广，以克服丢失数据和高水平噪声的挑战，同时消除对选择供体的专家领域知识的依赖。然而，SC和RSC（及其变体）在干预前的时间太短时，估计效果不佳。作为这项工作的主要贡献，我们提出了一个推广的一维RSC多维鲁棒综合控制，mRSC。我们提出的机制，mRSC，结合多种类型的测量（或指标），除了测量的兴趣估计合成控制，从而克服了由于有限的预干预数据量的推理差的挑战。我们表明，mRSC算法，当使用K相关的度量，导致一致的估计的合成控制的目标单位的利益在任何度量。我们的有限样本分析表明，我们的预测的均方误差（MSE）衰减到零的速度比RSC算法快K和K的因子，分别为训练（干预前）和测试（干预后）时期。此外，我们提出了一个原则性的计划，联合收割机多个指标的利益，通过诊断测试，评估如果添加一个指标可以预期，以改善推理。我们验证mRSC性能的机制也是这项工作的重要和相关贡献：时间序列预测。当时间概念是相对的而不是绝对的时，我们提出了一种基于有限数据预测时间序列未来演变的方法，即，在那里，我们可以获得一个已经经历了预期未来演变的捐助者库。我们进行了广泛的实验，以确定mRSC在三种不同情况下的功效：使用已知因子模型合成生成的数据预测感兴趣指标的演变，并分别预测沃尔玛商店和板球游戏的每周销售额和得分轨迹。
When evaluating the impact of a policy (e.g., gun control) on a metric of interest (e.g., crime-rate), it may not be possible or feasible to conduct a randomized control trial. In such settings where only observational data is available, synthetic control (SC) methods [2-4] provide a popular data-driven approach to estimate a "synthetic" or "virtual" control by combining measurements of "similar" alternatives or units (called "donors"). Recently, robust synthetic control (RSC) [7] was proposed as a generalization of SC to overcome the challenges of missing data and high levels of noise, while removing the reliance on expert domain knowledge for selecting donors. However, both SC and RSC (and its variants) suffer from poor estimation when the pre-intervention period is too short. As the main contribution of this work, we propose a generalization of unidimensional RSC to multi-dimensional Robust Synthetic Control, mRSC. Our proposed mechanism, mRSC, incorporates multiple types of measurements (or metrics) in addition to the measurement of interest for estimating a synthetic control, thus overcoming the challenge of poor inference due to limited amounts of pre-intervention data. We show that the mRSC algorithm, when using K relevant metrics, leads to a consistent estimator of the synthetic control for the target unit of interest under any metric. Our finite-sample analysis suggests that the mean-squared error (MSE) of our predictions decays to zero at a rate faster than the RSC algorithm by a factor of K and √K for the training (pre-intervention) and testing (post-intervention) periods, respectively. Additionally, we propose a principled scheme to combine multiple metrics of interest via a diagnostic test that evaluates if adding a metric can be expected to result in improved inference. Our mechanism for validating mRSC performance is also an important and related contribution of this work: time series prediction. We propose a method to predict the future evolution of a time series based on limited data when the notion of time is relative and not absolute, i.e., where we have access to a donor pool that has already undergone the desired future evolution. We conduct extensive experimentation to establish the efficacy of mRSC in three different scenarios: predicting the evolution of a metric of interest using synthetically generated data from a known factor model, and forecasting weekly sales and score trajectories of a Walmart store and Cricket game, respectively.