An Econometric Perspective of Algorithmic Sampling
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Datasets that are terabytes in size are increasingly common, but computer bottlenecks often frustrate a complete analysis of the data. While more data are better than less, diminishing returns suggest that we may not need terabytes of data to estimate a parameter or test a hypothesis. But which rows of data should we analyze, and might an arbitrary subset of rows preserve the features of the original data? This paper reviews a line of work that is grounded in theoretical computer science and numerical linear algebra, and which finds that an algorithmically desirable sketch of the data must have a subspace embedding property. Building on this work, we study how prediction and inference is affected by data sketching within a linear regression setup. The sketching error is small compared to the sample size effect which is within the control of the researcher. As a sketch size that is algorithmically optimal may not be suitable for prediction and inference, we use statistical arguments to provide `inference conscious' guides to the sketch size. When appropriately implemented, an estimator that pools over different sketches can be nearly as efficient as the infeasible one using the full sample.
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