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# Datamodels: Understanding Predictions with Data and Data with Predictions

*Proceedings of the 39th International Conference on Machine Learning*, PMLR 162:9525-9587, 2022.

#### Abstract

We present a conceptual framework,

*datamodeling*, for analyzing the behavior of a model class in terms of the training data. For any fixed “target” example $x$, training set $S$, and learning algorithm, a*datamodel*is a parameterized function $2^S \to \mathbb{R}$ that for any subset of $S’ \subset S$—using only information about which examples of $S$ are contained in $S’$—predicts the outcome of training a model on $S’$ and evaluating on $x$. Despite the complexity of the underlying process being approximated (e.g. end-to-end training and evaluation of deep neural networks), we show that even simple*linear*datamodels successfully predict model outputs. We then demonstrate that datamodels give rise to a variety of applications, such as: accurately predicting the effect of dataset counterfactuals; identifying brittle predictions; finding semantically similar examples; quantifying train-test leakage; and embedding data into a well-behaved and feature-rich representation space.