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Using Empirical Bayes to approximate posteriors for large "black box" estimators

The Unofficial Google Data Science Blog

Posteriors are useful to understand the system, measure accuracy, and make better decisions. But most common machine learning methods don’t give posteriors, and many don’t have explicit probability models. In our model, $theta$ doesn’t depend directly on $x$ — all the information in $x$ is captured in $t$.

KDD 40