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Given a large dataset and an estimation task, it is common to pre-process thedata by reducing them to a set of sufficient statistics. This step is oftenregarded as straightforward and advantageous (in that it simplifies statisticalanalysis). I show that -on the contrary- reducing data to sufficient statisticscan change a computationally tractable estimation problem into an intractableone. I discuss connections with recent work in theoretical computer science,and implications for some techniques to estimate graphical models.

Computational Implications of Reducing Data to Sufficient Statistics