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Elicitation Complexity of Statistical Properties. (arXiv:1506.07212v2 [cs.LG] UPDATED)
来源于:arXiv
A property, or statistical functional, is said to be elicitable if it
minimizes expected loss for some loss function. The study of which properties
are elicitable sheds light on the capabilities and limits of empirical risk
minimization. While several recent papers have asked which properties are
elicitable, we instead advocate for a more nuanced question: how many
dimensions are required to indirectly elicit a given property? This number is
called the elicitation complexity of the property. We lay the foundation for a
general theory of elicitation complexity, including several basic results about
how elicitation complexity behaves, and the complexity of standard properties
of interest. Building on this foundation, we establish several upper and lower
bounds for the broad class of Bayes risks. We apply these results by proving
tight complexity bounds, with respect to identifiable properties, for variance,
financial risk measures, entropy, norms, and new properties of interest. We
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