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Second-order induction in prediction problems
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DOI：10.1073/pnas.1901597116.png)
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Abstract
En 中文
Agents make predictions based on similar past cases, while also learning the relative importance of various attributes in judging similarity. We ask whether the resulting empirically optimal similarity function (EOSF) is unique and how easy it is to find it. We show that with many observations and few relevant variables, uniqueness holds. By contrast, when there are many variables relative to observations, nonuniqueness is the rule, and finding the EOSF is computationally hard. The results are interpreted as providing conditions under which rational agents who have access to the same observations are likely to converge on the same predictions and conditions under which they may entertain different probabilistic beliefs.
Keywords:
belief formation
empirically optimal similarity function
learning
kernel estimation
generalized context model
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