Anytime-Valid Generalized Universal Inference on Risk Minimizers
arxiv(2024)
摘要
A common goal in statistics and machine learning is estimation of unknowns.
Point estimates alone are of little value without an accompanying measure of
uncertainty, but traditional uncertainty quantification methods, such as
confidence sets and p-values, often require strong distributional or structural
assumptions that may not be justified in modern problems. The present paper
considers a very common case in machine learning, where the quantity of
interest is the minimizer of a given risk (expected loss) function. For such
cases, we propose a generalized universal procedure for inference on risk
minimizers that features a finite-sample, frequentist validity property under
mild distributional assumptions. One version of the proposed procedure is shown
to be anytime-valid in the sense that it maintains validity properties
regardless of the stopping rule used for the data collection process. We show
how this anytime-validity property offers protection against certain factors
contributing to the replication crisis in science.
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