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Register a new userSelective inference with a randomized response
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Added by
Xiaoying Tian Harris
Publication date
2015
fields
Mathematical Statistics
and research's language is
English
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Inspired by sample splitting and the reusable holdout introduced in the field of differential privacy, we consider selective inference with a randomized response. We discuss two major advantages of using a randomized response for model selection. First, the selectively valid tests are more powerful after randomized selection. Second, it allows consistent estimation and weak convergence of selective inference procedures. Under independent sampling, we prove a selective (or privatized) central limit theorem that transfers procedures valid under asymptotic normality without selection to their corresponding selective counterparts. This allows selective inference in nonparametric settings. Finally, we propose a framework of inference after combining multiple randomized selection procedures. We focus on the classical asymptotic setting, leaving the interesting high-dimensional asymptotic questions for future work.
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Selective inference is a recent research topic that tries to perform valid inference after using the data to select a reasonable statistical model. We propose MAGIC, a new method for selective inference that is general, powerful and tractable. MAGIC is a method for selective inference after solving a convex optimization problem with smooth loss and $ell_1$ penalty. Randomization is incorporated into the optimization problem to boost statistical power. Through reparametrization, MAGIC reduces the problem into a sampling problem with simple constraints. MAGIC applies to many $ell_1$ penalized optimization problem including the Lasso, logistic Lasso and neighborhood selection in graphical models, all of which we consider in this paper.
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