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Abstract:
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Many tensor data analysis methods correspond to statistical models that assume some sort low-rank structure, parameter sparsity, or other constraint. Such assumptions can be very useful in practice to aid in estimation stability and interpretation, but if false, can lead to uncalibrated inferences, such as prediction regions whose coverage probabilities do not match the nominal level. In this presentation, I show how in some settings, the set of all calibrated prediction regions can be characterized, and how a potentially incorrect model may be used to choose from among them. If the model is accurate, the predictions will be approximately optimal. If the model is poor, the predictions will still retain their nominal frequentist coverage levels.
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