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A Multi-resolution Theory for Approximating Infinite-$p$-Zero-$n$: Transitional Inference, Individualized Predictions, and a World Without Bias-Variance Trade-off by Li, Xinran; Meng, Xiao-Li is a scholarly article available to read on EtoBox.

What is A Multi-resolution Theory for Approximating Infinite-$p$-Zero-$n$: Transitional Inference, Individualized Predictions, and a World Without Bias-Variance Trade-off about?

Transitional inference is an empiricism concept, rooted and practiced in clinical medicine since ancient Greece. Knowledge and experiences gained from treating one entity are applied to treat a related but distinctively different one. This notion of "transition to the similar" renders individualized treatments an operational meaning, yet its theoretical foundation defies the familiar inductive inference framework. The uniqueness of entities is the result of potentially an infinite number of attributes (hence $p=\infty$), which entails zero direct training sample size (i.e., $n=0$) because genuine guinea pigs do not exist. However, the literature on wavelets and on sieve methods suggests a principled approximation theory for transitional inference via a multi-resolution (MR) perspective, where we use the resolution level to index the degree of approximation to ultimate individuality. MR inference seeks a primary resolution indexing an indirect training sample, which provides enough matched attributes to increase the relevance of the results to the target individuals and yet still accumulate sufficient indirect sample sizes for robust estimation. Theoretically, MR inference relies on

Author

Li, Xinran; Meng, Xiao-Li

Published

2020

Language

EN