Article,
On The Problem of Relevance in Statistical Inference
(2020)cite arxiv:2004.09588Comment: We'd love to hear your feedback. Email us. (We thank those who have already sent us their comments.).
Abstract
How many statistical inference tools we have for inference from massive data?
A huge number, but only when we are ready to assume the given database is
homogenous, consisting of a large cohort of "similar" cases. Why we need the
homogeneity assumption? To make `learning from the experience of others' or
`borrowing strength' possible. But, what if, we are dealing with a massive
database of heterogeneous cases (which is a norm in almost all modern
data-science applications including neuroscience, genomics, healthcare, and
astronomy)? How many methods we have in this situation? Not much, if not ZERO.
Why? It's not obvious how to go about gathering strength when each piece of
information is fuzzy. The danger is that, if we include irrelevant cases,
borrowing information might heavily damage the quality of the inference! This
raises some fundamental questions for big data inference: When (not) to borrow?
Whom (not) to borrow? How (not) to borrow? These questions are at the heart of
the "Problem of Relevance" in statistical inference -- a puzzle that has
remained too little addressed since its inception nearly half a century ago.
Here we offer the first practical theory of relevance with precisely
describable statistical formulation and algorithm. Through examples, we
demonstrate how our new statistical perspective answers previously unanswerable
questions in a realistic and feasible way.
