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12 - Fundamental Limits in Model Selection for Modern Data Analysis

Published online by Cambridge University Press:  22 March 2021

By
Jie Ding ,
Yuhong Yang  and
Vahid Tarokh
Edited by
Miguel R. D. Rodrigues  and
Yonina C. Eldar
Miguel R. D. Rodrigues
Affiliation:
University College London
Yonina C. Eldar
Affiliation:
Weizmann Institute of Science, Israel
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Summary

With rapid development in hardware storage, precision instrument manufacturing, and economic globalization etc., data in various forms have become ubiquitous in human life. This enormous amount of data can be a double-edged sword. While it provides the possibility of modeling the world with a higher fidelity and greater flexibility, improper modeling choices can lead to false discoveries, misleading conclusions, and poor predictions. Typical data-mining, machine-learning, and statistical-inference procedures learn from and make predictions on data by fitting parametric or non-parametric models. However, there exists no model that is universally suitable for all datasets and goals. Therefore, a crucial step in data analysis is to consider a set of postulated candidate models and learning methods (the model class) and select the most appropriate one. We provide integrated discussions on the fundamental limits of inference and prediction based on model-selection principles from modern data analysis. In particular, we introduce two recent advances of model-selection approaches, one concerning a new information criterion and the other concerning modeling procedure selection.

Keywords

model selectionmodeling procedure selectionAkaike information criterionBayesian information criterionBridge criterioncross-validation
Type
Chapter
Information
Information-Theoretic Methods in Data Science , pp. 359 - 382
Publisher: Cambridge University Press
Print publication year: 2021

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