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High-Dimensional Statistical Learning: Roots, Justifications, and Potential Machineries.

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Summary
This summary is machine-generated.

This study reviews advanced statistical methods for analyzing high-dimensional data, where variables exceed sample size. It aims to bridge the gap between complex techniques and practical application, promoting broader adoption of effective high-dimensional analysis tools.

Keywords:
G-analysisKolmogorov asymptoticscurse of dimensionalitydouble asymptoticshigh-dimensional analysisrandom matrix theoryridge estimationshrinkagesparsity

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • High-dimensional data, characterized by more variables than samples, challenges classical statistical learning methods.
  • Classical methods often fail to meet theoretical performance expectations with high-dimensional datasets.
  • Existing advanced techniques for high-dimensional data analysis are underutilized by practitioners.

Purpose of the Study:

  • To consolidate and overview diverse mathematical-statistical techniques for high-dimensional data analysis.
  • To elucidate the theoretical underpinnings and operating conditions of these advanced methods.
  • To encourage wider awareness and adoption of effective high-dimensional analysis tools.

Main Methods:

  • Literature review and synthesis of existing high-dimensional statistical learning techniques.
  • Analysis of theoretical results and practical operating conditions for various methods.
  • Referencing relevant review articles for in-depth information on specific subjects.

Main Results:

  • Identification of numerous advanced methodologies for high-dimensional data analysis.
  • Clarification of the conditions under which these methods are effective.
  • Highlighting the gap between the availability of advanced techniques and their current practical usage.

Conclusions:

  • There is a need to disseminate knowledge about advanced high-dimensional data analysis techniques.
  • Bridging the gap between theory and practice is crucial for effective utilization of these methods.
  • This work serves as a foundational resource for researchers and practitioners in high-dimensional statistics.