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2327 results in Pattern Recognition and Machine Learning

Page 32 of 117

Principles of Statistical Analysis
  • Learning from Randomized Experiments
  • Ery Arias-Castro
  • Published online:
    22 July 2022
    Print publication:
    25 August 2022
  • This compact course is written for the mathematically literate reader who wants to learn to analyze data in a principled fashion. The language of mathematics enables clear exposition that can go quite deep, quite quickly, and naturally supports an axiomatic and inductive approach to data analysis. Starting with a good grounding in probability, the reader moves to statistical inference via topics of great practical importance – simulation and sampling, as well as experimental design and data collection – that are typically displaced from introductory accounts. The core of the book then covers both standard methods and such advanced topics as multiple testing, meta-analysis, and causal inference.

  • 5 - Large Neural Networks

  • Romain Couillet, Zhenyu Liao
  • Book:
    Random Matrix Methods for Machine Learning
    Published online:
    30 June 2022
    Print publication:
    21 July 2022, pp 277-312

  • Summary

    This chapter covers large neural networks with random weights, in both feed-forward and recurrent settings. While being rather different from modern deep neural networks, these preliminary results shed new light on the interplay between data, network structure, and nonlinear neurons, leading to the somewhat surprising double descent phenomenon. The impact of gradient-based optimization method on the resulting network and more advanced consideration of deep networks are also discussed.

  • 6 - Large-Dimensional Convex Optimization

  • Romain Couillet, Zhenyu Liao
  • Book:
    Random Matrix Methods for Machine Learning
    Published online:
    30 June 2022
    Print publication:
    21 July 2022, pp 313-336

  • Summary

    This chapter discusses the generalized linear classifier that results from convex optimization problem and takes in general nonexplicit form. Random matrix theory is combined with leave-one-out arguments to handle the technical difficulty due to implicity. Again, counterintuitive phenomena arise in popular machine learning methods such as logistic regression or SMV in the large-dimensional setting, a well-defined solution may not even exist, and if it does, it behaves dramatically from its small-dimensional counterpart.

Page 32 of 117