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Sparse multinomial logistic regression: fast algorithms and generalization bounds.

Balaji Krishnapuram1, Lawrence Carin, Mário A T Figueiredo

  • 1Computer Aided Diagnosis and Therapy Group, Siemens Medical Solutions USA, Inc., 51 Valley Stream Pkwy, Malvern, PA 19355, USA. Balaji.Krishnapuram@siemens.com

IEEE Transactions on Pattern Analysis and Machine Intelligence
|June 10, 2005
PubMed
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This study introduces new algorithms for learning sparse multiclass classifiers using multinomial logistic regression. These efficient methods accurately handle large datasets and high-dimensional features, improving generalization.

Area of Science:

  • Machine Learning
  • Computer Science
  • Statistical Learning

Background:

  • Sparse classifiers are state-of-the-art in supervised learning, controlling model capacity via sparsity-promoting priors.
  • These methods minimize basis functions for improved generalization, but efficient multiclass extensions are limited.

Purpose of the Study:

  • To introduce a true multiclass formulation for sparse classifiers based on multinomial logistic regression.
  • To develop fast, exact algorithms for learning sparse multiclass classifiers.
  • To derive generalization bounds for the proposed binary sparse classifier.

Main Methods:

  • Developed a true multiclass formulation using multinomial logistic regression with sparsity-promoting priors.
  • Combined bound optimization with component-wise updates for efficient algorithm derivation.

Related Experiment Videos

  • Derived generalization bounds for the binary classification case.

    • Main Results:

    • Introduced the first exact algorithms for multinomial logistic regression with sparsity-promoting priors.
    • Algorithms demonstrate favorable scaling with sample size and feature dimensionality, suitable for large datasets.
    • Experimental results confirm accuracy, sparsity, and efficiency on benchmark datasets.

    Conclusions:

    • The proposed methods offer accurate, sparse, and efficient solutions for multiclass classification problems.
    • The developed algorithms are scalable to large datasets and high-dimensional feature spaces.
    • The work advances the field of sparse learning with novel multiclass formulations and efficient algorithms.