Accelerating Cross-Validation in Multinomial Logistic Regression with ℓ_1-Regularization

11/15/2017

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by   Tomoyuki Obuchi, et al.

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We develop an approximate formula for evaluating a cross-validation estimator of predictive likelihood for multinomial logistic regression regularized by an ℓ_1-norm. This allows us to avoid repeated optimizations required for literally conducting cross-validation; hence, the computational time can be significantly reduced. The formula is derived through a perturbative approach employing the largeness of the data size and the model dimensionality. Its usefulness is demonstrated on simulated data and the ISOLET dataset from the UCI machine learning repository.