Chunk #44 — 4 Regularized Multinomial Regression — 4.1 Regularization and Parameter Ambiguity

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Regularization Paths for Generalized Linear Models via Coordinate Descent.

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Theorem 1 Consider problem (28) for values α ∈ [0, 1]. Let β̄j be the mean of the βjℓ, andβjM a median of the βjℓ (and for simplicity assumeβ¯j≤βjM. Then we have (29)cj∈[β¯j,βjM], with the left endpoint achieved if α = 0, and the right if α = 1.