Chunk #38 — 4 Regularized Multinomial Regression

Source: Regularization Paths for Generalized Linear Models via Coordinate Descent.
Embedded: yes

Text

Denote by Y the N × K indicator response matrix, with elements yiℓ = I (gi = ℓ). Then we can write the log-likelihood part of (21) in the more explicit form (22)ℓ({β0ℓ,βℓ}1K)=1N∑i=1N[∑ℓ=1Kyiℓ(β0ℓ+xiTβℓ)−log(∑ℓ=1Keβ0ℓ+xiTβℓ)].