Maximises the multinomial log-likelihood minus lambda sum_k sum_j |beta_kj| in
the symmetric parametrisation (ESL eqs 18.10, 18.19) by cycling over the
classes with IRLS quadratic approximations and lasso coordinate descent, as
glmnet's ungrouped multinomial. Intercepts are centred; lambda is N times
glmnet's.
Usage
morie_esl_multinomial_l1(
X,
g,
lambda,
max_outer = 500,
max_inner = 10000,
tol = 1e-12
)
Arguments
- X
Predictors, n by p.
- g
Class labels.
- lambda
Penalty.
- max_outer, max_inner, tol
Iteration controls.
Value
Named list: intercepts, coefficients (K by p), classes, loglik,
objective, prob, converged.
References
Friedman, J., Hastie, T. & Tibshirani, R. (2010). JSS 33(1).
Examples
i <- 1:60
X <- cbind(sin(i), cos(3 * i))
morie_esl_multinomial_l1(X, ifelse(sin(i) > 0.3, 0, ifelse(cos(3 * i) > 0, 1, 2)), 1.5)$coefficients
#> [,1] [,2]
#> [1,] 4.961363 0.000000
#> [2,] 0.000000 2.275950
#> [3,] 0.000000 -1.910676
