ktd_estimate {ktweedie}

Estimate kernel Tweedie model coefficients

Description

ktd_estimate() estimates the coefficients of the kernel Tweedie model ktweedie and the sparse kernel Tweedie model sktweedie. The log of the expected Tweedie mean is modeled by a function in the reproducing kernel Hilbert space. The sktweedie has an integrated feature selection component that induces sparsity by applying weights on the features and penalizing the weights.

Usage

ktd_estimate(
  x,
  y,
  kern,
  lam1,
  rho = 1.5,
  ftol = 1e-08,
  partol = 1e-08,
  abstol = 0,
  maxit = 1e+06,
  sparsity = FALSE,
  lam2 = 0,
  innerpartol = 1e-06,
  innermaxit = 1e+06,
  verbose = FALSE
)

Arguments

x

Covariate matrix.

y

Outcome vector (e.g. insurance cost).

kern

Choice of kernel. See dots for details on supported kernel functions.

lam1

A vector of regularization coefficients.

rho

The power parameter of the Tweedie model. Default is 1.5 and can take any real value between 1 and 2.

ftol

Stopping criterion based on objective function value. Default is 1e-8. See Details.

partol

Stopping criterion based on the coefficient values. Default is 1e-8. See Details.

abstol

Stopping criterion based on absolute value of the objective function. Default is 0.

maxit

Maximum number of iterations.

sparsity

Logical If true, the sktweedie model with variable selection will be used. Default is false, for the ktweedie model.

lam2

Regularization coefficient for the sparsity-inducing penalty in the sktweedie model.

innerpartol

Stopping criterion for the inner loops that update kernel parameters and weights based on the coefficient values. See Details.

innermaxit

Maximum number of iterations for the inner loops that update kernel parameters and variable weights. See Details.

verbose

Logical indicating whether to show details of each update.

Details

ktd_estimate() stops when the absolute difference between the objective function values of the last two updates is smaller than ftol, or the sum of absolute differences between the coefficients of the last two updates is smaller than partol, or the objective function values is below abstol, before maxit is reached. For the sktweedie model, there are inner loops for the update of kernel regression coefficients and regularization weights. The innerpartol and innermaxit arguments are the counterparts of partol and maxit for the inner loops.

Value

A list of three items.

1. estimates: a list containing the final objective function values and kernel Tweedie regression coefficients for each lam1.

2. data: stores the inputs, including the predictor matrix, the kernel function used in the fitting and lam1.

3. sparsity: a logical variable indicating whether the ktweedie or sktweedie is fitted.

See Also

ktd_cv, ktd_cv2d, ktd_predict, rbfdot

Examples

###### ktweedie ######
# Provide a sequence of candidate values to the argument lam1.
# Provide a kernel object to the argument kern.
lam1.seq <- c(1e-5, 1e-4, 1e-3, 1e-2, 1e-1, 1e0, 1e1)
fit.ktd <- ktd_estimate(x = dat$x, y = dat$y,
                        kern = rbfdot(sigma = 1e-8),
                        lam1 = lam1.seq)
###### sktweedie ######
# Set sparsity to TRUE and a lam2 to control the level of sparsity
# Decrease lam2 if "WARNING: All weights are zero..."
fit.sktd <- ktd_estimate(x = dat$x,
                         y = dat$y,
                         kern = rbfdot(sigma = 0.1),
                         lam1 = 5,
                         sparsity = TRUE,
                         lam2 = 1)
# variables with fitted weight equal to 0 are not selected