NORMA (version 0.1)

ILF_cost_der: Cost Functions Derivatives

Description

ILF_cost_der computes the ILF derivative value at a given point.

zero_laplace_cost_der computes the value at a given point of the loss function derivative corresponding to a zero-mean Laplace distribution.

general_laplace_cost_der computes the value at a given point of the loss function derivative corresponding to a general Laplace distribution.

zero_gaussian_cost_der computes the value at a given point of the loss function derivative corresponding to a zero-mean Gaussian distribution.

general_gaussian_cost_der computes the value at a given point of the loss function derivative corresponding to a general Gaussian distribution.

beta_cost_der computes the value at a given point of the loss function derivative corresponding to a Beta distribution.

weibull_cost_der computes the value at a given point of the loss function derivative corresponding to a Weibull distribution.

moge_cost_der computes the value at a given point of the loss function derivative corresponding to a MOGE distribution.

Usage

ILF_cost_der(phi, epsilon = 0.1, nu = 0)
zero_laplace_cost_der(phi, sigma)
general_laplace_cost_der(phi, sigma, mu)
zero_gaussian_cost_der(phi, sigma_cuad)
general_gaussian_cost_der(phi, sigma_cuad, mu)
beta_cost_der(phi, alpha, beta)
weibull_cost_der(phi, lambda, kappa)
moge_cost_der(phi, lambda, alpha, theta)

Arguments

phi

point to use as argument of the loss function derivative.

epsilon

width of the insensitive band.

nu

parameter to control value of epsilon.

sigma

scale parameter of the Laplace distribution.

mu

location or mean parameter of the Laplace or Gaussian distribution, respectively.

sigma_cuad

variance parameter of the Gaussian distribution.

alpha

shape1 parameter of the Beta distribution or second parameter of the MOGE distribution.

beta

shape2 parameter of the Beta distribution.

lambda

lambda scale parameter of the Weibull distribution or first parameter of the MOGE distribution.

kappa

shape parameter of the Weibull distribution.

theta

third parameter of the MOGE distribution.

Value

Returns a numeric representing the derivative value at a given point.

Details

See also 'References'.

References

Link to the scientific paper

Prada, Jesus, and Jose Ramon Dorronsoro. "SVRs and Uncertainty Estimates in Wind Energy Prediction." Advances in Computational Intelligence. Springer International Publishing, 2015. 564-577,

with theoretical background for this package is provided below.

http://link.springer.com/chapter/10.1007/978-3-319-19222-2_47

Examples

# ILF derivative value at point phi=1 with default epsilon.
ILF_cost_der(1)

# ILF derivative value at point phi=1 with epsilon=2.
ILF_cost_der(1,2)

# Zero-mean Laplace loss function derivative value at point phi=1 with sigma=1.
zero_laplace_cost_der(1,1)

# General Laplace loss function derivative value at point phi=1 with mu=0 and sigma=1.
general_laplace_cost_der(1,1,0)

# Zero-mean Gaussian loss function derivative value at point phi=1 with sigma_cuad=1.
zero_gaussian_cost_der(1,1)

# General Gaussian loss function derivative value at point phi=1 with mu=0 and sigma_cuad=1.
general_gaussian_cost_der(1,1,0)

# Beta loss function derivative value at point phi=1 with alpha=2 and beta=3.
beta_cost_der(1,2,3)

# Weibull loss function derivative value at point phi=1 with lambda=2 and kappa=3.
weibull_cost_der(1,2,3)

# MOGE loss function derivative value at point phi=1 with lambda=2 ,alpha=3 and theta=4.
moge_cost_der(1,2,3,4)