Laurae: Advanced High Performance Data Science Toolbox for R

Description Usage Arguments Details Value Examples

This function computes the 1st and 2nd symbolic derivatives of the loss function (gradient/hessian) provided.

1 2	SymbolicLoss(fc, fc_ref = NULL, verbose = TRUE, plotting = TRUE, xmin = -10, xmax = 10, xpoint = 20, ...)

`fc`	The loss function to derivate twice. Gradient and hessian are computed and returned into a list to the user.
`fc_ref`	The loss function for reference to compare when using `plotting = TRUE`. Defaults to `NULL`.
`verbose`	Whether the functions should be printed to the console while being returned. Defaults to `TRUE`.
`plotting`	Whether the functions should be plotted for debugging purposes. Defaults to `TRUE`.
`xmin`	The x-axis minimum when plotting data when `plotting = TRUE`. Defaults to `-10`.
`xmax`	The x-axis maximum when plotting data when `plotting = TRUE`. Defaults to `10`.
`xpoint`	How many poitns to plot when `plotting = TRUE`. Defaults to `20`.
`...`	Arguments to pass to `fc` and `fc_ref`.

This function cannot handle any type of input. It cannot handle sums or loops in the function code. It handles the following, in the alphabetic order:

\*: Multiplication
/: Division
^: Power
abs: Absolute value function
acos: Arcosine function
acosh: Hyperbolic Arcosine function
asin: Arsine function
asinh: Hyperbolic Arcsine function
atan: Arctangent function
atan2: Arctangent angle function between the x-axis and the vector from the origin (x,y), atan=y/x if x>0 and y>0
atanh: Hyperbolic Arctangent function
besselI: Modified Bessel function of the first kind
besselJ: Bessel function of the first kind
besselK: Modified Bessel function of the second kind
besselY: Sphereical Bessel function
beta: Beta function (Eulerian integral of the first kind)
cos: Cosine function
cosh: Hyperbolic cosine function
cospi: Cosine function with argument multiplicand pi
dbinom: Density binomial function
digamma: First derivative of the logarithm of the gamma function
dnorm: Density normal function
exp: Exponential function
expm1: Exponential function minus 1
gamma: Gamma function (Mellin transform of the negative exponential function)
lbeta: Natural logarithm of the beta function
lgamma: Natural logarithm of the absolute value of the gamma function
log: Natural (e) logarithm function
log10: Common (10) logarithm function
log1p: Natural (e) logarithm function with 1 added to the argument
log2: Binary (2) logarithm function
logb: Logarithm function of base b (base)
pnorm: Normal distribution function
psigamma: Polygamma function (degree specified by deriv)
rep.int: Replicate "times" elements of vectors and lists
rep_len: Replicate "length.out" elements of vectors and lists
sign: Sign function
sin: Sine function
sinh: Hyperbolic sine function
sinpi: Sine function with argument multiplicand pi
sqrt: Square root function
tan: Tangent function
tanh: Hyperbolic tangent function
tanpi: Tangent function with argument multiplicand pi
trigamma: Second derivative of the logarithm of the gamma function

A list with grad as the gradient of the loss function and hess as the hessian of the loss function.

# Median Fair loss (just the Fair loss...)
library(Deriv) # loads the required library
fc <- function(x, c=2, t=0.5)
{(c^2) * ((abs(x) / c) - log(1 + (abs(x) / c))) * ifelse(x > 0, 2 * t, 2-2*t)}
fc_ref <- function(x) {x^2} # Quadratic loss, aka Mean Squared Error
SymbolicLoss(fc = fc,
             fc_ref = fc_ref,
             verbose = TRUE,
             plotting = TRUE)