Quadratic loss for regression tasks.

This loss can be used for regression with \(y \in \mathrm{R}\).

Format

S4 object.

Arguments

offset

(numeric(1) | matrix())
Numerical value or matrix to set a custom offset. If used, this value is returned instead of the loss optimal initialization.

Details

Loss Function: $$ L(y, f(x)) = \frac{1}{2}( y - f(x))^2 $$ Gradient: $$ \frac{\delta}{\delta f(x)}\ L(y, f(x)) = f(x) - y $$ Initialization: $$ \hat{f}^{[0]}(x) = \mathrm{arg~min}{c\in\mathrm{R}}{\mathrm{arg~min}}\ \frac{1}{n}\sum\limits_{i=1}^n L\left(y^{(i)}, c\right) = \bar{y} $$

Usage

LossQuadratic$new()
LossQuadratic$new(offset)

Inherited methods from Loss

• $loss(): matrix(), matrix() -> matrix()

• $gradient(): matrix(), matrix() -> matrix()

• $constInit(): matrix() -> matrix()

• $calculatePseudoResiduals(): matrix(), matrix() -> matrix()

• $getLossType(): () -> character(1)

Examples

# Create new loss object:
quadratic_loss = LossQuadratic$new()
quadratic_loss
#> LossQuadratic: L(y,x) = 0.5 * (y - f(x))^2
#>