com.imsl.datamining

Enum GradientBoosting.LossFunctionType

java.lang.Object

java.lang.Enum<GradientBoosting.LossFunctionType>

com.imsl.datamining.GradientBoosting.LossFunctionType

All Implemented Interfaces:

Serializable, Comparable<GradientBoosting.LossFunctionType>

Enclosing class:

GradientBoosting

public static enum GradientBoosting.LossFunctionType
extends Enum<GradientBoosting.LossFunctionType>

The loss function type as specified by the error measure.

Enum Constant Summary

Enum Constants

Enum Constant and Description
ADABOOST The loss criteria is the AdaBoost.M1 criterion.
BERNOULLI The loss criteria is the binomial or Bernoulli negative log-likelihood, or deviance.
HUBER_M The loss criteria is the Huber-M weighted squared error and absolute deviation error with parameter $\alpha$.
LEAST_ABSOLUTE_DEVIATION The loss criteria is least absolute deviation error.
LEAST_SQUARES The loss criteria is least squared error.
MULTINOMIAL_DEVIANCE The loss criteria is the (K-class) multinomial negative log-likelihood, or multinomial deviance.

Method Summary

Modifier and Type	Method and Description
static GradientBoosting.LossFunctionType	valueOf(String name) Returns the enum constant of this type with the specified name.
static GradientBoosting.LossFunctionType[]	values() Returns an array containing the constants of this enum type, in the order they are declared.

Methods inherited from class java.lang.Enum

clone, compareTo, equals, finalize, getDeclaringClass, hashCode, name, ordinal, toString, valueOf

Methods inherited from class java.lang.Object

getClass, notify, notifyAll, wait, wait, wait

Enum Constant Detail

LEAST_SQUARES

public static final GradientBoosting.LossFunctionType LEAST_SQUARES

The loss criteria is least squared error. That is, the loss function

$L({y_i,f(x_i)}) = \sum (y_i - f(x_i))^2$

LEAST_ABSOLUTE_DEVIATION

public static final GradientBoosting.LossFunctionType LEAST_ABSOLUTE_DEVIATION

The loss criteria is least absolute deviation error. That is, the loss function

$L({y_i,f(x_i)}) = \sum |(y_i - f(x_i))|$

HUBER_M

public static final GradientBoosting.LossFunctionType HUBER_M

The loss criteria is the Huber-M weighted squared error and absolute deviation error with parameter $\alpha$. That is, the loss function

$L({y_i,f(x_i)}) = \sum \Psi(y_i,f(x_i))$

where

$$\Psi(y,f(x)) = \left\{ \begin{array}{ll} (y-f(x))^2 & {\rm for}\;|y-f(x)| \le \delta\; \\ 2\delta(|y-f(x)| - \delta) & {\rm for}\;|y-f(x)| > \delta\; \end{array} \right.$$

And where $\delta$ is the $\alpha$ -empirical quantile of the residuals, ${y_i-f(x_i),i=1,...,n}$

ADABOOST

public static final GradientBoosting.LossFunctionType ADABOOST

The loss criteria is the AdaBoost.M1 criterion. The loss function

$L({y_i,f(x_i)}) = \sum \exp\left( -(2y_i-1)f(x_i)\right)$

MULTINOMIAL_DEVIANCE

public static final GradientBoosting.LossFunctionType MULTINOMIAL_DEVIANCE

The loss criteria is the (K-class) multinomial negative log-likelihood, or multinomial deviance. The loss function

$L({y_i,f(x_i)})=-2 \sum_i \sum_k y_{ik}\log(p_{ik})$

where

$p_{ik}=\frac{\exp{f_k(x_i)}}{(\sum_k \exp{f_k(x_i)})}$

BERNOULLI

public static final GradientBoosting.LossFunctionType BERNOULLI

The loss criteria is the binomial or Bernoulli negative log-likelihood, or deviance.

$L({y_i,f(x_i)}) = -2 \sum {(y_if(x_i) - \log(1+\exp(f(x_i)))}$

Method Detail

values

public static GradientBoosting.LossFunctionType[] values()

Returns an array containing the constants of this enum type, in the order they are declared. This method may be used to iterate over the constants as follows:

for (GradientBoosting.LossFunctionType c : GradientBoosting.LossFunctionType.values())
    System.out.println(c);

Returns:

an array containing the constants of this enum type, in the order they are declared

valueOf

public static GradientBoosting.LossFunctionType valueOf(String name)

Returns the enum constant of this type with the specified name. The string must match exactly an identifier used to declare an enum constant in this type. (Extraneous whitespace characters are not permitted.)

Parameters:

name - the name of the enum constant to be returned.

Returns:

the enum constant with the specified name

Throws:

IllegalArgumentException - if this enum type has no constant with the specified name

NullPointerException - if the argument is null