# Family

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Percentile

boost_family objects provide a convenient way to specify loss functions and corresponding risk functions to be optimized by one of the boosting algorithms implemented in this package.

Keywords
models
##### Usage
Family(ngradient, loss = NULL, risk = NULL,
offset = function(y, w) 0,
fW = function(f) rep(1, length(f)),
weights = TRUE, name = "user-specified")
Binomial()
GaussClass()
GaussReg()
Huber(d = NULL)
Laplace()
Poisson()
CoxPH()
##### Arguments
a function with arguments y, f and w implementing the negative gradient of the loss function (which is to be minimized!).
loss
an optional loss function with arguments y and f to be minimized (!).
risk
an optional risk function with arguments y, f and w, the weighted mean of the loss function by default.
offset
a function with argument y and w (weights) for computing a scalar offset.
fW
transformation of the fit for the diagonal weights matrix for an approximation of the boosting hat matrix for loss functions other than squared error.
weights
a logical indicating if weights are allowed.
name
a character giving the name of the loss function for pretty printing.
d
delta parameter for Huber loss function. If omitted, it is choosen adaptively.
##### Details

The boosting algorithms implemented in glmboost, gamboost or blackboost aim at minimizing the (weighted) empirical risk function risk(y, f, w) with respect to f. By default, the risk function is the weighted sum of the loss function loss(y, f) but can be choosen arbitrarily. The ngradient(y, f) function is the negative gradient of loss(y, f) with respect to f. For binary classification problems we assume that the response y is coded by $-1$ and $+1$.

Pre-fabricated functions for the most commonly used loss functions are available as well.

The offset function returns the population minimizers evaluated at the response, i.e., $1/2 \log(p / (1 - p))$ for Binomial() or AdaExp() and $(\sum w_i)^{-1} \sum w_i y_i$ for GaussReg and the median for Huber and Laplace.

##### Value

• An object of class boost_family.

• Family
• Binomial
• GaussClass
• GaussReg
• Huber
• Laplace
• Poisson
• CoxPH
##### Examples
Laplace()

Family(ngradient = function(y, f) y - f,
loss = function(y, f) (y - f)^2,
name = "My Gauss Variant")
Documentation reproduced from package mboost, version 0.4-10, License: GPL

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