scope.logistic: Computes solution for SCOPE logistic models

In CatReg: Solution Paths for Linear and Logistic Regression Models with Categorical Predictors, with SCOPE Penalty

Description

Computes solution for SCOPE logistic models, computing along a path and iterating local quadratic approximations at each point. Performs K-fold cross-validation for regularisation parameter lambda and can incorporate both linear and categorical (including logical) variables. This function uses a Proximal Newton algorithm and is not guaranteed to converge. It is recommended for developer use only.

Usage

scope.logistic(
  x,
  y,
  gamma = 8,
  lambda = NULL,
  nlambda = 100,
  lambda_min_ratio = 0.01,
  nfolds = 5,
  include_intercept = TRUE,
  return_full_beta = FALSE,
  max_iter = 1000,
  max_out_iter = 1000,
  early_stopping = ifelse(pshrink > 1, TRUE, FALSE),
  early_stopping_rounds = 20,
  early_stopping_criterion = "AIC",
  noise_variance = NULL,
  terminate_eps = 1e-07,
  silent = TRUE,
  only_cross_validate = FALSE,
  grid_safe = 10,
  block_order = NULL,
  fold_assignment = NULL,
  zero_penalty = FALSE
)

Arguments

x	Data frame of covariates: Can include a mix of continuous and categorical variables (no scaling of continuous covariates is performed within the program). By default an intercept will be added to the linear part; see include_intercept
y	Response vector of length n
gamma	Concavity parameter in MCP; see Zhang (2010)
lambda	If NULL default sequence will be generated. Matrix of values (p_categorical times nlambda) of penalty parameter lambda. Must be non-negative and each row decreasing. Note that if lambda = 0 then no shrinkage will occur.
nlambda	Length of default sequence of lambda values generated if lambda = NULL
lambda_min_ratio	Ratio of largest to smallest value on default sequence of lambda values
nfolds	Number of folds in cross-validation. If nfolds = 1, no cross-validation is performed
include_intercept	If TRUE, a column of 1s will be added to the (continuous) design matrix
return_full_beta	If TRUE with cross-validation, the entire solution path will be returned instead of just the optimal point
max_iter	Maximum number of iterations at each local quadratic approximation
max_out_iter	Maximum number of local quadratic approximations at each value of lambda
early_stopping	Early stopping based on information criterion. By default is TRUE if there are more than 1 categorical variables
early_stopping_rounds	Number of iterations that information criterion must have not decreased for to terminate
early_stopping_criterion	If "AIC", Akaike Information Criterion is used for early stopping. Otherwise if a positive number is given, modified Bayes Information Criterion is used with this integer as the parameter (Wang et al., 2009)
noise_variance	If noise variance is known, this will be used for scaling the default values of lambda. Otherwise this will be scaled automatically
terminate_eps	Epsilon for convergence criterion, is multiplied by null deviance to get terminate criterion for objective value
silent	If FALSE then progress updates will be printed as solutions are computed. Useful for tuning and diagnosing convergence issues.
only_cross_validate	If TRUE then cross-validation scores for each value of lambda will be returned, but not the estimates themselves
grid_safe	As the automatically generated sequence of lambda values is adjusted during the first fold but fixed thereafter. For subsequent folds, this sets computation to begin at a larger value of lambda to ensure that the first solution along the path is zero so as to maintain the advantages of the pathwise approach. This specifies how many larger values of lambda should be used
block_order	By default the order in block coordinate descent is randomly sampled. Alternatively a permutation vector can be included here
fold_assignment	By default the assignments for cross-validation are randomly sampled automatically. Alternatively assignments can be included here
zero_penalty	Fits unpenalised logistic regression model. Used for testing purposes only.

Value

A list of objects. Some may not be returned depending on value of arguments K, simply.cross.validated, return.full.beta.

• lambda - A matrix of the values of lambda used to compute the solution path. Columns correspond to different points on the path, rows correspond to the categorical variables. Lambda is scaled depending on the number of categories present in the data.

• cverrors - Provided nfolds > 1 then the cross-validation error for each point on the grid will be returned

• beta.full - Contains full solution path. If nfolds > 1 then will only be returned if simply.cross.validated = FALSE and return.full.beta = TRUE. First object [[ 1 ]] is coefficients of continuous variables, [[ 2 ]] is a list of coefficients for categorical variables

• beta.best - Contains solution at CV-optimal point. Requires nfolds > 1 to be returned. This must not be NULL in order to use predict.scope. First object [[ 1 ]] is coefficients of continuous variables, [[ 2 ]] is a list of coefficients for categorical variables

• fold.assign - Contains fold assignments for cross-validation

References

\insertRef

zhang2010CatReg

\insertRef

wangli2009CatReg

Examples

## Not run: 
x = UniformDesignMatrix(200, 5, 5)
y = (as.integer(x[ , 1 ]) < 3) + rnorm(200)
y = as.integer(y > 0.8)
scope_mod = scope.logistic(x, y)
x_new = UniformDesignMatrix(10, 5, 5)
predict(scope_mod, x_new)

## End(Not run)

CatReg documentation built on June 14, 2021, 5:07 p.m.