dcsvm: Density-Convoluted Support Vector Machine

In dcsvm: Density Convoluted Support Vector Machines

Density-Convoluted Support Vector Machine

Description

Fits the density-convoluted support vector machine (DCSVM) through kernel density convolutions.

Usage

dcsvm(
  x,
  y,
  nlambda = 100,
  lambda.factor = ifelse(nobs < nvars, 0.01, 1e-04),
  lambda = NULL,
  lam2 = 0,
  kern = c("gaussian", "uniform", "epanechnikov"),
  hval = 1,
  pf = rep(1, nvars),
  pf2 = rep(1, nvars),
  exclude,
  dfmax = nvars + 1,
  pmax = min(dfmax * 1.2, nvars),
  standardize = TRUE,
  eps = 1e-08,
  maxit = 1e+06,
  istrong = TRUE
)

Arguments

x	A numeric matrix with N rows and p columns representing predictors. Each row corresponds to an observation, and each column corresponds to a variable.
y	A numeric vector of length N representing binary responses. Elements must be either -1 or 1.
nlambda	Number of lambda values in the sequence. Default is 100.
lambda.factor	Ratio of the smallest to the largest lambda in the sequence: lambda.factor = min(lambda) / max(lambda). The default value is 0.0001 if N >= p or 0.01 if N < p. Takes no effect if a lambda sequence is specified.
lambda	An optional user-specified sequence of lambda values. If lambda = NULL (default), the sequence is computed based on nlambda and lambda.factor. The program automatically sorts user-defined lambda sequences in decreasing order.
lam2	Users may tune \lambda_2, which controls the L2 regularization strength. Default is 0 (lasso).
kern	Type of kernel method for smoothing. Options are "gaussian", "uniform", and "epanechnikov". Default is "epanechnikov".
hval	The bandwidth parameter for kernel smoothing. Default is 1.
pf	A numeric vector of length p representing the L1 penalty weights for each coefficient. A common choice is (\beta + 1/n)^{-1}, where n is the sample size and \beta is obtained from L1 DCSVM or enet DCSVM. Default is 1 for all predictors.
pf2	A numeric vector of length p representing the L2 penalty weights for each coefficient. A value of 0 indicates no L2 shrinkage. Default is 1 for all predictors.
exclude	Indices of predictors to exclude from the model. Equivalent to assigning an infinite penalty factor. Default is none.
dfmax	Maximum number of nonzero coefficients allowed in the model. Default is p + 1. Useful for large p when a partial path is acceptable.
pmax	Maximum number of variables allowed to ever be nonzero during the computation. Default is min(dfmax * 1.2, p).
standardize	Logical indicating whether predictors should be standardized to unit variance. Default is TRUE. Note that predictors are always centered.
eps	Convergence threshold. The algorithm stops when 4\max_j(\beta_j^{new} - \beta_j^{old})^2 is less than eps. Default is 1e-8.
maxit	Maximum number of iterations allowed. Default is 1e6. Consider increasing maxit if the algorithm does not converge.
istrong	Logical indicating whether to use the strong rule for faster computation. Default is TRUE.

Value

An object of class dcsvm containing the following components:

b0	Intercept values for each lambda.
beta	Sparse matrix of coefficients for each lambda. Use as.matrix() to convert.
df	Number of nonzero coefficients for each lambda.
dim	Dimensions of the coefficient matrix.
lambda	Sequence of lambda values used.
npasses	Total number of iterations across all lambda values.
jerr	Warnings and errors. 0 if no errors.
call	The matched call.

See Also

print.dcsvm, predict.dcsvm, coef.dcsvm, plot.dcsvm, and cv.dcsvm.

Examples

# Load the data
data(colon)
# Fit the elastic-net penalized DCSVM with lambda2 to be 1
fit <- dcsvm(colon$x, colon$y, lam2 = 1)
print(fit)
# Coefficients at some lambda value
c1 <- coef(fit, s = 0.005)
# Make predictions
predict(fit, newx = colon$x[1:10, ], s = c(0.01, 0.005))

dcsvm documentation built on April 3, 2025, 10:27 p.m.