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Derivative of the non-convex regularization penalty

Source: R/deriv.R
deriv.Rd

Compute the derivative of the specified non-convex regularization penalty.

Usage

deriv(penalty, Omega, lambda, gamma)

Arguments

penalty

A character string specifying the non-convex penalty to use. Available options include:

  1. "adapt": adaptive lasso (Zou 2006; Fan et al. 2009) .

  2. "atan": arctangent type penalty (Wang and Zhu 2016) .

  3. "exp": exponential type penalty (Wang et al. 2018) .

  4. "mcp": minimax concave penalty (Zou 2006) .

  5. "scad": smoothly clipped absolute deviation (Fan and Li 2001; Fan et al. 2009) .

Omega

The precision matrix.

lambda

A scalar specifying the regularization parameter.

gamma

A scalar specifying the hyperparameter for the penalty function. The defaults are:

  1. "adapt": 0.5

  2. "atan": 0.005

  3. "exp": 0.01

  4. "mcp": 3

  5. "scad": 3.7

Value

A numeric matrix.

References

Fan J, Feng Y, Wu Y (2009). “Network Exploration via the Adaptive LASSO and SCAD Penalties.” The Annals of Applied Statistics, 3(2), 521–541. doi:10.1214/08-aoas215 .

Fan J, Li R (2001). “Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties.” Journal of the American Statistical Association, 96(456), 1348–1360. doi:10.1198/016214501753382273 .

Wang Y, Fan Q, Zhu L (2018). “Variable Selection and Estimation using a Continuous Approximation to the \(L_0\) Penalty.” Annals of the Institute of Statistical Mathematics, 70(1), 191–214. doi:10.1007/s10463-016-0588-3 .

Wang Y, Zhu L (2016). “Variable Selection and Parameter Estimation with the Atan Regularization Method.” Journal of Probability and Statistics, 2016, 6495417. doi:10.1155/2016/6495417 .

Zou H (2006). “The Adaptive Lasso and Its Oracle Properties.” Journal of the American Statistical Association, 101(476), 1418–1429. doi:10.1198/016214506000000735 .