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Generate penalty matrix for regularization

penalty_matrix.Rd

Generate a penalty matrix for regularizing HRF basis coefficients. The penalty matrix encodes shape priors that discourage implausible or overly wiggly HRF estimates. Different HRF types use different penalty structures:

  • FIR/B-spline/Tent bases: Roughness penalties based on discrete derivatives

  • SPM canonical + derivatives: Differential shrinkage of derivative terms

  • Fourier bases: Penalties on high-frequency components

  • Daguerre bases: Increasing weights on higher-order terms

  • Default: Identity matrix (ridge penalty)

Usage

penalty_matrix(x, ...)

# S3 method for class 'HRF'
penalty_matrix(x, order = 2, ...)

# S3 method for class 'BSpline_HRF'
penalty_matrix(x, order = 2, ...)

# S3 method for class 'Tent_HRF'
penalty_matrix(x, order = 2, ...)

# S3 method for class 'FIR_HRF'
penalty_matrix(x, order = 2, ...)

# S3 method for class 'SPMG2_HRF'
penalty_matrix(x, order = 2, shrink_deriv = 2, ...)

# S3 method for class 'SPMG3_HRF'
penalty_matrix(x, order = 2, shrink_deriv = 2, ...)

# S3 method for class 'Fourier_HRF'
penalty_matrix(x, order = 2, ...)

# S3 method for class 'Daguerre_HRF'
penalty_matrix(x, order = 2, ...)

Arguments

x

The HRF object or basis specification

...

Additional arguments passed to specific methods

order

Integer specifying the order of the penalty (default: 2)

Value

A symmetric positive definite penalty matrix of dimension nbasis(x) × nbasis(x)

Details

The penalty matrix R is used in regularized estimation as λ * h^T R h, where h are the basis coefficients and λ is the regularization parameter. Well-designed penalty matrices can significantly improve HRF estimation by encoding smoothness or other shape constraints.

See also

[nbasis()], [HRF_objects]

Other hrf: HRF_objects

Examples

# FIR basis with smoothness penalty
fir_hrf <- HRF_FIR
R_fir <- penalty_matrix(fir_hrf)

# B-spline basis with second-order smoothness
bspline_hrf <- HRF_BSPLINE  
R_bspline <- penalty_matrix(bspline_hrf, order = 2)

# SPM canonical with derivative shrinkage
spmg3_hrf <- HRF_SPMG3
R_spmg3 <- penalty_matrix(spmg3_hrf, shrink_deriv = 4)