# Penalized Regression

### Description

Perform a penalized regression, as used in penalized discriminant analysis.

### Usage

1 |

### Arguments

`x, y, weights` |
the x and y matrix and possibly a weight vector. |

`lambda` |
the shrinkage penalty coefficient. |

`omega` |
a penalty object; omega is the eigendecomposition of the penalty matrix, and need not have full rank. By default, standard ridge is used. |

`df` |
an alternative way to prescribe lambda, using the notion of equivalent degrees of freedom. |

`...` |
currently not used. |

### Value

A generalized ridge regression, where the coefficients are penalized
according to omega. See the function definition for further details.
No functions are provided for producing one dimensional penalty
objects (omega).
`laplacian()`

creates a two-dimensional penalty
object, suitable for (small) images.

### See Also

`laplacian`