Penalties

Penalty matrix generators

pygam.penalties.concave(n, coef)

Builds a penalty matrix for P-Splines with continuous features. Penalizes violation of a concave feature function.

Parameters:
  • n (int) – number of splines
  • coef (array-like) – coefficients of the feature function
Returns:

penalty matrix
Return type:

sparse csc matrix of shape (n,n)
pygam.penalties.convex(n, coef)

Builds a penalty matrix for P-Splines with continuous features. Penalizes violation of a convex feature function.

Parameters:
  • n (int) – number of splines
  • coef (array-like) – coefficients of the feature function
Returns:

penalty matrix
Return type:

sparse csc matrix of shape (n,n)
pygam.penalties.convexity_(n, coef, convex=True)

Builds a penalty matrix for P-Splines with continuous features. Penalizes violation of convexity in the feature function.

Parameters:
  • n (int) – number of splines
  • coef (array-like) – coefficients of the feature function
  • convex (bool, default: True) – whether to enforce convex, or concave functions
Returns:

penalty matrix
Return type:

sparse csc matrix of shape (n,n)
pygam.penalties.derivative(n, coef, derivative=2, periodic=False)

Builds a penalty matrix for P-Splines with continuous features. Penalizes the squared differences between basis coefficients.

Parameters:
  • n (int) – number of splines
  • coef (unused) – for compatibility with constraints
  • derivative (int, default: 2) – which derivative do we penalize. derivative is 1, we penalize 1st order derivatives, derivative is 2, we penalize 2nd order derivatives, etc
Returns:

penalty matrix
Return type:

sparse csc matrix of shape (n,n)
pygam.penalties.l2(n, coef)

Builds a penalty matrix for P-Splines with categorical features. Penalizes the squared value of each basis coefficient.

Parameters:
  • n (int) – number of splines
  • coef (unused) – for compatibility with constraints
Returns:

penalty matrix
Return type:

sparse csc matrix of shape (n,n)
pygam.penalties.monotonic_dec(n, coef)

Builds a penalty matrix for P-Splines with continuous features. Penalizes violation of a monotonic decreasing feature function.

Parameters:
  • n (int) – number of splines
  • coef (array-like) – coefficients of the feature function
Returns:

penalty matrix
Return type:

sparse csc matrix of shape (n,n)
pygam.penalties.monotonic_inc(n, coef)

Builds a penalty matrix for P-Splines with continuous features. Penalizes violation of a monotonic increasing feature function.

Parameters:
  • n (int) – number of splines
  • coef (array-like, coefficients of the feature function) –
Returns:

penalty matrix
Return type:

sparse csc matrix of shape (n,n)
pygam.penalties.monotonicity_(n, coef, increasing=True)

Builds a penalty matrix for P-Splines with continuous features. Penalizes violation of monotonicity in the feature function.

Parameters:
  • n (int) – number of splines
  • coef (array-like) – coefficients of the feature function
  • increasing (bool, default: True) – whether to enforce monotic increasing, or decreasing functions
Returns:

penalty matrix
Return type:

sparse csc matrix of shape (n,n)
pygam.penalties.none(n, coef)

Build a matrix of zeros for features that should go unpenalized

Parameters:
  • n (int) – number of splines
  • coef (unused) – for compatibility with constraints
Returns:

penalty matrix
Return type:

sparse csc matrix of shape (n,n)
pygam.penalties.periodic(n, coef, derivative=2, _penalty=<function derivative>)
pygam.penalties.sparse_diff(array, n=1, axis=-1)

A ported sparse version of np.diff. Uses recursion to compute higher order differences

Parameters:
  • array (sparse array) –
  • n (int, default: 1) – differencing order
  • axis (int, default: -1) – axis along which differences are computed
Returns:

diff_array – same shape as input array, but ‘axis’ dimension is smaller by ‘n’.
Return type:

sparse array
pygam.penalties.wrap_penalty(p, fit_linear, linear_penalty=0.0)

tool to account for unity penalty on the linear term of any feature.

Example

p = wrap_penalty(derivative, fit_linear=True)(n, coef)

Parameters:
  • p (callable.) – penalty-matrix-generating function.
  • fit_linear (boolean.) – whether the current feature has a linear term or not.
  • linear_penalty (float, default: 0.) – penalty on the linear term
Returns:

wrapped_p – modified penalty-matrix-generating function
Return type:

callable