statsmodels.regression.dimred.SlicedInverseReg.fit_regularized

SlicedInverseReg.fit_regularized(ndim=1, pen_mat=None, slice_n=20, maxiter=100, gtol=0.001, **kwargs)

Estimate the EDR space using regularized SIR.

Parameters:

ndimint

The number of EDR directions to estimate

pen_matarray_like

A 2d array such that the squared Frobenius norm of dot(pen_mat, dirs)` is added to the objective function, where dirs is an orthogonal array whose columns span the estimated EDR space.

slice_nint, optional

Target number of observations per slice

maxiter :int

The maximum number of iterations for estimating the EDR space.

gtolfloat

If the norm of the gradient of the objective function falls below this value, the algorithm has converged.

Returns:

A results class instance.

Notes

If each row of exog can be viewed as containing the values of a function evaluated at equally-spaced locations, then setting the rows of pen_mat to [[1, -2, 1, …], [0, 1, -2, 1, ..], …] will give smooth EDR coefficients. This is a form of “functional SIR” using the squared second derivative as a penalty.

References

L. Ferre, A.F. Yao (2003). Functional sliced inverse regression analysis. Statistics: a journal of theoretical and applied statistics 37(6) 475-488.