`fracridge`.fracridge¶

fracridge(X, y, fracs=None, tol=1e-10, jit=True)[source]¶

Approximates alpha parameters to match desired fractions of OLS length.

Parameters

Xndarray, shape (n, p): Design matrix for regression, with n number of observations and p number of model parameters.
yndarray, shape (n, b): Data, with n number of observations and b number of targets.
fracsfloat or 1d array, optional: The desired fractions of the parameter vector length, relative to OLS solution. If 1d array, the shape is (f,). This input is required to be sorted. Otherwise, raises ValueError. Default: np.arange(.1, 1.1, .1).
jitbool, optional: Whether to speed up computations by using a just-in-time compiled version of core computations. This may not work well with very large datasets. Default: True

Returns

coefndarray, shape (p, f, b): The full estimated parameters across units of measurement for every desired fraction. If fracs is a float or y is a vector, the second or third dimensions are squeezed, correspondingly.
alphasndarray, shape (f, b): The alpha coefficients associated with each solution

Examples

Generate random data:

>>> np.random.seed(0)
>>> y = np.random.randn(100)
>>> X = np.random.randn(100, 10)

Calculate coefficients with naive OLS:

>>> coef = np.linalg.inv(X.T @ X) @ X.T @ y
>>> print(np.linalg.norm(coef))  
0.35

Call fracridge function:

>>> coef2, alpha = fracridge(X, y, 0.3)
>>> print(np.linalg.norm(coef2))  
0.10
>>> print(np.linalg.norm(coef2) / np.linalg.norm(coef))  
0.3

Calculate coefficients with naive RR:

>>> alphaI = alpha * np.eye(X.shape[1])
>>> coef3 = np.linalg.inv(X.T @ X + alphaI) @ X.T @ y
>>> print(np.linalg.norm(coef2 - coef3))  
0.0

fracridge.fracridge¶