Regression Robustness

The robustness also translates to the regression procedure

>>> from regmmd import MMDRegressor
>>> from regmmd.utils import print_summary
>>> from sklearn.linear_model import LinearRegression
>>>
>>> p = 3
>>> x = rng.normal(loc=0, scale=1.5, size=(50, p))
>>> beta = np.array([1, 2, 3])
>>> noise = rng.normal(loc=0, scale=0.5, size=(50,))
>>> y = x @ beta + noise
>>> # We contaminate  only one sample
>>> y[42] = 100
>>>
>>> # Fit a standard model
>>> lin_reg = LinearRegression(fit_intercept=False)
>>> _ = lin_reg.fit(x, y)
>>>
>>> mmd_reg = MMDRegressor(
...     model="linear-gaussian-loc",
...     par_v=None,
...     par_c=None,
...     fit_intercept=False,
...     bandwidth_X=1,
...     bandwidth_y=0.5,
...     kernel_X="Laplace",
...     kernel_y="Laplace",
...     solver={"burnin": 500,
...             "n_step": 10000,
...             "stepsize": 1,
...             "epsilon": 1e-8
...      },
...      random_state=42
... )
>>> res = mmd_reg.fit(X=x, y=y)
>>> lin_reg_error = np.abs(lin_reg.coef_ - beta).sum()
>>> print(lin_reg.coef_)
[-0.46385604  2.60706584  2.26142131]
>>> print(lin_reg_error)
2.8095005652996297
>>> mmd_reg_error = np.abs(res["estimator"] - beta).sum()
>>> print(res["estimator"])
[0.74946784 3.5982815  2.87334419]
>>> print(mmd_reg_error)
1.9754694658571772