Example 2: Regression

Here is an example of how to use the regmmd.regression module. In the following example the linear beta coefficient is estimated in a Gamma Regression task.

>>> from regmmd import MMDRegressor
>>> from regmmd.utils import print_summary
>>> from regmmd.regression import GammaRegressionLoc
>>> n = 1000
>>> p = 4
>>> beta = np.arange(1, 5)
>>> model_true = GammaRegressionLoc(par_v=beta, par_c=1, random_state=12)
>>>
>>> rng = np.random.default_rng(seed=123)
>>> X = rng.normal(loc=0, scale=1, size=(n, p))
>>> mu_given_x = model_true.predict(X=X)
>>> y = model_true.sample_n(n=n, mu_given_x=mu_given_x)
>>>
>>> beta_init = np.array([0.5, 1.5, 2.5, 3.2])
>>>
>>> mmd_reg = MMDRegressor(
...     model="gamma-regression-loc",
...     par_v=beta_init,
...     par_c=1.5,
...     fit_intercept=False,
...     bandwidth_X=0,
...     bandwidth_y=1,
...     kernel_y="Gaussian",
...     solver={
...         "burnin": 500,
...         "n_step": 10000,
...         "stepsize": 1,
...         "epsilon": 1e-8,
...     },
...     random_state=20
... )
>>> res = mmd_reg.fit(X, y)
>>> print_summary(res)

==================================================
            MMD Result Summary Report
==================================================

Initial Parameters:
    par_v: [0.5 1.5 2.5 3.2]
    par_c: 1.5

Stepsize: 1
Bandwidth: 1

Estimated Parameters:
     par_v: [1.00998778 1.98323581 3.00644719 3.6917812 ]

Trajectory Summary:
    Number of steps: 1056
    Final trajectory values: [ 1.0100, 1.9832, 3.0064, 3.6918 ]

==================================================
                  End of Report
==================================================

Compared to the MMDEstimator class, now that the model is fitted it is possible to also predict with the fitted model.

>>> X_test = rng.normal(loc=0, scale=1, size=(10, p))
>>> mmd_reg.predict(X_test)
array([6.66346287e+01, 9.92225472e+01, 1.06434759e+02, 6.30142110e-06,
       1.59249268e+01, 1.53260190e-03, 2.60517750e+00, 4.61954372e+05,
       6.08289686e+00, 1.75059655e-01])

Available Models

There are several pre-defined models available in the package, and these should cover most standard use-cases. The available estimation models can be found at Regression Models.

It is also possible to create your own model using the prescribed class regmmd.models.base_model.RegressionModel. A more detailed example can be found Here Example 3: Writing your own EstimationModel or RegressionModel.