Distributed Estimation

This notebook goes through a couple of examples to show how to use distributed_estimation. We import the DistributedModel class and make the exog and endog generators.

import numpy as np
from scipy.stats.distributions import norm
from statsmodels.base.distributed_estimation import DistributedModel


def _exog_gen(exog, partitions):
    """partitions exog data"""

    n_exog = exog.shape[0]
    n_part = np.ceil(n_exog / partitions)

    ii = 0
    while ii < n_exog:
        jj = int(min(ii + n_part, n_exog))
        yield exog[ii:jj, :]
        ii += int(n_part)


def _endog_gen(endog, partitions):
    """partitions endog data"""

    n_endog = endog.shape[0]
    n_part = np.ceil(n_endog / partitions)

    ii = 0
    while ii < n_endog:
        jj = int(min(ii + n_part, n_endog))
        yield endog[ii:jj]
        ii += int(n_part)

Next we generate some random data to serve as an example.

X = np.random.normal(size=(1000, 25))
beta = np.random.normal(size=25)
beta *= np.random.randint(0, 2, size=25)
y = norm.rvs(loc=X.dot(beta))
m = 5

This is the most basic fit, showing all of the defaults, which are to use OLS as the model class, and the debiasing procedure.

debiased_OLS_mod = DistributedModel(m)
debiased_OLS_fit = debiased_OLS_mod.fit(
    zip(_endog_gen(y, m), _exog_gen(X, m)), fit_kwds={"alpha": 0.2}
)

Then we run through a slightly more complicated example which uses the GLM model class.

from statsmodels.genmod.generalized_linear_model import GLM
from statsmodels.genmod.families import Gaussian

debiased_GLM_mod = DistributedModel(
    m, model_class=GLM, init_kwds={"family": Gaussian()}
)
debiased_GLM_fit = debiased_GLM_mod.fit(
    zip(_endog_gen(y, m), _exog_gen(X, m)), fit_kwds={"alpha": 0.2}
)

We can also change the estimation_method and the join_method. The below example show how this works for the standard OLS case. Here we using a naive averaging approach instead of the debiasing procedure.

from statsmodels.base.distributed_estimation import _est_regularized_naive, _join_naive


naive_OLS_reg_mod = DistributedModel(
    m, estimation_method=_est_regularized_naive, join_method=_join_naive
)
naive_OLS_reg_params = naive_OLS_reg_mod.fit(
    zip(_endog_gen(y, m), _exog_gen(X, m)), fit_kwds={"alpha": 0.2}
)

Finally, we can also change the results_class used. The following example shows how this work for a simple case with an unregularized model and naive averaging.

from statsmodels.base.distributed_estimation import (
    _est_unregularized_naive,
    DistributedResults,
)


naive_OLS_unreg_mod = DistributedModel(
    m,
    estimation_method=_est_unregularized_naive,
    join_method=_join_naive,
    results_class=DistributedResults,
)
naive_OLS_unreg_params = naive_OLS_unreg_mod.fit(
    zip(_endog_gen(y, m), _exog_gen(X, m)), fit_kwds={"alpha": 0.2}
)