SC: check robustness of results (frequentist)

[drbenvincent]

I've experienced clearly sub-optimal weightings when running the the WeightedProportion custom scikit-learn model. It is likely due to bad optimisation, perhaps getting stuck by local optima. So we need to explore the dependence of the results upon w_start.

CausalPy/causalpy/skl_models.py

Lines 22 to 33 in 815c14c

	def fit(self, X, y):
	w_start = [1 / X.shape[1]] * X.shape[1]
	coef_ = fmin_slsqp(
	partial(self.loss, X=X, y=y),
	np.array(w_start),
	f_eqcons=lambda w: np.sum(w) - 1,
	bounds=[(0.0, 1.0)] * len(w_start),
	disp=False,
	)
	self.coef_ = np.atleast_2d(coef_) # return as column vector
	self.mse = self.loss(W=self.coef_, X=X, y=y)
	return self

One way to approach making the results more reliable (more likely to represent the global minimum) is to use a particle swarm type approach where we run the optimisation multiple times, each with different w_start.

• Look into the relevant fitting procedures in scikit-learn.