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Include a lower bound attribute of BaseMixture #28492

@a-wozniakowski

Description

@a-wozniakowski

Describe the workflow you want to enable

Currently, there exists a lower_bound_ attribute in the fit_predict method of BaseMixture. However, the entire sequence of lower bounds is not accessible, which makes a convergence analysis more difficult to a user.

Describe your proposed solution

In addition to the lower_bound_ attribute, create a new attribute called lower_bounds_, which is a list of floats where each float is a lower bound set in

lower_bound = self._compute_lower_bound(log_resp, log_prob_norm)
.

Describe alternatives you've considered, if relevant

No response

Additional context

Creating the list and appending to it would increase memory costs (but not by much). Is this a possible concern?

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