My concerns are described in #14338.

Basically there is no common definition of what convergence means from what I know. In particular, the common case of MissForest where the regressor is a random forest regressor has no useful convergence criterion on scikit-learn.

Thanks. This would be helpful to add to the documentation in the "Note" box on the IterativeImputer page. Maybe that'd make it easier for people to get involved in fixing the convergence issue.

PR welcome, @skeller88

Quick question: are there any plans to support categorical features with IterativeImputer? The original MICE implementation (paper) supports this.

I did some testing and basic functionality can be achieved by allowing the estimator parameter to an array-like of estimators of shape (n_features,). That way you can specify a different estimator for each feature, and some can be classifiers.

The trickier part is handling pre-processing steps to those estimators. If some of the features are categorical, they would need to be OneHot encoded between the initial imputation step (which fills in the missing values) and the iterative estimator fitting/predicting.

Since IterableImputer splices out one feature at a time (neighbor_feat_idx and feat_idx), the application of transformers needs to be dynamic. At the same time, it would not be good to refit the transformers each time. An ideal solution would be some type of dynamic ColumnTransformer where you run fit_transform once and then dynamically select which columns to apply transform to. Then at the end you'd apply inverse_transform to the imputed X. You can't apply ColumnTransformer.transform and then splice out the feat_idx because there is no way to keep track of which transformed features correspond to feat_idx (i.e., OneHotEncoder could map a single feature to many!).

The other issue is convergence. I think there is no logical way to quantify convergence from a single ItearativeImputer with this type of mixed imputation, multiple imputation (to compare variance within IterativeImputers to variance between branches) or something else would be needed.