More memory efficient LinearClassifierMixin.predict

I'm running out of memory with LogisticRegression.predict on a dataset with,

• n_samples = 1M, n_feature=8k, n_classes=800

This happens as LinearClassifierMixin.predict, needs to compute the decision function for all classes which involves a (n_samples, n_features) x (n_features, n_classes) multiplication, resulting in a (n_samples, n_classes) dense matrix (in my case ~6 GB).

Batching in n_samples is a solution, but it would have been nice to have a standard way of doing that, either as a util function that would be used to decorate e.g. batch_apply(LinearClassifierMixin.predict)(X) or a fit param LinearClassifierMixin.predict(X, batch_size=1000).

This is somewhat related to parallizing predict in general (since there batching also happens). Can't find the corresponding issue right now.

This particular case is made worse by the fact that LogisticRegression.coef_ is not enforced to be float32 for float32 sparse training input (with the liblinear solver) related https://github.com/scikit-learn/scikit-learn/issues/8769.

Start at LinearClassifierMixin.predict and follow how LogisticRegression.predict computes the decision function for all classes. Reproduce the reported large-input memory behavior, then evaluate the proposed batching approaches and their API implications. Done means prediction handles large sample and class dimensions without requiring the full dense decision matrix in memory.