Maybe this should be named strategy="sample".

This also requires not using statistics_ at transform time, so I suspect it should be a different class

Since I'm currently working on the SimpleImputer, I'd like to help on that.
Right now, statistics_ stores 1 statistic per column since the implemented strategies only need to impute a constant value in each column. This strategy is therefor quite different from the other ones. However, it's still a simple strategy, compared to the MICEImputer.
We can make a new class, say SampleImputer (maybe to close to SimpleImputer ?).
Another solution could be to store the induced probability distribution in statistics_ and make a special treatment for "sample" strategy at transform time.

I'd prefer SamplingImputer to SimpleImputer!

@RianneSchouten also volunteered to contribute this: #8478 (comment)

Ideas for tests. For any single-column training data X with non-zero nanvar, the following should hold:

values = np.unique(X)
values = values[~_get_mask(values, missing_values)]

Xts = []
for i in range(100):
    Xt = imputer.set_params(random_state=i).fit_transform(X)
    assert_array_equal(values, np.unique(Xt))
    Xts.append(Xt)

assert not np.allclose(Xts[-1], Xts[-2])  # or more strictly, some indices should fail np.allclose
assert np.mean(np.concatenate(Xts)) == pytest.approx(np.nanmean(X))

Behaviour at test time (i.e. transform might be harder to define) because we don't have many stochastic transformers. If a random seed is fixed, should every call to transform with the same data produce the same imputation? This would imply that fit_transform and transform are likely to draw the same samples. I'm not sure how problematic that is.

Is someone working actively on this? Otherwise can I take a look?

I thought @RianneSchouten was working on it, so I decided to step back, but I already have some code for that. Now that it seems that she's not actively working on that, I'll make a PR soon.

I don't mind whoever does it. I am quite busy so if you can are faster with making a PR, don't hesitate.

I made a PR to add this feature. Since I was not sure about new strategy vs new class, I made both. Tell me which one you think is best.

I agree on adding a different class and by default use binning.

Hi guys, is any of you still working on this issue or not, i want to help

There is discussing surrounding this issue in #11368

At a high level, it looks like the solution needs benchmarking to see how it performs when compared to other imputing strategies.

@thomasjpfan Thanks for letting me know, i'll try to catch up

Any updates on this? I would love to use random imputation as a baseline for comparing the performance of other imputation methods. This would be equivalent to DummyClassifier with strategy="uniform".

I don't think this is trivial, as the imputer should ideally:

• Support both categorical and numerical
• Support both continuous and discrete numerical variables (this could be fixed after imputation by the end-user)
• Support randomly sampling from a list of user-provided values
• Support sampling from a uniform distribution with a min/max value provided by the user

Probably the easier and faster way to implement this and provide minimum functionality would be sampling from a uniform distribution where the min/max values are the min/max non-missing values, column-wise. The end-user can then round the values to discretize them, if needed