How do scikit-learn's SimpleImputer, KNNImputer and IterativeImputer differ?

## The shared contract All three live in `sklearn.impute` and are ordinary transformers: `fit()` learns whatever it needs from training data, `transform()` fills. That matters because the naive alternative — filling with a mean computed over the whole frame before splitting — derives the fill value from rows that include the test set, so information crosses the split. Imputers exist so the fill value becomes part of the fitted model. All of them accept `missing_values` (default `np.nan`, but you can point it at a sentinel like `-999`), `add_indicator`, and `keep_empty_features`, which controls whether a column that was entirely missing during fit survives as zeros rather than being dropped. ## SimpleImputer One statistic per column, held in `statistics_`: - `'mean'` and `'median'` — numeric only; median is the robust choice when the column is skewed or has outliers. - `'most_frequent'` — works on numeric and string/object columns, and is what you use ahead of an encoder. - `'constant'` with `fill_value` — fills with a literal, including a string like `'missing'` that then becomes its own category downstream. It is fast, its fitted state is tiny, and it is what you should reach for first. Its weakness is that it flattens variance: filling everything with one number pulls the column towards its centre and understates uncertainty, which biases downstream variance estimates. ## KNNImputer For each row with a missing value, it finds the `n_neighbors` closest training rows using the `nan_euclidean` distance — a Euclidean distance computed over the coordinates both rows have present, then rescaled for the number of missing coordinates — and fills with their average, optionally distance-weighted via `weights='distance'`. It preserves relationships between correlated columns far better than a column mean. The costs are real: the fitted object retains the training matrix, transform is a neighbour search per row rather than a lookup, and because distance is Euclidean the features should be on comparable scales or the largest-unit column dominates the neighbourhood. ## IterativeImputer The most expressive of the three. It initialises the missing entries (`initial_strategy`, default `'mean'`), then treats each column with missing values in turn as the regression target and the others as predictors, fitting the supplied `estimator` (a `BayesianRidge` by default) and replacing that column's missing entries with predictions. It repeats the round-robin for `max_iter` passes or until the change falls below `tol`. `imputation_order` controls the sweep order, and `sample_posterior=True` draws from the posterior instead of taking the point estimate, which is how you build multiple-imputation-style variability. Two API facts to state: as of scikit-learn 1.9 it is still gated behind the experimental flag, so `from sklearn.experimental import enable_iterative_imputer` must execute before `from sklearn.impute import IterativeImputer` or the import fails; and it fits one model per column per iteration, so on a wide matrix it is dramatically slower than the alternatives, at both fit and transform time. ## The missingness indicator `add_indicator=True` appends binary columns — the same thing `MissingIndicator` produces standalone — flagging which entries were missing. This is often the highest-value line in the whole preprocessing stack, because missingness is frequently informative: a blank income field may say more about the applicant than any imputed value would. Filling without an indicator destroys that signal; filling with one lets the model decide. ## Choosing Start with `SimpleImputer(strategy='median')` for numeric columns and `'most_frequent'` or `'constant'` for categorical, both with `add_indicator=True`, and treat that as the baseline. Move to `KNNImputer` or `IterativeImputer` only when a measured comparison — same splits, same model — shows the extra cost buys accuracy. The sophisticated imputers also complicate serving: `KNNImputer` ships the training data inside the artifact, and `IterativeImputer` runs a set of models on every prediction. ## How to answer Name what each one learns (`statistics_`, the training rows, per-column estimators), name the cost of each, mention the experimental import for `IterativeImputer`, and finish with `add_indicator`. The interviewer is checking whether you know these are fitted objects rather than one-line frame operations.