Explain KNN or MICE imputation principles

What's really being asked

The interviewer checks whether you understand that naive mean or median fill shrinks variance and flattens correlations, and whether you can describe a principled alternative that respects relationships between features and the uncertainty of the missing values themselves.

The full answer

KNN imputation finds the k rows most similar to the one with a missing value, using a distance computed over the observed features, then fills the gap with a (often distance-weighted) average of those neighbors. Because similar rows tend to share similar values, this preserves local structure that mean fill destroys. MICE, or Multiple Imputation by Chained Equations, treats each variable with missingness as the target of a regression on all other variables. It cycles through variables one at a time, repeatedly re-imputing until estimates stabilize, and crucially runs the whole process several times to generate multiple completed datasets. Analyses are run on each and pooled, so the final standard errors reflect the extra uncertainty introduced by imputation.

The mistakes people make

Saying mean imputation is adequate, or describing single imputation as equivalent to multiple imputation. Single fills understate variance and bias correlations toward zero.

What usually comes next

What missingness mechanism do these methods assume, MCAR, MAR, or MNAR? Why does multiple imputation give better confidence intervals? How does KNN scale on large or high-dimensional data?

A concrete example

A health dataset is missing some blood-pressure readings. Mean fill would assign every gap the same value, weakening its true correlation with age and weight. KNN instead pulls readings from patients with similar age, weight, and history. MICE goes further, regressing blood pressure on those features, generating five completed datasets, fitting the downstream model on each, and pooling results so reported uncertainty is honest.