How to implement single Imputation from conditional distribution?

This is just an intuitive explanation of a group of a strategy for imputing missing data.

In practice, the distribution $P(x_{mis}|x_{obs};mathbf{theta})$ is unknown and can be estimated at best. The best way to estimate this probability is use-case specific. Understanding how the training data was collected can help you in estimating/defining this conditional distribution.

In practice, we often do not try to get a good estimation. Keeping things simple and assuming all features are sampled from a normal distribution might get you started.

This is $x_{mis}$ follows $N(mu, sigma)$ where

• $mu = sum_i^N frac{x_{obs,i}}{N}$
• $sigma = sum_i^N frac{(x_{obs,i}-mu)^2}{N-1}$

. However, such assumptions are rarely realistic and will do guarantee good models. See this.