# How to impute Missing values not the usual way?

I have a dataset of 4712 records working on binary classification. Label 1 is 33% and Label 0 is 67%. I can't drop records because my sample is already small. Because there are few columns which has around 250-350 missing records.

How do I know whether this is missing at random, missing completely at random or missing not at random. For ex: 4400 patients have the readings and 330 patients don't have the readings. But we expect these 330 to have the readings because it is a very usual measurement. So what is this called?

In addition, for my dataset it doesn't make sense to use mean or median straight away to fill missing values. I have been reading about algorithms like Multiple Imputation and Maximum Likelihood etc.

Is there any other algorithms that is good in filling the missing values in a robust way?

Is there any python packages for this?

Can someone help me with this?

To decide which strategy is appropriate, it is important to investigate the mechanism that led to the missing values to find out whether the missing data is missing completely at random (MCAR), missing at random (MAR), or missing not at random (MNAR).

• MCAR means that there is no relationship between the missingness of the data and any of the values.
• MAR means that that there is a systematic relationship between the propensity of missing values and the observed data, but not the missing data.
• MNAR means that there is a systematic relationship between the propensity of a value to be missing and its values.

Given what you have told its likely that its MCAR. (assumption is that you already tried to find this propensity yourself (domain knowledge) or build a model between the missing columns and other features and failed in doing so)

Some other techniques to impute the data, I would suggest looking at KNN imputation (from experience always solid results) but you should try different methods

fancy impute supports such kind of imputation, using the following API:

from fancyimpute import KNN

# Use 10 nearest rows which have a feature to fill in each row's missing features
X_fill_knn = KNN(k=10).fit_transform(X)


Here are different methods also supported by this package:

•SimpleFill: Replaces missing entries with the mean or median of each column.

•KNN: Nearest neighbor imputations which weights samples using the mean squared difference on features for which two rows both have observed data.

•SoftImpute: Matrix completion by iterative soft thresholding of SVD decompositions. Inspired by the softImpute package for R, which is based on Spectral Regularization Algorithms for Learning Large Incomplete Matrices by Mazumder et. al.

•IterativeSVD: Matrix completion by iterative low-rank SVD decomposition. Should be similar to SVDimpute from Missing value estimation methods for DNA microarrays by Troyanskaya et. al.

•MICE: Reimplementation of Multiple Imputation by Chained Equations.

•MatrixFactorization: Direct factorization of the incomplete matrix into low-rank U and V, with an L1 sparsity penalty on the elements of U and an L2 penalty on the elements of V. Solved by gradient descent.

•NuclearNormMinimization: Simple implementation of Exact Matrix Completion via Convex Optimization by Emmanuel Candes and Benjamin Recht using cvxpy. Too slow for large matrices.

•BiScaler: Iterative estimation of row/column means and standard deviations to get doubly normalized matrix. Not guaranteed to converge but works well in practice. Taken from Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares.

EDIT: MICE was deprecated and they moved it to sklearn under iterative imputer

• Hi @Noah Weber. Thanks for the response. Upvoted. but i see in the doc that MICE is missing. It is not available? Jan 11 '20 at 12:07
• Is it available in any other package? Everything is present in the doc except MICE approach Jan 11 '20 at 12:09
• Yes it was deprecated and they moved it to sklearn under iterative imputer scikit-learn.org/stable/modules/generated/… Jan 11 '20 at 12:17
• So I see it's experimental version. So this is the only way to do MICE? Jan 11 '20 at 12:41
• Can you expand on why you think this is MCAR? I'd have suspected missing measurements on patient data to be MAR or even MNAR: when there's a reason not to take the measurement (e.g. instrument availability, time constraints, ...) the decision to skip measurement for a particular patient will likely depend on how important the medical staff judges this measurement to be for that patient. Jan 12 '20 at 13:25

A trick I have seen on Kaggle.

Step 1: replace NAN with the mean or the median. The mean, if the data is normally distributed, otherwise the median.

In my case, I have NANs in Age.

Step 2: Add a new column "NAN_Age." 1 for NAN, 0 otherwise. If there's a pattern in NAN, you help the algorithm catch it. A nice bonus is that this strategy doesn't care if it's MAR or MNAR (see above).

• Thanks for the response @FrancoSwiss. Good to know. useful. upvoted Jan 11 '20 at 12:57
• Theoretically mean and median of normal distribution are equal, why not just replace missing values with median all the time? Jan 11 '20 at 18:46
• Hi @FrancoSwiss - a quick question. might be a basic question. Let's say I have a varible called blood pressure. Out of 4712 records, let's say we have NA for 3400 records. Now if I replace based on median and code a new variable NA_blood_pressure as 1 and 0, what's the use if my model says that NA_blood_pressure is an important predictor? Is it any useful? How do I interpret this? Should I then interpret it as , blood pressure with median values are important in influencing the outcome? Can you explain me like I am 5. because I am new to ML and trying to learn Jan 12 '20 at 1:05
• So, lets' say we have 10 features. Out of which weight and blood pressure are two of them.They leave these two fields empty and we code two new variables like NA_weight and NA_blood_pressure. During our analysis, if our model returns that NA_weight and NA_blood_pressure as significant risk factors, how am I supposed to interpret this? Because NA_weight has both 0's and 1's. Or another example is, what if my model returns weight and NA_weight as important/signifnicant variables Jan 12 '20 at 7:51
• So as we fill NA values of weight column with median/mean, it becomes a non-null column and finally we have weight as one important factor. But what's the use of having NA_weight categorical column. Anyway you are replacing na values with median/mean. So how is NA_weight used? We can do the same without having NA_weight. Is there any advantage to having NA_weight? Jan 13 '20 at 0:20

A small remark to the often suggested mean/median imputation.

Applying this method would assume that your analysis is only dependent on the first moment of your variable´s distribution.

Just imagine you would impute all values of your variable with mean/median. The mean/median probably would have very low bias. But the variance would go (close to) zero. Skewness / Kurtosis would also be biased significantly.

A way around this would be to add a random value x to each imputation, with E(x) = 0 and E(x^2) > 0.

• Hi, thanks for the response. upvoted..would you mind to explain with an example? I am new to ML and would be helpful Jan 12 '20 at 1:06

scikit learn itself has some good ready to use packages for imputation. details here

MICE is not available in scikit learn as far as i know. Please check statsmodel for MICE statsmodels.imputation.mice.MICEDATA

• That's probably more useful for a regression task. In a classification task, missing data might indicate a pattern. Thus, you want to "communicate" to the algorithm that there was a NAN. That's best achieved by adding a column with 1,0 for NANAs. Jan 11 '20 at 19:34
• Welcome to SO vivek. thanks for the response. Upvoted. Jan 12 '20 at 1:07