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Imputes missing data with MICE + random forests

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miceforest: Fast Imputation with Random Forests in Python

Fast, memory efficient Multiple Imputation by Chained Equations (MICE) with random forests. It can impute categorical and numeric data without much setup, and has an array of diagnostic plots available. The R version of this package may be found here.

This document contains a thorough walkthrough of the package, benchmarks, and an introduction to multiple imputation. More information on MICE can be found in Stef van Buuren’s excellent online book, which you can find here.

Table of Contents:

Package Meta

miceforest has 4 main classes which the user will interact with:

  • KernelDataSet - a kernel data set is a dataset on which the mice algorithm is performed. Models are saved inside the instance, which can also be called on to impute new data. Several plotting methods are included to run diagnostics on the imputed data.
  • MultipleImputedKernel - a collection of KernelDataSets. Has additional methods for accessing and comparing multiple kernel datasets together.
  • ImputedDataSet - a single dataset that has been imputed. These are returned after impute_new_data() is called.
  • MultipleImputedDataSet - A collection of datasets that have been imputed. Has additional methods for comparing the imputations between datasets.

You can download the latest stable version from PyPi:

$ pip install miceforest

You can also download the latest development version from this repository:

$ pip install git+https://github.com/AnotherSamWilson/miceforest.git

Using miceforest

In these examples we will be looking at a few simple examples of imputation. We need to load the packages, and define the data:

import miceforest as mf
from sklearn.datasets import load_iris
import pandas as pd
import numpy as np

# Load data and introduce missing values
iris = pd.concat(load_iris(as_frame=True,return_X_y=True),axis=1)
iris['target'] = iris['target'].astype('category')
iris_amp = mf.ampute_data(iris,perc=0.25,random_state=1991)

Imputing a Single Dataset

If you only want to create a single imputed dataset, you can use KernelDataSet:

# Create kernel. 
kds = mf.KernelDataSet(
  iris_amp,
  save_all_iterations=True,
  random_state=1991
)

# Run the MICE algorithm for 3 iterations
kds.mice(3)

# Return the completed kernel data
completed_data = kds.complete_data()

There are also an array of plotting functions available, these are discussed below in the section Diagnostic Plotting. The plotting behavior between single imputed datasets and multi-imputed datasets is slightly different.

Simple Example of Multiple Imputation

We can also create a class which contains multiple KernelDataSets, along with easy ways to compare them:

# Create kernel. 
kernel = mf.MultipleImputedKernel(
  iris_amp,
  datasets=4,
  save_all_iterations=True,
  random_state=1991
)

# Run the MICE algorithm for 3 iterations on each of the datasets
kernel.mice(3)

Printing the MultipleImputedKernel object will tell you some high level information:

print(kernel)
##               Class: MultipleImputedKernel
##        Models Saved: Last Iteration
##            Datasets: 4
##          Iterations: 3
##   Imputed Variables: 5
## save_all_iterations: True

Controlling Tree Growth

A very nice thing about random forests is that they are trivially parallelizable. We can save a lot of time by setting the n_jobs parameter in both the fit and predict methods for the random forests:

# Run the MICE algorithm for 2 more iterations on the kernel, 
kernel.mice(2,n_jobs=2)

Any other arguments may be passed to either class (RandomForestClassifier,RandomForestRegressor). In our example, we may not have saved much (if any) time. This is because there is overhead with using multiple cores, and our data is very small.

Creating a Custom Imputation Schema

It is possible to customize our imputation procedure by variable. By passing a named list to variable_schema, you can specify the predictors for each variable to impute. You can also select which variables should be imputed using mean matching, as well as the mean matching candidates, by passing a dict tomean_match_candidates:

var_sch = {
    'sepal width (cm)': ['target','petal width (cm)'],
    'petal width (cm)': ['target','sepal length (cm)']
}
var_mmc = {
    'sepal width (cm)': 5,
    'petal width (cm)': 0
}

cust_kernel = mf.MultipleImputedKernel(
    iris_amp,
    datasets=3,
    variable_schema=var_sch,
    mean_match_candidates=var_mmc
)
cust_kernel.mice(2)

Imputing New Data with Existing Models

Multiple Imputation can take a long time. If you wish to impute a dataset using the MICE algorithm, but don’t have time to train new models, it is possible to impute new datasets using a MultipleImputedKernel object. The impute_new_data() function uses the random forests collected by MultipleImputedKernel to perform multiple imputation without updating the random forest at each iteration:

# Our 'new data' is just the first 15 rows of iris_amp
new_data = iris_amp.iloc[range(15)]
new_data_imputed = kernel.impute_new_data(new_data=new_data)
print(new_data_imputed)
##               Class: MultipleImputedDataSet
##            Datasets: 4
##          Iterations: 5
##   Imputed Variables: 5
## save_all_iterations: False

All of the imputation parameters (variable_schema, mean_match_candidates, etc) will be carried over from the original MultipleImputedKernel object. When mean matching, the candidate values are pulled from the original kernel dataset. To impute new data, the save_models parameter in MultipleImputedKernel must be > 0. If save_models == 1, the model from the latest iteration is saved for each variable. If save_models > 1, the model from each iteration is saved. This allows for new data to be imputed in a more similar fashion to the original mice procedure.

Diagnostic Plotting

As of now, miceforest has four diagnostic plots available.

Distribution of Imputed-Values

We probably want to know how the imputed values are distributed. We can plot the original distribution beside the imputed distributions in each dataset by using the plot_imputed_distributions method of an MultipleImputedKernel object:

kernel.plot_imputed_distributions(wspace=0.3,hspace=0.3)

The red line is the original data, and each black line are the imputed values of each dataset.

Convergence of Correlation

We are probably interested in knowing how our values between datasets converged over the iterations. The plot_correlations method shows you a boxplot of the correlations between imputed values in every combination of datasets, at each iteration. This allows you to see how correlated the imputations are between datasets, as well as the convergence over iterations:

kernel.plot_correlations()

Variable Importance

We also may be interested in which variables were used to impute each variable. We can plot this information by using the plot_feature_importance method.

kernel.plot_feature_importance(annot=True,cmap="YlGnBu",vmin=0, vmax=1)

The numbers shown are returned from the sklearn random forest _feature_importance attribute. Each square represents the importance of the column variable in imputing the row variable.

Mean Convergence

If our data is not missing completely at random, we may see that it takes a few iterations for our models to get the distribution of imputations right. We can plot the average value of our imputations to see if this is occurring:

kernel.plot_mean_convergence(wspace=0.3, hspace=0.4)

Our data was missing completely at random, so we don’t see any convergence occurring here.

Using the Imputed Data

To return the imputed data simply use the complete_data method:

dataset_1 = kernel.complete_data(0)

This will return a single specified dataset. Multiple datasets are typically created so that some measure of confidence around each prediction can be created.

Since we know what the original data looked like, we can cheat and see how well the imputations compare to the original data:

acclist = []
for iteration in range(kernel.iteration_count()+1):
    target_na_count = kernel.na_counts['target']
    compdat = kernel.complete_data(dataset=0,iteration=iteration)

    # Record the accuract of the imputations of target.
    acclist.append(
      round(1-sum(compdat['target'] != iris['target'])/target_na_count,2)
    )

# acclist shows the accuracy of the imputations
# over the iterations.
print(acclist)
## [0.32, 0.76, 0.78, 0.81, 0.86, 0.86]

In this instance, we went from a ~32% accuracy (which is expected with random sampling) to an accuracy of ~86%. We managed to replace the missing target values with a pretty high degree of accuracy!

The MICE Algorithm

Multiple Imputation by Chained Equations ‘fills in’ (imputes) missing data in a dataset through an iterative series of predictive models. In each iteration, each specified variable in the dataset is imputed using the other variables in the dataset. These iterations should be run until it appears that convergence has been met.

This process is continued until all specified variables have been imputed. Additional iterations can be run if it appears that the average imputed values have not converged, although no more than 5 iterations are usually necessary.

Common Use Cases

Data Leakage:

MICE is particularly useful if missing values are associated with the target variable in a way that introduces leakage. For instance, let’s say you wanted to model customer retention at the time of sign up. A certain variable is collected at sign up or 1 month after sign up. The absence of that variable is a data leak, since it tells you that the customer did not retain for 1 month.

Funnel Analysis:

Information is often collected at different stages of a ‘funnel’. MICE can be used to make educated guesses about the characteristics of entities at different points in a funnel.

Confidence Intervals:

MICE can be used to impute missing values, however it is important to keep in mind that these imputed values are a prediction. Creating multiple datasets with different imputed values allows you to do two types of inference:

  • Imputed Value Distribution: A profile can be built for each imputed value, allowing you to make statements about the likely distribution of that value.
  • Model Prediction Distribution: With multiple datasets, you can build multiple models and create a distribution of predictions for each sample. Those samples with imputed values which were not able to be imputed with much confidence would have a larger variance in their predictions.

Predictive Mean Matching

miceforest can make use of a procedure called predictive mean matching (PMM) to select which values are imputed. PMM involves selecting a datapoint from the original, nonmissing data which has a predicted value close to the predicted value of the missing sample. The closest N (mean_match_candidates parameter) values are chosen as candidates, from which a value is chosen at random. This can be specified on a column-by-column basis. Going into more detail from our example above, we see how this works in practice:

This method is very useful if you have a variable which needs imputing which has any of the following characteristics:

  • Multimodal
  • Integer
  • Skewed

Effects of Mean Matching

As an example, let’s construct a dataset with some of the above characteristics:

randst = np.random.RandomState(1991)
# random uniform variable
nrws = 1000
uniform_vec = randst.uniform(size=nrws)

def make_bimodal(mean1,mean2,size):
    bimodal_1 = randst.normal(size=nrws, loc=mean1)
    bimodal_2 = randst.normal(size=nrws, loc=mean2)
    bimdvec = []
    for i in range(size):
        bimdvec.append(randst.choice([bimodal_1[i], bimodal_2[i]]))
    return np.array(bimdvec)

# Make 2 Bimodal Variables
close_bimodal_vec = make_bimodal(2,-2,nrws)
far_bimodal_vec = make_bimodal(3,-3,nrws)


# Highly skewed variable correlated with Uniform_Variable
skewed_vec = np.exp(uniform_vec*randst.uniform(size=nrws)*3) + randst.uniform(size=nrws)*3

# Integer variable correlated with Close_Bimodal_Variable and Uniform_Variable
integer_vec = np.round(uniform_vec + close_bimodal_vec/3 + randst.uniform(size=nrws)*2)

# Make a DataFrame
dat = pd.DataFrame(
    {
    'uniform_var':uniform_vec,
    'close_bimodal_var':close_bimodal_vec,
    'far_bimodal_var':far_bimodal_vec,
    'skewed_var':skewed_vec,
    'integer_var':integer_vec
    }
)

# Ampute the data.
ampdat = mf.ampute_data(dat,perc=0.25,random_state=randst)

# Plot the original data
import seaborn as sns
import matplotlib.pyplot as plt
g = sns.PairGrid(dat)
g.map(plt.scatter,s=5)
We can see how our variables are distributed and correlated in the graph above. Now let’s run our imputation process twice, once using mean matching, and once using the model prediction.
kernelmeanmatch <- mf.MultipleImputedKernel(ampdat,mean_match_candidates=5)
kernelmodeloutput <- mf.MultipleImputedKernel(ampdat,mean_match_candidates=0)

kernelmeanmatch.mice(5)
kernelmodeloutput.mice(5)

Let’s look at the effect on the different variables.

With Mean Matching
kernelmeanmatch.plot_imputed_distributions(wspace=0.2,hspace=0.4)
Without Mean Matching
kernelmodeloutput.plot_imputed_distributions(wspace=0.2,hspace=0.4)

You can see the effects that mean matching has, depending on the distribution of the data. Simply returning the value from the model prediction, while it may provide a better ‘fit’, will not provide imputations with a similair distribution to the original. This may be beneficial, depending on your goal.

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