miceforest 4.0.2

Imputes missing data with MICE + random forests

miceforest: Fast Imputation with lightgbm 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
• The Basics
  • Single Imputation
  • Multiple Imputation
  • Controlling Tree Growth
  • Preserving Data Assumptions
  • Imputing With Gradient Boosted Trees
• Advanced Features
  • Customizing the Imputation Process
  • Tuning Parameters
  • Imputing New Data with Existing Models
  • How to Make the Process Faster
• Diagnostic Plotting
  • Imputed Distributions
  • Correlation Convergence
  • Variable Importance
  • Mean Convergence
• Using the Imputed Data
• The MICE Algorithm
  • Introduction
  • Common Use Cases
  • Predictive Mean Matching
  • Effects of Mean Matching

Package Meta

News

New major update = 4.0.0.

• Huge performance improvements, especially if categorical variables were being imputed.
• Ability to tune parameters of models, and use best parameters for mice.
• Improvements to code layout - got rid of ImputationSchema.
• Raw data is now stored as a numpy array to save space and improve indexing.
• Numpy arrays can be imputed, if you want to avoid pandas.
• Options of multiple built-in mean matching functions.

Installation

This package can be installed using either pip or conda, through conda-forge:

# Using pip
$ pip install miceforest

# Using conda
$ conda install -c conda-forge miceforest

You can also download the latest development version from this repository. If you want to install from github with conda, you must first run conda install pip git.

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

Classes

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. A KernelDataSet represents a single imputed dataset.
• MultipleImputedKernel - a collection of KernelDataSets. Has additional methods for accessing and comparing multiple kernel datasets together. Subsetting a MultipleImputedKernel will result in a KernelDataSet. Methods of this class tend to affect all of the kernel datasets contained within, unless a certain dataset is specified.
• ImputedDataSet - a single dataset that has been imputed. These are returned after impute_new_data() is called. Has some plotting functionality, but contains no models.
• MultipleImputedDataSet - A collection of datasets that have been imputed. Has additional methods for comparing the imputations between datasets.

The Basics

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(2)

# 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

In statistics, multiple imputation is a process by which the uncertainty/other effects caused by missing values can be examined by creating multiple different imputed datasets. We can 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=1
)

# Run the MICE algorithm for 2 iterations on each of the datasets
kernel.mice(2)

# We can subset out MultipleImputedKernel to get access to the different KernelDataSets:
print(kernel[0])

##               Class: KernelDataSet
##          Iterations: 2
##   Imputed Variables: 5
## save_all_iterations: True

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

print(kernel)

##               Class: MultipleImputedKernel
##        Models Saved: Last Iteration
##            Datasets: 4
##          Iterations: 2
##   Imputed Variables: 5
## save_all_iterations: True

Controlling Tree Growth

Parameters can be passed directly to lightgbm in several different ways. Parameters you wish to apply globally to every model can simply be passed as kwargs to mice:

# Run the MICE algorithm for 1 more iteration on the kernel with new parameters
kernel.mice(1,n_estimators=50)

You can also pass pass variable-specific arguments to variable_parameters in mice. For instance, let’s say you noticed the imputation of the [target] column was taking a little longer, because it is multiclass. You could decrease the n_estimators specifically for that column with:

# Run the MICE algorithm for 2 more iterations on the kernel 
kernel.mice(1,variable_parameters={'target': {'n_estimators': 25}},n_estimators=50)

In this scenario, any parameters specified in variable_parameters takes presidence over the kwargs.

Preserving Data Assumptions

If your data contains count data, or any other data which can be parameterized by lightgbm, you can simply specify that variable to be modeled with the corresponding objective function. For example, let’s pretend sepal width (cm) is a count field which can be parameterized by a Poisson distribution:

# Create kernel. 
cust_kernel = mf.KernelDataSet(
  iris_amp,
  save_all_iterations=True,
  random_state=1
)

cust_kernel.mice(1, variable_parameters={'sepal width (cm)': {'objective': 'poisson'}})

Other nice parameters like monotone_constraints can also be passed.

Imputing with Gradient Boosted Trees

Since any arbitrary parameters can be passed to lightgbm.train(), it is possible to change the algrorithm entirely. This can be done simply like so:

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

# We need to add a small minimum hessian, or lightgbm will complain:
kds_gbdt.mice(3, boosting='gbdt', min_sum_hessian_in_leaf=0.01)

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

Note: It is HIGHLY recommended to run parameter tuning if using gradient boosted trees. The parameter tuning process returns the optimal number of iterations, and usually results in much more useful parameter sets. See the section Tuning Parameters for more details.

Advanced Features

There are many ways to alter the imputation procedure to fit your specific dataset.

Customizing the Imputation Process

It is possible to heavily 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 specify mean_match_candidates and mean_match_subset by variable by passing a dict of valid values, with variable names as keys. You can even replace the entire default mean matching function if you wish:

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
}
var_mms = {
  'sepal width (cm)': 50
}

# The mean matching function requires these parameters, even
# if it does not use them.
def mmf(
  mmc,
  mms,
  model,
  candidate_features,
  bachelor_features,
  candidate_values,
  random_state
):

    bachelor_preds = model.predict(bachelor_features)
    imp_values = random_state.choice(candidate_values, size=bachelor_preds.shape[0])

    return imp_values

cust_kernel = mf.MultipleImputedKernel(
    iris_amp,
    datasets=3,
    variable_schema=var_sch,
    mean_match_candidates=var_mmc,
    mean_match_subset=var_mms,
    mean_match_function=mmf
)
cust_kernel.mice(1)

Tuning Parameters

miceforest allows you to tune the parameters on a kernel dataset. These parameters can then be used to build the models in future iterations of mice. In its most simple invocation, you can just call the function with the desired optimization steps:

# Using the first KernelDataSet in kernel to tune parameters
# with the default settings.
optimal_parameters, losses = kernel[0].tune_parameters(
  optimization_steps=5
)

# Run mice with our newly tuned parameters.
kernel.mice(1, variable_parameters=optimal_parameters)

# The optimal parameters are kept in KernelDataSet.optimal_parameters:
print(kernel[0].optimal_parameters)

## {0: {'boosting': 'gbdt', 'max_depth': 8, 'num_leaves': 13, 'min_data_in_leaf': 5, 'min_sum_hessian_in_leaf': 0.0001, 'min_gain_to_split': 0.0, 'bagging_fraction': 0.37682973025732225, 'feature_fraction': 1.0, 'feature_fraction_bynode': 0.547703450726179, 'bagging_freq': 1, 'verbosity': -1, 'objective': 'regression', 'seed': 636898, 'learning_rate': 0.05, 'num_iterations': 80}, 1: {'boosting': 'gbdt', 'max_depth': 8, 'num_leaves': 44, 'min_data_in_leaf': 7, 'min_sum_hessian_in_leaf': 0.0001, 'min_gain_to_split': 0.0, 'bagging_fraction': 0.9446955888574227, 'feature_fraction': 1.0, 'feature_fraction_bynode': 0.9736751332478455, 'bagging_freq': 1, 'verbosity': -1, 'objective': 'regression', 'seed': 995364, 'learning_rate': 0.05, 'num_iterations': 98}, 2: {'boosting': 'gbdt', 'max_depth': 8, 'num_leaves': 46, 'min_data_in_leaf': 16, 'min_sum_hessian_in_leaf': 0.0001, 'min_gain_to_split': 0.0, 'bagging_fraction': 0.9418843111072678, 'feature_fraction': 1.0, 'feature_fraction_bynode': 0.8549603507783645, 'bagging_freq': 1, 'verbosity': -1, 'objective': 'regression', 'seed': 417328, 'learning_rate': 0.05, 'num_iterations': 101}, 3: {'boosting': 'gbdt', 'max_depth': 8, 'num_leaves': 42, 'min_data_in_leaf': 15, 'min_sum_hessian_in_leaf': 0.0001, 'min_gain_to_split': 0.0, 'bagging_fraction': 0.5508856111545465, 'feature_fraction': 1.0, 'feature_fraction_bynode': 0.7566610407113622, 'bagging_freq': 1, 'verbosity': -1, 'objective': 'regression', 'seed': 687630, 'learning_rate': 0.05, 'num_iterations': 168}, 4: {'boosting': 'gbdt', 'max_depth': 8, 'num_leaves': 25, 'min_data_in_leaf': 32, 'min_sum_hessian_in_leaf': 0.0001, 'min_gain_to_split': 0.0, 'bagging_fraction': 0.9782829438066223, 'feature_fraction': 1.0, 'feature_fraction_bynode': 0.5178493607898189, 'bagging_freq': 1, 'verbosity': -1, 'objective': 'multiclass', 'num_class': 3, 'seed': 517288, 'learning_rate': 0.05, 'num_iterations': 137}}

This will perform 10 fold cross validation on random samples of parameters. By default, all variables models are tuned. If you are curious about the default parameter space that is searched within, check out the miceforest.default_lightgbm_parameters module.

The parameter tuning is pretty flexible. If you wish to set some model parameters static, or to change the bounds that are searched in, you can simply pass this information to either the variable_parameters parameter, **kwbounds, or both:

# Using a complicated setup:
optimal_parameters, losses = kernel[0].tune_parameters(
  variables = ['sepal width (cm)','target','petal width (cm)'],
  variable_parameters = {
    'sepal width (cm)': {'bagging_fraction': 0.5},
    'target': {'bagging_freq': (5,10)}
  },
  optimization_steps=5,
  extra_trees = [True, False]
)

kernel.mice(1, variable_parameters=optimal_parameters)

In this example, we did a few things - we specified that only sepal width (cm), target, and petal width (cm) should be tuned. We also specified some specific parameters in variable_parameters. Notice that bagging_fraction was passed as a scalar, 0.5. This means that, for the variable sepal width (cm), the parameter bagging_fraction will be set as that number and not be tuned. We did the opposite for bagging_freq. We specified bounds that the process should search in. We also passed the argument extra_trees as a list. Since it was passed to **kwbounds, this parameter will apply to all variables that are being tuned. Passing values as a list tells the process that it should randomly sample values from the list, instead of treating them as set of counts to search within.

The tuning process follows these rules for different parameter values it finds:

• Scalar: That value is used, and not tuned.
• Tuple: Should be length 2. Treated as the lower and upper bound to search in.
• List: Treated as a distinct list of values to try randomly.

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: 6
##   Imputed Variables: 5
## save_all_iterations: True

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.

How to Make the Process Faster

Multiple Imputation is one of the most robust ways to handle missing data - but it can take a long time. There are several strategies you can use to decrease the time a process takes to run:

• Decrease mean_match_subset. By default all non-missing datapoints are considered as candidates. This can cause the nearest-neighbors search to take a long time for large data. A subset of these points can be searched instead by using mean_match_subset.
• Decrease mean_match_candidates. If your data is large, the default mean_match_candidates for each variable is 0.001 * (# non-missing datapoints). This can grow to be an unweidly large number of neighbors that need to be found.
• Use different lightgbm parameters. lightgbm is usually not the problem, however if a certain variable has a large number of classes, then the max number of trees actually grown is (# classes) * (n_estimators). You can specifically decrease the bagging fraction or n_estimators for large multi-class variables.
• Use a faster mean matching function. The default mean matching function uses the scipy.Spatial.KDtree algorithm. There are faster alternatives out there, if you think mean matching is the holdup.

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 lightgbm.Booster.feature_importance() function. 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[4]
    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)

## [0.22, 0.65, 0.7, 0.81, 0.78, 0.86, 0.81]

In this instance, we went from a ~32% accuracy (which is expected with random sampling) to an accuracy of ~65% after the first iteration. This isn’t the best example, since our kernel so far has been abused to show the flexability of the imputation procedure.

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.