Imputes missing data with MICE + random forests
Project description
miceforest: Fast, Memory Efficient Imputation with lightgbm
Fast, memory efficient Multiple Imputation by Chained Equations (MICE) with lightgbm. The R version of this package may be found here.
miceforest
was designed to be:
 Fast Uses lightgbm as a backend, and has efficient mean matching solutions.
 Memory Efficient Capable of performing multiple imputation without copying the dataset. If the dataset can fit in memory, it can (probably) be imputed.
 Flexible Can handle pandas DataFrames and numpy arrays. The imputation process can be completely customized. Can handle categorical data automatically.
 Used In Production Kernels can be saved and impute new, unseen
datasets. Imputing new data is often orders of magnitude faster than
including the new data in a new
mice
procedure. Imputation models can be built off of a kernel dataset, even if there are no missing values. New data can also be imputed in place.
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 Buurenâ€™s excellent online book, which you can find here.
Table of Contents:
 Package Meta
 The Basics
 Advanced Features
 Diagnostic Plotting
 Using the Imputed Data
 The MICE Algorithm
Package Meta
News
New Major Update = 5.0.0
 New main classes (
ImputationKernel
,ImputedData
) replace (KernelDataSet
,MultipleImputedKernel
,ImputedDataSet
,MultipleImputedDataSet
).  Data can now be referenced and imputed in place. This saves a lot of memory allocation and is much faster.
 Data can now be completed in place. This allows for only a single copy of the dataset to be in memory at any given time, even if performing multiple imputation.
mean_match_subset
parameter has been replaced withdata_subset.
This subsets the data used to build the model as well as the candidates. More performance improvements around when data is copied and where it is stored.
 Raw data is now stored as the original. Can handle pandas
DataFrame
and numpyndarray
.
Installation
This package can be installed using either pip or conda, through condaforge:
# Using pip $ pip install miceforest nocachedir # Using conda $ conda install c condaforge 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 2 main classes which the user will interact with:
ImputationKernel
 This class contains the raw data off of which themice
algorithm is performed. During this process, models will be trained, and the imputed (predicted) values will be stored. These values can be used to fill in the missing values of the raw data. The raw data can be copied, or referenced directly. Models can be saved, and used to impute new datasets.ImputedData
 The result ofImputationKernel.impute_new_data(new_data)
. This contains the raw data innew_data
as well as the imputed values.
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.rename({"target": "species"}, inplace=True, axis=1) iris['species'] = iris['species'].astype('category') iris_amp = mf.ampute_data(iris,perc=0.25,random_state=1991)
Basic Examples
If you only want to create a single imputed dataset, you can set the
datasets
parameter to 1:
# Create kernel. kds = mf.ImputationKernel( iris_amp, datasets=1, save_all_iterations=True, random_state=1991 ) # Run the MICE algorithm for 3 iterations kds.mice(2)
There are also an array of plotting functions available, these are discussed below in the section Diagnostic Plotting.
We usually donâ€™t want to impute just a single dataset. 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. ImputationKernel
can contain an arbitrary number of
different datasets, all of which have gone through mutually exclusive
imputation processes:
# Create kernel. kernel = mf.ImputationKernel( 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) # Printing the kernel will show you some high level information. print(kernel)
## Class: ImputationKernel
## Datasets: 4
## Iterations: 2
## Imputed Variables: 5
## save_all_iterations: True
After we have run mice, we can obtain our completed dataset directly from the kernel:
completed_dataset = kernel.complete_data(dataset=0, inplace=False) print(completed_dataset.isnull().sum(0))
## sepal length (cm) 0
## sepal width (cm) 0
## petal length (cm) 0
## petal width (cm) 0
## species 0
## dtype: int64
Using inplace=False
returns a copy of the completed data. Since the
raw data is already stored in kernel.working_data
, you can set
inplace=True
to complete the data without returning a copy:
kernel.complete_data(dataset=0, inplace=True) print(kernel.working_data.isnull().sum(0))
## sepal length (cm) 0
## sepal width (cm) 0
## petal length (cm) 0
## petal width (cm) 0
## species 0
## dtype: int64
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(iterations=1,n_estimators=50)
You can also pass pass variablespecific arguments to
variable_parameters
in mice. For instance, letâ€™s say you noticed the
imputation of the [species]
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(iterations=1,variable_parameters={'species': {'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, letâ€™s
pretend sepal width (cm)
is a count field which can be parameterized
by a Poisson distribution:
# Create kernel. cust_kernel = mf.ImputationKernel( iris_amp, datasets=1, random_state=1 ) cust_kernel.mice(iterations=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.ImputationKernel( iris_amp, datasets=1, save_all_iterations=True, random_state=1991 ) # We need to add a small minimum hessian, or lightgbm will complain: kds_gbdt.mice(iterations=1, boosting='gbdt', min_sum_hessian_in_leaf=0.01) # Return the completed kernel data completed_data = kds_gbdt.complete_data(dataset=0)
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 data_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)': ['species','petal width (cm)'], 'petal width (cm)': ['species','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, 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.ImputationKernel( iris_amp, datasets=3, variable_schema=var_sch, mean_match_candidates=var_mmc, data_subset=var_mms, mean_match_function=mmf ) cust_kernel.mice(1)
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 donâ€™t have time to train new
models, it is possible to impute new datasets using a ImputationKernel
object. The impute_new_data()
function uses the random forests
collected by ImputationKernel
to perform multiple imputation without
updating the random forest at each iteration:
# Our 'new data' is just the first 15 rows of iris_amp from datetime import datetime # Define our new data as the first 15 rows new_data = iris_amp.iloc[range(15)] start_t = datetime.now() new_data_imputed = kernel.impute_new_data(new_data=new_data) print(f"New Data imputed in {(datetime.now()  start_t).total_seconds()} seconds")
## New Data imputed in 0.688156 seconds
All of the imputation parameters (variable_schema,
mean_match_candidates, etc) will be carried over from the original
ImputationKernel
object. When mean matching, the candidate values are
pulled from the original kernel dataset. To impute new data, the
save_models
parameter in ImputationKernel
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.
Building Models on Nonmissing Data
The MICE process itself is used to impute missing data in a dataset.
However, sometimes a variable can be fully recognized in the training
data, but needs to be imputed later on in a different dataset. It is
possible to train models to impute variables even if they have no
missing values by setting train_nonmissing=True
. In this case,
variable_schema
is treated as the list of variables to train models
on. imputation_order
only affects which variables actually have their
values imputed, it does not affect which variables have models trained:
orig_missing_cols = ["sepal length (cm)", "sepal width (cm)"] new_missing_cols = ["sepal length (cm)", "sepal width (cm)", "species"] # Training data only contains 2 columns with missing data iris_amp2 = iris.copy() iris_amp2[orig_missing_cols] = mf.ampute_data( iris_amp2[orig_missing_cols], perc=0.25, random_state=1991 ) # Specify that models should also be trained for species column var_sch = new_missing_cols cust_kernel = mf.ImputationKernel( iris_amp2, datasets=1, variable_schema=var_sch, train_nonmissing=True ) cust_kernel.mice(1) # New data has missing values in species column iris_amp2_new = iris.iloc[range(10),:].copy() iris_amp2_new[new_missing_cols] = mf.ampute_data( iris_amp2_new[new_missing_cols], perc=0.25, random_state=1991 ) # Species column can still be imputed iris_amp2_new_imp = cust_kernel.impute_new_data(iris_amp2_new) iris_amp2_new_imp.complete_data(0).isnull().sum()
## sepal length (cm) 0
## sepal width (cm) 0
## petal length (cm) 0
## petal width (cm) 0
## species 0
## dtype: int64
Here, we knew that the species column in our new data would need to be
imputed. Therefore, we specified that a model should be built for all 3
variables in the variable_schema
(passing a dict of target  feature
pairs would also have worked).
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 ImputationKernel in kernel to tune parameters # with the default settings. optimal_parameters, losses = kernel.tune_parameters( dataset=0, optimization_steps=5 ) # Run mice with our newly tuned parameters. kernel.mice(1, variable_parameters=optimal_parameters) # The optimal parameters are kept in ImputationKernel.optimal_parameters: print(optimal_parameters)
## {0: {'boosting': 'gbdt', 'num_iterations': 65, 'max_depth': 8, 'num_leaves': 10, 'min_data_in_leaf': 1, 'min_sum_hessian_in_leaf': 0.1, 'min_gain_to_split': 0.0, 'bagging_fraction': 0.39791299065921537, 'feature_fraction': 1.0, 'feature_fraction_bynode': 0.6937388234549196, 'bagging_freq': 1, 'verbosity': 1, 'objective': 'regression', 'seed': 849382, 'learning_rate': 0.05, 'cat_smooth': 11.663587284343516}, 1: {'boosting': 'gbdt', 'num_iterations': 49, 'max_depth': 8, 'num_leaves': 9, 'min_data_in_leaf': 5, 'min_sum_hessian_in_leaf': 0.1, 'min_gain_to_split': 0.0, 'bagging_fraction': 0.6179134070114273, 'feature_fraction': 1.0, 'feature_fraction_bynode': 0.31478518263603694, 'bagging_freq': 1, 'verbosity': 1, 'objective': 'regression', 'seed': 586321, 'learning_rate': 0.05, 'cat_smooth': 13.957164461191296}, 2: {'boosting': 'gbdt', 'num_iterations': 65, 'max_depth': 8, 'num_leaves': 7, 'min_data_in_leaf': 4, 'min_sum_hessian_in_leaf': 0.1, 'min_gain_to_split': 0.0, 'bagging_fraction': 0.9979861290119383, 'feature_fraction': 1.0, 'feature_fraction_bynode': 0.5730380093960374, 'bagging_freq': 1, 'verbosity': 1, 'objective': 'regression', 'seed': 961902, 'learning_rate': 0.05, 'cat_smooth': 20.39766682094556}, 3: {'boosting': 'gbdt', 'num_iterations': 61, 'max_depth': 8, 'num_leaves': 11, 'min_data_in_leaf': 6, 'min_sum_hessian_in_leaf': 0.1, 'min_gain_to_split': 0.0, 'bagging_fraction': 0.7560736024385001, 'feature_fraction': 1.0, 'feature_fraction_bynode': 0.8058628021146634, 'bagging_freq': 1, 'verbosity': 1, 'objective': 'regression', 'seed': 449169, 'learning_rate': 0.05, 'cat_smooth': 16.369979689010446}, 4: {'boosting': 'gbdt', 'num_iterations': 99, 'max_depth': 8, 'num_leaves': 16, 'min_data_in_leaf': 8, 'min_sum_hessian_in_leaf': 0.1, 'min_gain_to_split': 0.0, 'bagging_fraction': 0.7186091265251624, 'feature_fraction': 1.0, 'feature_fraction_bynode': 0.10283114841793521, 'bagging_freq': 1, 'verbosity': 1, 'objective': 'multiclass', 'num_class': 3, 'seed': 933848, 'learning_rate': 0.05, 'cat_smooth': 10.956325813024653}}
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.tune_parameters( dataset=0, variables = ['sepal width (cm)','species','petal width (cm)'], variable_parameters = { 'sepal width (cm)': {'bagging_fraction': 0.5}, 'species': {'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)
, species
, 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.
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
data_subset
. By default all nonmissing datapoints for each variable are used to train the model and perform mean matching. This can cause the model training nearestneighbors search to take a long time for large data. A subset of these points can be searched instead by usingdata_subset
.  Convert your data to a numpy array. Numpy arrays are much faster to
index. While indexing overhead is avoided as much as possible, there
is no getting around it. Consider comverting to
float32
datatype as well, as it will cause the resulting object to take up much less memory.  Decrease
mean_match_candidates
. The maximum number of neighbors that are considered with the default parameters is 10. However, for large datasets, this can still be an expensive operation. Consider explicitly settingmean_match_candidates
lower.  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 multiclass variables, or grow less trees in general.
 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.
Imputing Data In Place
It is possible to run the entire process without copying the dataset. If
copy_data=False
, then the data is referenced directly:
kernel_inplace = mf.ImputationKernel( iris_amp, datasets=1, copy_data=False ) kernel_inplace.mice(2)
Note, that this probably wonâ€™t (but could) change the original dataset
in undesirable ways. Throughout the mice
procedure, imputed values are
stored directly in the original data. At the end, the missing values are
put back as np.NaN
.
We can also complete our original data in place:
kernel_inplace.complete_data(dataset=0, inplace=True) print(iris_amp.isnull().sum(0))
## sepal length (cm) 0
## sepal width (cm) 0
## petal length (cm) 0
## petal width (cm) 0
## species 0
## dtype: int64
This is useful if the dataset is large, and copies canâ€™t be made in memory.
Diagnostic Plotting
As of now, miceforest has four diagnostic plots available.
Distribution of ImputedValues
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
ImputationKernel
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(dataset=0, 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 donâ€™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): species_na_count = kernel.na_counts[4] compdat = kernel.complete_data(dataset=0,iteration=iteration) # Record the accuract of the imputations of species. acclist.append( round(1sum(compdat['species'] != iris['species'])/species_na_count,2) ) # acclist shows the accuracy of the imputations # over the iterations. print(acclist)
## [0.35, 0.7, 0.78, 0.86, 0.84, 0.89, 0.86]
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 isnâ€™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 â€˜fills inâ€™ (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, letâ€™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 â€˜funnelâ€™. 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
columnbycolumn 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, letâ€™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 letâ€™s run our imputation process twice, once using mean matching, and once using the model prediction.
kernelmeanmatch = mf.ImputationKernel(ampdat, datasets=1,mean_match_candidates=5) kernelmodeloutput = mf.ImputationKernel(ampdat, datasets=1,mean_match_candidates=0) kernelmeanmatch.mice(2) kernelmodeloutput.mice(2)
Letâ€™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 â€˜fitâ€™, will not provide imputations with a similair distribution to the original. This may be beneficial, depending on your goal.
Project details
Release history Release notifications  RSS feed
Download files
Download the file for your platform. If you're not sure which to choose, learn more about installing packages.
Source Distribution
Built Distribution
Hashes for miceforest5.2.2py3noneany.whl
Algorithm  Hash digest  

SHA256  fb308ced3886047e4ca829b5498feb801c6c792c85c0dda85d82cb0ce1569915 

MD5  0f28ea5bd17f27cecc8bccb4e7195c4b 

BLAKE2256  692d22d86ceb63bbd9440e1a3a354ca0d21fc783e05e6a7ec1b4df452f1edaf4 