Missingpy

missingpy

missingpy is a library for missing data imputation in Python. It has an API consistent with scikit-learn, so users already comfortable with that interface will find themselves in familiar terrain. Currently, the library supports the following algorithms:

1. k-Nearest Neighbors imputation
2. Random Forest imputation (MissForest)

We plan to add other imputation tools in the future so please stay tuned!

Installation

pip install missingpy

1. k-Nearest Neighbors (kNN) Imputation

Example

# Let X be an array containing missing values
from missingpy import KNNImputer
imputer = KNNImputer()
X_imputed = imputer.fit_transform(X)

Description

The KNNImputer class provides imputation for completing missing values using the k-Nearest Neighbors approach. Each sample's missing values are imputed using values from n_neighbors nearest neighbors found in the training set. Note that if a sample has more than one feature missing, then the sample can potentially have multiple sets of n_neighbors donors depending on the particular feature being imputed.

Each missing feature is then imputed as the average, either weighted or unweighted, of these neighbors. Where the number of donor neighbors is less than n_neighbors, the training set average for that feature is used for imputation. The total number of samples in the training set is, of course, always greater than or equal to the number of nearest neighbors available for imputation, depending on both the overall sample size as well as the number of samples excluded from nearest neighbor calculation because of too many missing features (as controlled by row_max_missing). For more information on the methodology, see [1].

The following snippet demonstrates how to replace missing values, encoded as np.nan, using the mean feature value of the two nearest neighbors of the rows that contain the missing values::

>>> import numpy as np
>>> from missingpy import KNNImputer
>>> nan = np.nan
>>> X = [[1, 2, nan], [3, 4, 3], [nan, 6, 5], [8, 8, 7]]
>>> imputer = KNNImputer(n_neighbors=2, weights="uniform")
>>> imputer.fit_transform(X)
array([[1. , 2. , 4. ],
       [3. , 4. , 3. ],
       [5.5, 6. , 5. ],
       [8. , 8. , 7. ]])

API

KNNImputer(missing_values="NaN", n_neighbors=5, weights="uniform", 
                 metric="masked_euclidean", row_max_missing=0.5, 
                 col_max_missing=0.8, copy=True)
             
Parameters
----------
missing_values : integer or "NaN", optional (default = "NaN")
    The placeholder for the missing values. All occurrences of
    `missing_values` will be imputed. For missing values encoded as
    ``np.nan``, use the string value "NaN".

n_neighbors : int, optional (default = 5)
    Number of neighboring samples to use for imputation.

weights : str or callable, optional (default = "uniform")
    Weight function used in prediction.  Possible values:

    - 'uniform' : uniform weights.  All points in each neighborhood
      are weighted equally.
    - 'distance' : weight points by the inverse of their distance.
      in this case, closer neighbors of a query point will have a
      greater influence than neighbors which are further away.
    - [callable] : a user-defined function which accepts an
      array of distances, and returns an array of the same shape
      containing the weights.

metric : str or callable, optional (default = "masked_euclidean")
    Distance metric for searching neighbors. Possible values:
    - 'masked_euclidean'
    - [callable] : a user-defined function which conforms to the
    definition of _pairwise_callable(X, Y, metric, **kwds). In other
    words, the function accepts two arrays, X and Y, and a
    ``missing_values`` keyword in **kwds and returns a scalar distance
    value.

row_max_missing : float, optional (default = 0.5)
    The maximum fraction of columns (i.e. features) that can be missing
    before the sample is excluded from nearest neighbor imputation. It
    means that such rows will not be considered a potential donor in
    ``fit()``, and in ``transform()`` their missing feature values will be
    imputed to be the column mean for the entire dataset.

col_max_missing : float, optional (default = 0.8)
    The maximum fraction of rows (or samples) that can be missing
    for any feature beyond which an error is raised.

copy : boolean, optional (default = True)
    If True, a copy of X will be created. If False, imputation will
    be done in-place whenever possible. Note that, if metric is
    "masked_euclidean" and copy=False then missing_values in the
    input matrix X will be overwritten with zeros.

Attributes
----------
statistics_ : 1-D array of length {n_features}
    The 1-D array contains the mean of each feature calculated using
    observed (i.e. non-missing) values. This is used for imputing
    missing values in samples that are either excluded from nearest
    neighbors search because they have too many ( > row_max_missing)
    missing features or because all of the sample's k-nearest neighbors
    (i.e., the potential donors) also have the relevant feature value
    missing.

Methods
-------
fit(X, y=None):
    Fit the imputer on X.

    Parameters
    ----------
    X : {array-like}, shape (n_samples, n_features)
        Input data, where ``n_samples`` is the number of samples and
        ``n_features`` is the number of features.

    Returns
    -------
    self : object
        Returns self.
        
        
transform(X):
    Impute all missing values in X.

    Parameters
    ----------
    X : {array-like}, shape = [n_samples, n_features]
        The input data to complete.

    Returns
    -------
    X : {array-like}, shape = [n_samples, n_features]
        The imputed dataset.


fit_transform(X, y=None, **fit_params):
    Fit KNNImputer and impute all missing values in X.

    Parameters
    ----------
    X : {array-like}, shape (n_samples, n_features)
        Input data, where ``n_samples`` is the number of samples and
        ``n_features`` is the number of features.

    Returns
    -------
    X : {array-like}, shape (n_samples, n_features)
        Returns imputed dataset.       

References

1. Olga Troyanskaya, Michael Cantor, Gavin Sherlock, Pat Brown, Trevor Hastie, Robert Tibshirani, David Botstein and Russ B. Altman, Missing value estimation methods for DNA microarrays, BIOINFORMATICS Vol. 17 no. 6, 2001 Pages 520-525.

2. Random Forest Imputation (MissForest)

Example

# Let X be an array containing missing values
from missingpy import MissForest
imputer = MissForest()
X_imputed = imputer.fit_transform(X)

Description

MissForest imputes missing values using Random Forests in an iterative fashion [1]. By default, the imputer begins imputing missing values of the column (which is expected to be a variable) with the smallest number of missing values -- let's call this the candidate column. The first step involves filling any missing values of the remaining, non-candidate, columns with an initial guess, which is the column mean for columns representing numerical variables and the column mode for columns representing categorical variables. Note that the categorical variables need to be explicitly identified during the imputer's fit() method call (see API for more information). After that, the imputer fits a random forest model with the candidate column as the outcome variable and the remaining columns as the predictors over all rows where the candidate column values are not missing. After the fit, the missing rows of the candidate column are imputed using the prediction from the fitted Random Forest. The rows of the non-candidate columns act as the input data for the fitted model. Following this, the imputer moves on to the next candidate column with the second smallest number of missing values from among the non-candidate columns in the first round. The process repeats itself for each column with a missing value, possibly over multiple iterations or epochs for each column, until the stopping criterion is met. The stopping criterion is governed by the "difference" between the imputed arrays over successive iterations. For numerical variables (num_vars_), the difference is defined as follows:

 sum((X_new[:, num_vars_] - X_old[:, num_vars_]) ** 2) /
 sum((X_new[:, num_vars_]) ** 2)

For categorical variables(cat_vars_), the difference is defined as follows:

sum(X_new[:, cat_vars_] != X_old[:, cat_vars_])) / n_cat_missing

where X_new is the newly imputed array, X_old is the array imputed in the previous round, n_cat_missing is the total number of categorical values that are missing, and the sum() is performed both across rows and columns. Following [1], the stopping criterion is considered to have been met when difference between X_new and X_old increases for the first time for both types of variables (if available).

Note: The categorical variables need to be one-hot-encoded (also known as dummy encoded) and they need to be explicitly identified during the imputer's fit() method call. See the API section for more information.

>>> from missingpy import MissForest
>>> nan = float("NaN")
>>> X = [[1, 2, nan], [3, 4, 3], [nan, 6, 5], [8, 8, 7]]
>>> imputer = MissForest(random_state=1337)
>>> imputer.fit_transform(X)
Iteration: 0
Iteration: 1
Iteration: 2
array([[1.  , 2. , 3.92 ],
       [3.  , 4. , 3. ],
       [2.71, 6. , 5. ],