missingpy 0.2.0

Missing Data Imputation for Python

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 k-Nearest Neighbors based imputation and Random Forest based imputation (MissForest) but we plan to add other imputation tools in the future so please stay tuned!

Installation

pip install missingpy

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.

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).

>>> from missingpy import MissForest
>>> nan = float("NaN")
>>> X = [[1, 2, nan], [3, 4, 3], [nan, 6, 5], [8, 8, 7]]
>>> imputer = MissForest()
>>> imputer.fit_transform(X)
Iteration: 0
Iteration: 1
Iteration: 2
Iteration: 3
array([[1.  , 2. , 4. ],
       [3.  , 4. , 3. ],
       [3.16, 6. , 5. ],
       [8.  , 8. , 7. ]])

API

MissForest(max_iter=10, decreasing=False, missing_values=np.nan,
             copy=True, n_estimators=100, criterion=('mse', 'gini'),
             max_depth=None, min_samples_split=2, min_samples_leaf=1,
             min_weight_fraction_leaf=0.0, max_features='auto',
             max_leaf_nodes=None, min_impurity_decrease=0.0,
             bootstrap=True, oob_score=False, n_jobs=-1, random_state=None,
             verbose=0, warm_start=False, class_weight=None)

Parameters
----------
NOTE: Most parameter definitions below are taken verbatim from the
Scikit-Learn documentation at [2] and [3].

max_iter : int, optional (default = 10)
    The maximum iterations of the imputation process. Each column with a
    missing value is imputed exactly once in a given iteration.

decreasing : boolean, optional (default = False)
    If set to True, columns are sorted according to decreasing number of
    missing values. In other words, imputation will move from imputing
    columns with the largest number of missing values to columns with
    fewest number of missing values.

missing_values : np.nan, integer, optional (default = np.nan)
    The placeholder for the missing values. All occurrences of
    `missing_values` will be imputed.

copy : boolean, optional (default = True)
    If True, a copy of X will be created. If False, imputation will
    be done in-place whenever possible.

criterion : tuple, optional (default = ('mse', 'gini'))
    The function to measure the quality of a split.The first element of
    the tuple is for the Random Forest Regressor (for imputing numerical
    variables) while the second element is for the Random Forest
    Classifier (for imputing categorical variables).

n_estimators : integer, optional (default=100)
    The number of trees in the forest.

max_depth : integer or None, optional (default=None)
    The maximum depth of the tree. If None, then nodes are expanded until
    all leaves are pure or until all leaves contain less than
    min_samples_split samples.

min_samples_split : int, float, optional (default=2)
    The minimum number of samples required to split an internal node:
    - If int, then consider `min_samples_split` as the minimum number.
    - If float, then `min_samples_split` is a fraction and
      `ceil(min_samples_split * n_samples)` are the minimum
      number of samples for each split.

min_samples_leaf : int, float, optional (default=1)
    The minimum number of samples required to be at a leaf node.
    A split point at any depth will only be considered if it leaves at
    least ``min_samples_leaf`` training samples in each of the left and
    right branches.  This may have the effect of smoothing the model,
    especially in regression.
    - If int, then consider `min_samples_leaf` as the minimum number.
    - If float, then `min_samples_leaf` is a fraction and
      `ceil(min_samples_leaf * n_samples)` are the minimum
      number of samples for each node.

min_weight_fraction_leaf : float, optional (default=0.)
    The minimum weighted fraction of the sum total of weights (of all
    the input samples) required to be at a leaf node. Samples have
    equal weight when sample_weight is not provided.

max_features : int, float, string or None, optional (default="auto")
    The number of features to consider when looking for the best split:
    - If int, then consider `max_features` features at each split.
    - If float, then `max_features` is a fraction and
      `int(max_features * n_features)` features are considered at each
      split.
    - If "auto", then `max_features=sqrt(n_features)`.
    - If "sqrt", then `max_features=sqrt(n_features)` (same as "auto").
    - If "log2", then `max_features=log2(n_features)`.
    - If None, then `max_features=n_features`.
    Note: the search for a split does not stop until at least one
    valid partition of the node samples is found, even if it requires to
    effectively inspect more than ``max_features`` features.

max_leaf_nodes : int or None, optional (default=None)
    Grow trees with ``max_leaf_nodes`` in best-first fashion.
    Best nodes are defined as relative reduction in impurity.
    If None then unlimited number of leaf nodes.

min_impurity_decrease : float, optional (default=0.)
    A node will be split if this split induces a decrease of the impurity
    greater than or equal to this value.
    The weighted impurity decrease equation is the following::
        N_t / N * (impurity - N_t_R / N_t * right_impurity
                            - N_t_L / N_t * left_impurity)
    where ``N`` is the total number of samples, ``N_t`` is the number of
    samples at the current node, ``N_t_L`` is the number of samples in the
    left child, and ``N_t_R`` is the number of samples in the right child.
    ``N``, ``N_t``, ``N_t_R`` and ``N_t_L`` all refer to the weighted sum,
    if ``sample_weight`` is passed.

bootstrap : boolean, optional (default=True)
    Whether bootstrap samples are used when building trees.

oob_score : bool (default=False)
    Whether to use out-of-bag samples to estimate
    the generalization accuracy.

n_jobs : int or None, optional (default=None)
    The number of jobs to run in parallel for both `fit` and `predict`.
    ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
    ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
    for more details.

random_state : int, RandomState instance or None, optional (default=None)
    If int, random_state is the seed used by the random number generator;
    If RandomState instance, random_state is the random number generator;
    If None, the random number generator is the RandomState instance used
    by `np.random`.

verbose : int, optional (default=0)
    Controls the verbosity when fitting and predicting.

warm_start : bool, optional (default=False)
    When set to ``True``, reuse the solution of the previous call to fit
    and add more estimators to the ensemble, otherwise, just fit a whole
    new forest. See :term:`the Glossary <warm_start>`.

class_weight : dict, list of dicts, "balanced", "balanced_subsample" or \
None, optional (default=None)
    Weights associated with classes in the form ``{class_label: weight}``.
    If not given, all classes are supposed to have weight one. For
    multi-output problems, a list of dicts can be provided in the same
    order as the columns of y.
    Note that for multioutput (including multilabel) weights should be
    defined for each class of every column in its own dict. For example,
    for four-class multilabel classification weights should be
    [{0: 1, 1: 1}, {0: 1, 1: 5}, {0: 1, 1: 1}, {0: 1, 1: 1}] instead of
    [{1:1}, {2:5}, {3:1}, {4:1}].
    The "balanced" mode uses the values of y to automatically adjust
    weights inversely proportional to class frequencies in the input data
    as ``n_samples / (n_classes * np.bincount(y))``
    The "balanced_subsample" mode is the same as "balanced" except that
    weights are computed based on the bootstrap sample for every tree
    grown.
    For multi-output, the weights of each column of y will be multiplied.
    Note that these weights will be multiplied with sample_weight (passed
    through the fit method) if sample_weight is specified.
    NOTE: This parameter is only applicable for Random Forest Classifier
    objects (i.e., for categorical variables).

Attributes
----------
statistics_ : Dictionary of length two
    The first element is an array with the mean of each numerical feature
    being imputed while the second element is an array of modes of
    categorical features being imputed (if available, otherwise it
    will be None).

Methods
-------
fit(self, X, y=None, cat_vars=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.

    cat_vars : int or array of ints, optional (default = None)
        An int or an array containing column indices of categorical
        variable(s)/feature(s) present in the dataset X.
        ``None`` if there are no categorical variables in the dataset.

    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 MissForest 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] Stekhoven, Daniel J., and Peter Bühlmann. "MissForest—non-parametric missing value imputation for mixed-type data." Bioinformatics 28.1 (2011): 112-118.
• [2] https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestRegressor.html#sklearn.ensemble.RandomForestRegressor
• [3] https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html#sklearn.ensemble.RandomForestClassifier