In [1]:

    

import sklearn.ensemble
import shap
import numpy as np
import numba
import time


    

In [2]:

    

X,y = shap.datasets.boston()
X.shape


    

    
Out[2]:





(506, 13)

In [3]:

    

model = sklearn.ensemble.RandomForestRegressor(n_estimators=1000, max_depth=4)
model.fit(X, y)


    

    
Out[3]:





RandomForestRegressor(bootstrap=True, criterion='mse', max_depth=4,
           max_features='auto', max_leaf_nodes=None,
           min_impurity_decrease=0.0, min_impurity_split=None,
           min_samples_leaf=1, min_samples_split=2,
           min_weight_fraction_leaf=0.0, n_estimators=1000, n_jobs=1,
           oob_score=False, random_state=None, verbose=0, warm_start=False)

In [4]:

    

class TreeExplainer:
    def __init__(self, model, **kwargs):
        
        if str(type(model)).endswith("sklearn.ensemble.forest.RandomForestRegressor'>"):
            self.trees = [Tree(e.tree_) for e in model.estimators_]
            
        # Preallocate space for the unique path data
        maxd = np.max([t.max_depth for t in self.trees]) + 2
        print(maxd)
        s = (maxd * (maxd + 1)) // 2
        self.feature_indexes = np.zeros(s, dtype=np.int32)
        self.zero_fractions = np.zeros(s, dtype=np.float64)
        self.one_fractions = np.zeros(s, dtype=np.float64)
        self.pweights = np.zeros(s, dtype=np.float64)

    def shap_values(self, X, **kwargs):
        # convert dataframes
        if str(type(X)).endswith("pandas.core.series.Series'>"):
            X = X.values
        elif str(type(X)).endswith("'pandas.core.frame.DataFrame'>"):
            X = X.values

        assert str(type(X)).endswith("'numpy.ndarray'>"), "Unknown instance type: " + str(type(X))
        assert len(X.shape) == 1 or len(X.shape) == 2, "Instance must have 1 or 2 dimensions!"

        # single instance
        if len(X.shape) == 1:
            phi = np.zeros(X.shape[0] + 1)
            x_missing = np.zeros(X.shape[0], dtype=np.bool)
            for t in self.trees:
                self.tree_shap(t, X, x_missing, phi)
            phi /= len(self.trees)
        elif len(X.shape) == 2:
            phi = np.zeros((X.shape[0], X.shape[1] + 1))
            x_missing = np.zeros(X.shape[1], dtype=np.bool)
            for i in range(X.shape[0]):
                for t in self.trees:
                    self.tree_shap(t, X[i,:], x_missing, phi[i,:])
            phi /= len(self.trees)
        return phi
    
    def tree_shap(self, tree, x, x_missing, phi, condition=0, condition_feature=0):

        # update the bias term, which is the last index in phi
        # (note the paper has this as phi_0 instead of phi_M)
        if condition == 0:
            phi[-1] += tree.values[0]

        # start the recursive algorithm
        tree_shap_recursive(
            tree.children_left, tree.children_right, tree.children_default, tree.features,
            tree.thresholds, tree.values, tree.node_sample_weight,
            x, x_missing, phi, 0, 0, self.feature_indexes, self.zero_fractions, self.one_fractions, self.pweights,
            1, 1, -1, condition, condition_feature, 1
        )


    

In [5]:

    

# extend our decision path with a fraction of one and zero extensions
@numba.jit(
    numba.types.void(
        numba.types.int32[:],
        numba.types.float64[:],
        numba.types.float64[:],
        numba.types.float64[:],
        numba.types.int32,
        numba.types.float64,
        numba.types.float64,
        numba.types.int32
    ), nopython=True, nogil=True
)
def extend_path(feature_indexes, zero_fractions, one_fractions, pweights,
                unique_depth, zero_fraction, one_fraction, feature_index):
    feature_indexes[unique_depth] = feature_index
    zero_fractions[unique_depth] = zero_fraction
    one_fractions[unique_depth] = one_fraction
    if unique_depth == 0: 
        pweights[unique_depth] = 1
    else:
        pweights[unique_depth] = 0
    
    for i in range(unique_depth - 1, -1, -1):
        pweights[i+1] += one_fraction * pweights[i] * (i + 1) / (unique_depth + 1)
        pweights[i] = zero_fraction * pweights[i] * (unique_depth - i) / (unique_depth + 1)
        
# undo a previous extension of the decision path
@numba.jit(
    numba.types.void(
        numba.types.int32[:],
        numba.types.float64[:],
        numba.types.float64[:],
        numba.types.float64[:],
        numba.types.int32,
        numba.types.int32
    ), nopython=True, nogil=True
)
def unwind_path(feature_indexes, zero_fractions, one_fractions, pweights,
                unique_depth, path_index):
    one_fraction = one_fractions[path_index]
    zero_fraction = zero_fractions[path_index]
    next_one_portion = pweights[unique_depth]

    for i in range(unique_depth - 1, -1, -1):
        if one_fraction != 0:
            tmp = pweights[i]
            pweights[i] = next_one_portion * (unique_depth + 1) / ((i + 1) * one_fraction)
            next_one_portion = tmp - pweights[i] * zero_fraction * (unique_depth - i) / (unique_depth + 1)
        else:
            pweights[i] = (pweights[i] * (unique_depth + 1)) / (zero_fraction * (unique_depth - i))

    for i in range(path_index, unique_depth):
        feature_indexes[i] = feature_indexes[i+1]
        zero_fractions[i] = zero_fractions[i+1]
        one_fractions[i] = one_fractions[i+1]
        
# determine what the total permuation weight would be if
# we unwound a previous extension in the decision path
@numba.jit(
    numba.types.float64(
        numba.types.int32[:],
        numba.types.float64[:],
        numba.types.float64[:],
        numba.types.float64[:],
        numba.types.int32,
        numba.types.int32
    ),
    nopython=True, nogil=True
)
def unwound_path_sum(feature_indexes, zero_fractions, one_fractions, pweights, unique_depth, path_index):
    one_fraction = one_fractions[path_index]
    zero_fraction = zero_fractions[path_index]
    next_one_portion = pweights[unique_depth]
    total = 0
    
    for i in range(unique_depth - 1, -1, -1):
        if one_fraction != 0:
            tmp = next_one_portion * (unique_depth + 1) / ((i + 1) * one_fraction)
            total += tmp;
            next_one_portion = pweights[i] - tmp * zero_fraction * ((unique_depth - i) / (unique_depth + 1))
        else:
            total += (pweights[i] / zero_fraction) / ((unique_depth - i) / (unique_depth + 1))

    return total


class Tree:
    def __init__(self, children_left, children_right, children_default, feature, threshold, value, node_sample_weight):
        self.children_left = children_left.astype(np.int32)
        self.children_right = children_right.astype(np.int32)
        self.children_default = children_default.astype(np.int32)
        self.features = feature.astype(np.int32)
        self.thresholds = threshold
        self.values = value
        self.node_sample_weight = node_sample_weight
        
        self.max_depth = compute_expectations(
            self.children_left, self.children_right, self.node_sample_weight,
            self.values, 0
        )
    
    def __init__(self, tree):
        if str(type(tree)).endswith("'sklearn.tree._tree.Tree'>"):
            self.children_left = tree.children_left.astype(np.int32)
            self.children_right = tree.children_right.astype(np.int32)
            self.children_default = self.children_left # missing values not supported in sklearn
            self.features = tree.feature.astype(np.int32)
            self.thresholds = tree.threshold.astype(np.float64)
            self.values = tree.value[:,0,0] # assume only a single output for now
            self.node_sample_weight = tree.weighted_n_node_samples.astype(np.float64)
            
            # we recompute the expectations to make sure they follow the SHAP logic
            self.max_depth = compute_expectations(
                self.children_left, self.children_right, self.node_sample_weight,
                self.values, 0
            )

@numba.jit(nopython=True)
def compute_expectations(children_left, children_right, node_sample_weight, values, i, depth=0):
    if children_right[i] == -1:
        values[i] = values[i]
        return 0
    else:
        li = children_left[i]
        ri = children_right[i]
        depth_left = compute_expectations(children_left, children_right, node_sample_weight, values, li, depth + 1)
        depth_right = compute_expectations(children_left, children_right, node_sample_weight, values, ri, depth + 1)
        left_weight = node_sample_weight[li]
        right_weight = node_sample_weight[ri]
        v = (left_weight * values[li] + right_weight * values[ri]) / (left_weight + right_weight)
        values[i] = v
        return max(depth_left, depth_right) + 1
        
# recursive computation of SHAP values for a decision tree
@numba.jit(
    numba.types.void(
        numba.types.int32[:],
        numba.types.int32[:],
        numba.types.int32[:],
        numba.types.int32[:],
        numba.types.float64[:],
        numba.types.float64[:],
        numba.types.float64[:],
        numba.types.float64[:],
        numba.types.boolean[:],
        numba.types.float64[:],
        numba.types.int64,
        numba.types.int64,
        numba.types.int32[:],
        numba.types.float64[:],
        numba.types.float64[:],
        numba.types.float64[:],
        numba.types.float64,
        numba.types.float64,
        numba.types.int64,
        numba.types.int64,
        numba.types.int64,
        numba.types.float64,
    ),
    nopython=True, nogil=True
)
def tree_shap_recursive(children_left, children_right, children_default, features, thresholds, values, node_sample_weight,
                        x, x_missing, phi, node_index, unique_depth, parent_feature_indexes,
                        parent_zero_fractions, parent_one_fractions, parent_pweights, parent_zero_fraction,
                        parent_one_fraction, parent_feature_index, condition, condition_feature, condition_fraction):

    # stop if we have no weight coming down to us
    if condition_fraction == 0:
        return

    # extend the unique path
    feature_indexes = parent_feature_indexes[unique_depth + 1:]
    feature_indexes[:unique_depth + 1] = parent_feature_indexes[:unique_depth + 1]
    zero_fractions = parent_zero_fractions[unique_depth + 1:]
    zero_fractions[:unique_depth + 1] = parent_zero_fractions[:unique_depth + 1]
    one_fractions = parent_one_fractions[unique_depth + 1:]
    one_fractions[:unique_depth + 1] = parent_one_fractions[:unique_depth + 1]
    pweights = parent_pweights[unique_depth + 1:]
    pweights[:unique_depth + 1] = parent_pweights[:unique_depth + 1]

    if condition == 0 or condition_feature != parent_feature_index:
        extend_path(
            feature_indexes, zero_fractions, one_fractions, pweights,
            unique_depth, parent_zero_fraction, parent_one_fraction, parent_feature_index
        )

    split_index = features[node_index]

    # leaf node
    if children_right[node_index] == -1:
        for i in range(1, unique_depth+1):
            w = unwound_path_sum(feature_indexes, zero_fractions, one_fractions, pweights, unique_depth, i)
            phi[feature_indexes[i]] += w * (one_fractions[i] - zero_fractions[i]) * values[node_index] * condition_fraction

    # internal node
    else:
        # find which branch is "hot" (meaning x would follow it)
        hot_index = 0
        cleft = children_left[node_index]
        cright = children_right[node_index]
        if x_missing[split_index] == 1:
            hot_index = children_default[node_index]
        elif x[split_index] < thresholds[node_index]:
            hot_index = cleft
        else:
            hot_index = cright
        cold_index = (cright if hot_index == cleft else cleft)
        w = node_sample_weight[node_index]
        hot_zero_fraction = node_sample_weight[hot_index] / w
        cold_zero_fraction = node_sample_weight[cold_index] / w
        incoming_zero_fraction = 1
        incoming_one_fraction = 1

        # see if we have already split on this feature,
        # if so we undo that split so we can redo it for this node
        path_index = 0
        while (path_index <= unique_depth):
            if feature_indexes[path_index] == split_index:
                break
            path_index += 1

        if path_index != unique_depth + 1:
            incoming_zero_fraction = zero_fractions[path_index]
            incoming_one_fraction = one_fractions[path_index]
            unwind_path(feature_indexes, zero_fractions, one_fractions, pweights, unique_depth, path_index)
            unique_depth -= 1

        # divide up the condition_fraction among the recursive calls
        hot_condition_fraction = condition_fraction
        cold_condition_fraction = condition_fraction
        if condition > 0 and split_index == condition_feature:
            cold_condition_fraction = 0;
            unique_depth -= 1
        elif condition < 0 and split_index == condition_feature:
            hot_condition_fraction *= hot_zero_fraction
            cold_condition_fraction *= cold_zero_fraction
            unique_depth -= 1

        tree_shap_recursive(
            children_left, children_right, children_default, features, thresholds, values, node_sample_weight,
            x, x_missing, phi, hot_index, unique_depth + 1,
            feature_indexes, zero_fractions, one_fractions, pweights,
            hot_zero_fraction * incoming_zero_fraction, incoming_one_fraction,
            split_index, condition, condition_feature, hot_condition_fraction
        )

        tree_shap_recursive(
            children_left, children_right, children_default, features, thresholds, values, node_sample_weight,
            x, x_missing, phi, cold_index, unique_depth + 1,
            feature_indexes, zero_fractions, one_fractions, pweights,
            cold_zero_fraction * incoming_zero_fraction, 0,
            split_index, condition, condition_feature, cold_condition_fraction
        )


    

In [6]:

    

x = np.ones(X.shape[1])
TreeExplainer(model).shap_values(x)


    

    




6






    
Out[6]:





array([ 3.86778154e-01, -2.91701989e-04,  2.21392679e-02,  3.21670105e-02,
       -2.43900987e-01, -1.72050637e+00, -7.88487600e-03,  1.32586529e+01,
       -2.50914664e-02,  1.64892740e-01,  1.16804717e-01, -4.67221730e-01,
        9.75267653e+00,  2.25335138e+01])