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import itertools
import re
import numpy as np
import scipy.special
import xgboost as xgb
from xgboost import testing as tm
class TestSHAP:
def test_feature_importances(self) -> None:
rng = np.random.RandomState(1994)
data = rng.randn(100, 5)
target = np.array([0, 1] * 50)
features = ["Feature1", "Feature2", "Feature3", "Feature4", "Feature5"]
dm = xgb.DMatrix(data, label=target, feature_names=features)
params = {
"objective": "multi:softprob",
"eval_metric": "mlogloss",
"eta": 0.3,
"num_class": 3,
}
bst = xgb.train(params, dm, num_boost_round=10)
# number of feature importances should == number of features
scores1 = bst.get_score()
scores2 = bst.get_score(importance_type="weight")
scores3 = bst.get_score(importance_type="cover")
scores4 = bst.get_score(importance_type="gain")
scores5 = bst.get_score(importance_type="total_cover")
scores6 = bst.get_score(importance_type="total_gain")
assert len(scores1) == len(features)
assert len(scores2) == len(features)
assert len(scores3) == len(features)
assert len(scores4) == len(features)
assert len(scores5) == len(features)
assert len(scores6) == len(features)
# check backwards compatibility of get_fscore
fscores = bst.get_fscore()
assert scores1 == fscores
dtrain, dtest = tm.load_agaricus(__file__)
def fn(max_depth: int, num_rounds: int) -> None:
# train
params = {"max_depth": max_depth, "eta": 1}
bst = xgb.train(params, dtrain, num_boost_round=num_rounds)
# predict
preds = bst.predict(dtest)
contribs = bst.predict(dtest, pred_contribs=True)
# result should be (number of features + BIAS) * number of rows
assert contribs.shape == (dtest.num_row(), dtest.num_col() + 1)
# sum of contributions should be same as predictions
np.testing.assert_array_almost_equal(np.sum(contribs, axis=1), preds)
# for max_depth, num_rounds in itertools.product(range(0, 3), range(1, 5)):
# yield fn, max_depth, num_rounds
# check that we get the right SHAP values for a basic AND example
# (https://arxiv.org/abs/1706.06060)
X = np.zeros((4, 2))
X[0, :] = 1
X[1, 0] = 1
X[2, 1] = 1
y = np.zeros(4)
y[0] = 1
param = {"max_depth": 2, "base_score": 0.0, "eta": 1.0, "lambda": 0}
bst = xgb.train(param, xgb.DMatrix(X, label=y), 1)
out = bst.predict(xgb.DMatrix(X[0:1, :]), pred_contribs=True)
assert out[0, 0] == 0.375
assert out[0, 1] == 0.375
assert out[0, 2] == 0.25
def parse_model(model: xgb.Booster) -> list:
trees = []
r_exp = r"([0-9]+):\[f([0-9]+)<([0-9\.e-]+)\] yes=([0-9]+),no=([0-9]+).*cover=([0-9e\.]+)"
r_exp_leaf = r"([0-9]+):leaf=([0-9\.e-]+),cover=([0-9e\.]+)"
for tree in model.get_dump(with_stats=True):
lines = list(tree.splitlines())
trees.append([None for i in range(len(lines))])
for line in lines:
match = re.search(r_exp, line)
if match is not None:
ind = int(match.group(1))
assert trees[-1] is not None
while ind >= len(trees[-1]):
assert isinstance(trees[-1], list)
trees[-1].append(None)
trees[-1][ind] = {
"yes_ind": int(match.group(4)),
"no_ind": int(match.group(5)),
"value": None,
"threshold": float(match.group(3)),
"feature_index": int(match.group(2)),
"cover": float(match.group(6)),
}
else:
match = re.search(r_exp_leaf, line)
ind = int(match.group(1))
while ind >= len(trees[-1]):
trees[-1].append(None)
trees[-1][ind] = {
"value": float(match.group(2)),
"cover": float(match.group(3)),
}
return trees
def exp_value_rec(tree, z, x, i=0):
if tree[i]["value"] is not None:
return tree[i]["value"]
else:
ind = tree[i]["feature_index"]
if z[ind] == 1:
# 1e-6 for numeric error from parsing text dump.
if x[ind] + 1e-6 <= tree[i]["threshold"]:
return exp_value_rec(tree, z, x, tree[i]["yes_ind"])
else:
return exp_value_rec(tree, z, x, tree[i]["no_ind"])
else:
r_yes = tree[tree[i]["yes_ind"]]["cover"] / tree[i]["cover"]
out = exp_value_rec(tree, z, x, tree[i]["yes_ind"])
val = out * r_yes
r_no = tree[tree[i]["no_ind"]]["cover"] / tree[i]["cover"]
out = exp_value_rec(tree, z, x, tree[i]["no_ind"])
val += out * r_no
return val
def exp_value(trees, z, x):
"E[f(z)|Z_s = X_s]"
return np.sum([exp_value_rec(tree, z, x) for tree in trees])
def all_subsets(ss):
return itertools.chain(
*map(lambda x: itertools.combinations(ss, x), range(0, len(ss) + 1))
)
def shap_value(trees, x, i, cond=None, cond_value=None):
M = len(x)
z = np.zeros(M)
other_inds = list(set(range(M)) - set([i]))
if cond is not None:
other_inds = list(set(other_inds) - set([cond]))
z[cond] = cond_value
M -= 1
total = 0.0
for subset in all_subsets(other_inds):
if len(subset) > 0:
z[list(subset)] = 1
v1 = exp_value(trees, z, x)
z[i] = 1
v2 = exp_value(trees, z, x)
total += (v2 - v1) / (scipy.special.binom(M - 1, len(subset)) * M)
z[i] = 0
z[list(subset)] = 0
return total
def shap_values(trees, x):
vals = [shap_value(trees, x, i) for i in range(len(x))]
vals.append(exp_value(trees, np.zeros(len(x)), x))
return np.array(vals)
def interaction_values(trees, x):
M = len(x)
out = np.zeros((M + 1, M + 1))
for i in range(len(x)):
for j in range(len(x)):
if i != j:
out[i, j] = interaction_value(trees, x, i, j) / 2
svals = shap_values(trees, x)
main_effects = svals - out.sum(1)
out[np.diag_indices_from(out)] = main_effects
return out
def interaction_value(trees, x, i, j):
M = len(x)
z = np.zeros(M)
other_inds = list(set(range(M)) - set([i, j]))
total = 0.0
for subset in all_subsets(other_inds):
if len(subset) > 0:
z[list(subset)] = 1
v00 = exp_value(trees, z, x)
z[i] = 1
v10 = exp_value(trees, z, x)
z[j] = 1
v11 = exp_value(trees, z, x)
z[i] = 0
v01 = exp_value(trees, z, x)
z[j] = 0
total += (v11 - v01 - v10 + v00) / (
scipy.special.binom(M - 2, len(subset)) * (M - 1)
)
z[list(subset)] = 0
return total
# test a simple and function
M = 2
N = 4
X = np.zeros((N, M))
X[0, :] = 1
X[1, 0] = 1
X[2, 1] = 1
y = np.zeros(N)
y[0] = 1
param = {"max_depth": 2, "base_score": 0.0, "eta": 1.0, "lambda": 0}
bst = xgb.train(param, xgb.DMatrix(X, label=y), 1)
brute_force = shap_values(parse_model(bst), X[0, :])
fast_method = bst.predict(xgb.DMatrix(X[0:1, :]), pred_contribs=True)
assert np.linalg.norm(brute_force - fast_method[0, :]) < 1e-4
brute_force = interaction_values(parse_model(bst), X[0, :])
fast_method = bst.predict(xgb.DMatrix(X[0:1, :]), pred_interactions=True)
assert np.linalg.norm(brute_force - fast_method[0, :, :]) < 1e-4
# test a random function
M = 2
N = 4
X = rng.randn(N, M)
y = rng.randn(N)
param = {"max_depth": 2, "base_score": 0.0, "eta": 1.0, "lambda": 0}
bst = xgb.train(param, xgb.DMatrix(X, label=y), 1)
brute_force = shap_values(parse_model(bst), X[0, :])
fast_method = bst.predict(xgb.DMatrix(X[0:1, :]), pred_contribs=True)
assert np.linalg.norm(brute_force - fast_method[0, :]) < 1e-4
brute_force = interaction_values(parse_model(bst), X[0, :])
fast_method = bst.predict(xgb.DMatrix(X[0:1, :]), pred_interactions=True)
assert np.linalg.norm(brute_force - fast_method[0, :, :]) < 1e-4
# test another larger more complex random function
M = 5
N = 100
X = rng.randn(N, M)
y = rng.randn(N)
base_score = 1.0
param = {"max_depth": 5, "base_score": base_score, "eta": 0.1, "gamma": 2.0}
bst = xgb.train(param, xgb.DMatrix(X, label=y), 10)
brute_force = shap_values(parse_model(bst), X[0, :])
brute_force[-1] += base_score
fast_method = bst.predict(xgb.DMatrix(X[0:1, :]), pred_contribs=True)
assert np.linalg.norm(brute_force - fast_method[0, :]) < 1e-4
brute_force = interaction_values(parse_model(bst), X[0, :])
brute_force[-1, -1] += base_score
fast_method = bst.predict(xgb.DMatrix(X[0:1, :]), pred_interactions=True)
assert np.linalg.norm(brute_force - fast_method[0, :, :]) < 1e-4
def test_shap_values(self) -> None:
from sklearn.datasets import make_classification, make_regression
def assert_same(X: np.ndarray, y: np.ndarray) -> None:
Xy = xgb.DMatrix(X, y)
booster = xgb.train({}, Xy, num_boost_round=4)
shap_dm = booster.predict(Xy, pred_contribs=True)
Xy = xgb.QuantileDMatrix(X, y)
shap_qdm = booster.predict(Xy, pred_contribs=True)
np.testing.assert_allclose(shap_dm, shap_qdm)
margin = booster.predict(Xy, output_margin=True)
np.testing.assert_allclose(
np.sum(shap_qdm, axis=len(shap_qdm.shape) - 1), margin, 1e-3, 1e-3
)
shap_dm = booster.predict(Xy, pred_interactions=True)
Xy = xgb.QuantileDMatrix(X, y)
shap_qdm = booster.predict(Xy, pred_interactions=True)
np.testing.assert_allclose(shap_dm, shap_qdm)
X, y = make_regression()
assert_same(X, y)
X, y = make_classification()
assert_same(X, y)
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