import numpy as np
from collections import Counter, Iterable
import pandas
import numbers
from warnings import warn
from sklearn.base import BaseEstimator
from sklearn.utils.validation import check_X_y, check_array, check_is_fitted
from sklearn.utils.multiclass import check_classification_targets
from sklearn.tree import DecisionTreeClassifier, DecisionTreeRegressor
from sklearn.ensemble import BaggingClassifier, BaggingRegressor
from sklearn.externals import six
from sklearn.tree import _tree
from .rule import Rule
INTEGER_TYPES = (numbers.Integral, np.integer)
[docs]class SkopeRules(BaseEstimator):
""" An easy-interpretable classifier optimizing simple logical rules.
Parameters
----------
feature_names : list of str, optional
The names of each feature to be used for returning rules in string
format.
precision_min : float, optional (default=0.5)
The minimal precision of a rule to be selected.
recall_min : float, optional (default=0.01)
The minimal recall of a rule to be selected.
n_estimators : int, optional (default=10)
The number of base estimators (rules) to use for prediction. More are
built before selection. All are available in the estimators_ attribute.
max_samples : int or float, optional (default=.8)
The number of samples to draw from X to train each decision tree, from
which rules are generated and selected.
- If int, then draw `max_samples` samples.
- If float, then draw `max_samples * X.shape[0]` samples.
If max_samples is larger than the number of samples provided,
all samples will be used for all trees (no sampling).
max_samples_features : int or float, optional (default=1.0)
The number of features to draw from X to train each decision tree, from
which rules are generated and selected.
- If int, then draw `max_features` features.
- If float, then draw `max_features * X.shape[1]` features.
bootstrap : boolean, optional (default=False)
Whether samples are drawn with replacement.
bootstrap_features : boolean, optional (default=False)
Whether features are drawn with replacement.
max_depth : integer or List or None, optional (default=3)
The maximum depth of the decision trees. If None, then nodes are
expanded until all leaves are pure or until all leaves contain less
than min_samples_split samples.
If an iterable is passed, you will train n_estimators
for each tree depth. It allows you to create and compare
rules of different length.
max_depth_duplication : integer, optional (default=None)
The maximum depth of the decision tree for rule deduplication,
if None then no deduplication occurs.
max_features : int, float, string or None, optional (default="auto")
The number of features considered (by each decision tree) when looking
for the best split:
- If int, then consider `max_features` features at each split.
- If float, then `max_features` is a percentage 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.
min_samples_split : int, float, optional (default=2)
The minimum number of samples required to split an internal node for
each decision tree.
- If int, then consider `min_samples_split` as the minimum number.
- If float, then `min_samples_split` is a percentage and
`ceil(min_samples_split * n_samples)` are the minimum
number of samples for each split.
n_jobs : integer, optional (default=1)
The number of jobs to run in parallel for both `fit` and `predict`.
If -1, then the number of jobs is set to the number of cores.
random_state : int, RandomState instance or None, optional
- 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 of the tree building process.
Attributes
----------
rules_ : dict of tuples (rule, precision, recall, nb).
The collection of `n_estimators` rules used in the ``predict`` method.
The rules are generated by fitted sub-estimators (decision trees). Each
rule satisfies recall_min and precision_min conditions. The selection
is done according to OOB precisions.
estimators_ : list of DecisionTreeClassifier
The collection of fitted sub-estimators used to generate candidate
rules.
estimators_samples_ : list of arrays
The subset of drawn samples (i.e., the in-bag samples) for each base
estimator.
estimators_features_ : list of arrays
The subset of drawn features for each base estimator.
max_samples_ : integer
The actual number of samples
n_features_ : integer
The number of features when ``fit`` is performed.
classes_ : array, shape (n_classes,)
The classes labels.
"""
def __init__(self,
feature_names=None,
precision_min=0.5,
recall_min=0.01,
n_estimators=10,
max_samples=.8,
max_samples_features=1.,
bootstrap=False,
bootstrap_features=False,
max_depth=3,
max_depth_duplication=None,
max_features=1.,
min_samples_split=2,
n_jobs=1,
random_state=None,
verbose=0):
self.precision_min = precision_min
self.recall_min = recall_min
self.feature_names = feature_names
self.n_estimators = n_estimators
self.max_samples = max_samples
self.max_samples_features = max_samples_features
self.bootstrap = bootstrap
self.bootstrap_features = bootstrap_features
self.max_depth = max_depth
self.max_depths = max_depth \
if isinstance(max_depth, Iterable) else [max_depth]
self.max_depth_duplication = max_depth_duplication
self.max_features = max_features
self.min_samples_split = min_samples_split
self.n_jobs = n_jobs
self.random_state = random_state
self.verbose = verbose
[docs] def fit(self, X, y, sample_weight=None):
"""Fit the model according to the given training data.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Training vector, where n_samples is the number of samples and
n_features is the number of features.
y : array-like, shape (n_samples,)
Target vector relative to X. Has to follow the convention 0 for
normal data, 1 for anomalies.
sample_weight : array-like, shape (n_samples,) optional
Array of weights that are assigned to individual samples, typically
the amount in case of transactions data. Used to grow regression
trees producing further rules to be tested.
If not provided, then each sample is given unit weight.
Returns
-------
self : object
Returns self.
"""
X, y = check_X_y(X, y)
check_classification_targets(y)
self.n_features_ = X.shape[1]
self.classes_ = np.unique(y)
n_classes = len(self.classes_)
if n_classes < 2:
raise ValueError("This method needs samples of at least 2 classes"
" in the data, but the data contains only one"
" class: %r" % self.classes_[0])
if not isinstance(self.max_depth_duplication, int) \
and self.max_depth_duplication is not None:
raise ValueError("max_depth_duplication should be an integer"
)
if not set(self.classes_) == set([0, 1]):
warn("Found labels %s. This method assumes target class to be"
" labeled as 1 and normal data to be labeled as 0. Any label"
" different from 0 will be considered as being from the"
" target class."
% set(self.classes_))
y = (y > 0)
# ensure that max_samples is in [1, n_samples]:
n_samples = X.shape[0]
if isinstance(self.max_samples, six.string_types):
raise ValueError('max_samples (%s) is not supported.'
'Valid choices are: "auto", int or'
'float' % self.max_samples)
elif isinstance(self.max_samples, INTEGER_TYPES):
if self.max_samples > n_samples:
warn("max_samples (%s) is greater than the "
"total number of samples (%s). max_samples "
"will be set to n_samples for estimation."
% (self.max_samples, n_samples))
max_samples = n_samples
else:
max_samples = self.max_samples
else: # float
if not (0. < self.max_samples <= 1.):
raise ValueError("max_samples must be in (0, 1], got %r"
% self.max_samples)
max_samples = int(self.max_samples * X.shape[0])
self.max_samples_ = max_samples
self.rules_ = {}
self.estimators_ = []
self.estimators_samples_ = []
self.estimators_features_ = []
# default columns names of the form ['c0', 'c1', ...]:
feature_names_ = (self.feature_names if self.feature_names is not None
else ['c' + x for x in
np.arange(X.shape[1]).astype(str)])
self.feature_names_ = feature_names_
clfs = []
regs = []
for max_depth in self.max_depths:
bagging_clf = BaggingClassifier(
base_estimator=DecisionTreeClassifier(
max_depth=max_depth,
max_features=self.max_features,
min_samples_split=self.min_samples_split),
n_estimators=self.n_estimators,
max_samples=self.max_samples_,
max_features=self.max_samples_features,
bootstrap=self.bootstrap,
bootstrap_features=self.bootstrap_features,
# oob_score=... XXX may be added
# if selection on tree perf needed.
# warm_start=... XXX may be added to increase computation perf.
n_jobs=self.n_jobs,
random_state=self.random_state,
verbose=self.verbose)
bagging_reg = BaggingRegressor(
base_estimator=DecisionTreeRegressor(
max_depth=max_depth,
max_features=self.max_features,
min_samples_split=self.min_samples_split),
n_estimators=self.n_estimators,
max_samples=self.max_samples_,
max_features=self.max_samples_features,
bootstrap=self.bootstrap,
bootstrap_features=self.bootstrap_features,
# oob_score=... XXX may be added
# if selection on tree perf needed.
# warm_start=... XXX may be added to increase computation perf.
n_jobs=self.n_jobs,
random_state=self.random_state,
verbose=self.verbose)
clfs.append(bagging_clf)
regs.append(bagging_reg)
# define regression target:
if sample_weight is not None:
if sample_weight is not None:
sample_weight = check_array(sample_weight, ensure_2d=False)
weights = sample_weight - sample_weight.min()
contamination = float(sum(y)) / len(y)
y_reg = (
pow(weights, 0.5) * 0.5 / contamination * (y > 0) -
pow((weights).mean(), 0.5) * (y == 0))
y_reg = 1. / (1 + np.exp(-y_reg)) # sigmoid
else:
y_reg = y # same as an other classification bagging
for clf in clfs:
clf.fit(X, y)
self.estimators_ += clf.estimators_
self.estimators_samples_ += clf.estimators_samples_
self.estimators_features_ += clf.estimators_features_
for reg in regs:
reg.fit(X, y_reg)
self.estimators_ += reg.estimators_
self.estimators_samples_ += reg.estimators_samples_
self.estimators_features_ += reg.estimators_features_
rules_ = []
for estimator, samples, features in zip(self.estimators_,
self.estimators_samples_,
self.estimators_features_):
# Create mask for OOB samples
mask = ~samples
if sum(mask) == 0:
warn("OOB evaluation not possible: doing it in-bag."
" Performance evaluation is likely to be wrong"
" (overfitting) and selected rules are likely to"
" not perform well! Please use max_samples < 1.")
mask = samples
rules_from_tree = self._tree_to_rules(
estimator, np.array(self.feature_names_)[features])
# XXX todo: idem without dataframe
X_oob = pandas.DataFrame((X[mask, :])[:, features],
columns=np.array(
self.feature_names_)[features])
if X_oob.shape[1] > 1: # otherwise pandas bug (cf. issue #16363)
y_oob = y[mask]
y_oob = np.array((y_oob != 0))
# Add OOB performances to rules:
rules_from_tree = [(r, self._eval_rule_perf(r, X_oob, y_oob))
for r in set(rules_from_tree)]
rules_ += rules_from_tree
# Factorize rules before semantic tree filtering
rules_ = [
tuple(rule)
for rule in
[Rule(r, args=args) for r, args in rules_]]
# keep only rules verifying precision_min and recall_min:
for rule, score in rules_:
if score[0] >= self.precision_min and score[1] >= self.recall_min:
if rule in self.rules_:
# update the score to the new mean
c = self.rules_[rule][2] + 1
b = self.rules_[rule][1] + 1. / c * (
score[1] - self.rules_[rule][1])
a = self.rules_[rule][0] + 1. / c * (
score[0] - self.rules_[rule][0])
self.rules_[rule] = (a, b, c)
else:
self.rules_[rule] = (score[0], score[1], 1)
self.rules_ = sorted(self.rules_.items(),
key=lambda x: (x[1][0], x[1][1]), reverse=True)
# Deduplicate the rule using semantic tree
if self.max_depth_duplication is not None:
self.rules_ = self.deduplicate(self.rules_)
self.rules_ = sorted(self.rules_, key=lambda x: - self.f1_score(x))
return self
[docs] def predict(self, X):
"""Predict if a particular sample is an outlier or not.
Parameters
----------
X : array-like, shape (n_samples, n_features)
The input samples. Internally, it will be converted to
``dtype=np.float32``
Returns
-------
is_outlier : array, shape (n_samples,)
For each observations, tells whether or not (1 or 0) it should
be considered as an outlier according to the selected rules.
"""
return np.array((self.decision_function(X) > 0), dtype=int)
[docs] def decision_function(self, X):
"""Average anomaly score of X of the base classifiers (rules).
The anomaly score of an input sample is computed as
the weighted sum of the binary rules outputs, the weight being
the respective precision of each rule.
Parameters
----------
X : array-like, shape (n_samples, n_features)
The training input samples.
Returns
-------
scores : array, shape (n_samples,)
The anomaly score of the input samples.
The higher, the more abnormal. Positive scores represent outliers,
null scores represent inliers.
"""
# Check if fit had been called
check_is_fitted(self, ['rules_', 'estimators_', 'estimators_samples_',
'max_samples_'])
# Input validation
X = check_array(X)
if X.shape[1] != self.n_features_:
raise ValueError("X.shape[1] = %d should be equal to %d, "
"the number of features at training time."
" Please reshape your data."
% (X.shape[1], self.n_features_))
df = pandas.DataFrame(X, columns=self.feature_names_)
selected_rules = self.rules_
scores = np.zeros(X.shape[0])
for (r, w) in selected_rules:
scores[list(df.query(r).index)] += w[0]
return scores
[docs] def rules_vote(self, X):
"""Score representing a vote of the base classifiers (rules).
The score of an input sample is computed as the sum of the binary
rules outputs: a score of k means than k rules have voted positively.
Parameters
----------
X : array-like, shape (n_samples, n_features)
The training input samples.
Returns
-------
scores : array, shape (n_samples,)
The score of the input samples.
The higher, the more abnormal. Positive scores represent outliers,
null scores represent inliers.
"""
# Check if fit had been called
check_is_fitted(self, ['rules_', 'estimators_', 'estimators_samples_',
'max_samples_'])
# Input validation
X = check_array(X)
if X.shape[1] != self.n_features_:
raise ValueError("X.shape[1] = %d should be equal to %d, "
"the number of features at training time."
" Please reshape your data."
% (X.shape[1], self.n_features_))
df = pandas.DataFrame(X, columns=self.feature_names_)
selected_rules = self.rules_
scores = np.zeros(X.shape[0])
for (r, _) in selected_rules:
scores[list(df.query(r).index)] += 1
return scores
[docs] def score_top_rules(self, X):
"""Score representing an ordering between the base classifiers (rules).
The score is high when the instance is detected by a performing rule.
If there are n rules, ordered by increasing OOB precision, a score of k
means than the kth rule has voted positively, but not the (k-1) first
rules.
Parameters
----------
X : array-like, shape (n_samples, n_features)
The training input samples.
Returns
-------
scores : array, shape (n_samples,)
The score of the input samples.
Positive scores represent outliers, null scores represent inliers.
"""
# Check if fit had been called
check_is_fitted(self, ['rules_', 'estimators_', 'estimators_samples_',
'max_samples_'])
# Input validation
X = check_array(X)
if X.shape[1] != self.n_features_:
raise ValueError("X.shape[1] = %d should be equal to %d, "
"the number of features at training time."
" Please reshape your data."
% (X.shape[1], self.n_features_))
df = pandas.DataFrame(X, columns=self.feature_names_)
selected_rules = self.rules_
scores = np.zeros(X.shape[0])
for (k, r) in enumerate(list((selected_rules))):
scores[list(df.query(r[0]).index)] = np.maximum(
len(selected_rules) - k,
scores[list(df.query(r[0]).index)])
return scores
[docs] def predict_top_rules(self, X, n_rules):
"""Predict if a particular sample is an outlier or not,
using the n_rules most performing rules.
Parameters
----------
X : array-like, shape (n_samples, n_features)
The input samples. Internally, it will be converted to
``dtype=np.float32``
n_rules : int
The number of rules used for the prediction. If one of the
n_rules most performing rules is activated, the prediction
is equal to 1.
Returns
-------
is_outlier : array, shape (n_samples,)
For each observations, tells whether or not (1 or 0) it should
be considered as an outlier according to the selected rules.
"""
return np.array((self.score_top_rules(X) > len(self.rules_) - n_rules),
dtype=int)
def _tree_to_rules(self, tree, feature_names):
"""
Return a list of rules from a tree
Parameters
----------
tree : Decision Tree Classifier/Regressor
feature_names: list of variable names
Returns
-------
rules : list of rules.
"""
# XXX todo: check the case where tree is build on subset of features,
# ie max_features != None
tree_ = tree.tree_
feature_name = [
feature_names[i] if i != _tree.TREE_UNDEFINED else "undefined!"
for i in tree_.feature
]
rules = []
def recurse(node, base_name):
if tree_.feature[node] != _tree.TREE_UNDEFINED:
name = feature_name[node]
symbol = '<='
symbol2 = '>'
threshold = tree_.threshold[node]
text = base_name + ["{} {} {}".format(name, symbol, threshold)]
recurse(tree_.children_left[node], text)
text = base_name + ["{} {} {}".format(name, symbol2,
threshold)]
recurse(tree_.children_right[node], text)
else:
rule = str.join(' and ', base_name)
rule = (rule if rule != ''
else ' == '.join([feature_names[0]] * 2))
# a rule selecting all is set to "c0==c0"
rules.append(rule)
recurse(0, [])
return rules if len(rules) > 0 else 'True'
def _eval_rule_perf(self, rule, X, y):
detected_index = list(X.query(rule).index)
if len(detected_index) <= 1:
return (0, 0)
y_detected = y[detected_index]
true_pos = y_detected[y_detected > 0].sum()
if true_pos == 0:
return (0, 0)
pos = y[y > 0].sum()
return y_detected.mean(), float(true_pos) / pos
def deduplicate(self, rules):
return [max(rules_set, key=self.f1_score)
for rules_set in self._find_similar_rulesets(rules)]
def _find_similar_rulesets(self, rules):
"""Create clusters of rules using a decision tree based
on the terms of the rules
Parameters
----------
rules : List, List of rules
The rules that should be splitted in subsets of similar rules
Returns
-------
rules : List of list of rules
The different set of rules. Each set should be homogeneous
"""
def split_with_best_feature(rules, depth, exceptions=[]):
"""
Method to find a split of rules given most represented feature
"""
if depth == 0:
return rules
rulelist = [rule.split(' and ') for rule, score in rules]
terms = [t.split(' ')[0] for term in rulelist for t in term]
counter = Counter(terms)
# Drop exception list
for exception in exceptions:
del counter[exception]
if len(counter) == 0:
return rules
most_represented_term = counter.most_common()[0][0]
# Proceed to split
rules_splitted = [[], [], []]
for rule in rules:
if (most_represented_term + ' <=') in rule[0]:
rules_splitted[0].append(rule)
elif (most_represented_term + ' >') in rule[0]:
rules_splitted[1].append(rule)
else:
rules_splitted[2].append(rule)
new_exceptions = exceptions+[most_represented_term]
# Choose best term
return [split_with_best_feature(ruleset,
depth-1,
exceptions=new_exceptions)
for ruleset in rules_splitted]
def breadth_first_search(rules, leaves=None):
if len(rules) == 0 or not isinstance(rules[0], list):
if len(rules) > 0:
return leaves.append(rules)
else:
for rules_child in rules:
breadth_first_search(rules_child, leaves=leaves)
return leaves
leaves = []
res = split_with_best_feature(rules, self.max_depth_duplication)
breadth_first_search(res, leaves=leaves)
return leaves
def f1_score(self, x):
return 2 * x[1][0] * x[1][1] / \
(x[1][0] + x[1][1]) if (x[1][0] + x[1][1]) > 0 else 0