"""Splitting algorithms in the construction of a tree. This module contains the main splitting algorithms for constructing a tree. Splitting is concerned with finding the optimal partition of the data into two groups. The impurity of the groups is minimized, and the impurity is measured by some criterion, which is typically the Gini impurity or the entropy. Criterion are implemented in the ``_criterion`` module. Splitting evaluates a subset of features (defined by `max_features` also known as mtry in the literature). The module supports two primary types of splitting strategies: - Best Split: A greedy approach to find the optimal split. This method ensures that the best possible split is chosen by examining various thresholds for each candidate feature. - Random Split: A stochastic approach that selects a split randomly from a subset of the best splits. This method is faster but does not guarantee the optimal split. """ # Authors: The scikit-learn developers # SPDX-License-Identifier: BSD-3-Clause from libc.string cimport memcpy from sklearn.utils._typedefs cimport int8_t from sklearn.tree._criterion cimport Criterion from sklearn.tree._partitioner cimport ( FEATURE_THRESHOLD, DensePartitioner, SparsePartitioner, shift_missing_values_to_left_if_required ) from sklearn.tree._utils cimport RAND_R_MAX, rand_int, rand_uniform import numpy as np # Introduce a fused-class to make it possible to share the split implementation # between the dense and sparse cases in the node_split_best and node_split_random # functions. The alternative would have been to use inheritance-based polymorphism # but it would have resulted in a ~10% overall tree fitting performance # degradation caused by the overhead frequent virtual method lookups. ctypedef fused Partitioner: DensePartitioner SparsePartitioner cdef float64_t INFINITY = np.inf cdef inline void _init_split(SplitRecord* self, intp_t start_pos) noexcept nogil: self.impurity_left = INFINITY self.impurity_right = INFINITY self.pos = start_pos self.feature = 0 self.threshold = 0. self.improvement = -INFINITY self.missing_go_to_left = False self.n_missing = 0 cdef class Splitter: """Abstract splitter class. Splitters are called by tree builders to find the best splits on both sparse and dense data, one split at a time. """ def __cinit__( self, Criterion criterion, intp_t max_features, intp_t min_samples_leaf, float64_t min_weight_leaf, object random_state, const int8_t[:] monotonic_cst, ): """ Parameters ---------- criterion : Criterion The criterion to measure the quality of a split. max_features : intp_t The maximal number of randomly selected features which can be considered for a split. min_samples_leaf : intp_t The minimal number of samples each leaf can have, where splits which would result in having less samples in a leaf are not considered. min_weight_leaf : float64_t The minimal weight each leaf can have, where the weight is the sum of the weights of each sample in it. random_state : object The user inputted random state to be used for pseudo-randomness monotonic_cst : const int8_t[:] Monotonicity constraints """ self.criterion = criterion self.n_samples = 0 self.n_features = 0 self.max_features = max_features self.min_samples_leaf = min_samples_leaf self.min_weight_leaf = min_weight_leaf self.random_state = random_state self.monotonic_cst = monotonic_cst self.with_monotonic_cst = monotonic_cst is not None def __getstate__(self): return {} def __setstate__(self, d): pass def __reduce__(self): return (type(self), (self.criterion, self.max_features, self.min_samples_leaf, self.min_weight_leaf, self.random_state, self.monotonic_cst), self.__getstate__()) cdef int init( self, object X, const float64_t[:, ::1] y, const float64_t[:] sample_weight, const uint8_t[::1] missing_values_in_feature_mask, ) except -1: """Initialize the splitter. Take in the input data X, the target Y, and optional sample weights. Returns -1 in case of failure to allocate memory (and raise MemoryError) or 0 otherwise. Parameters ---------- X : object This contains the inputs. Usually it is a 2d numpy array. y : ndarray, dtype=float64_t This is the vector of targets, or true labels, for the samples represented as a Cython memoryview. sample_weight : ndarray, dtype=float64_t The weights of the samples, where higher weighted samples are fit closer than lower weight samples. If not provided, all samples are assumed to have uniform weight. This is represented as a Cython memoryview. has_missing : bool At least one missing values is in X. """ self.rand_r_state = self.random_state.randint(0, RAND_R_MAX) cdef intp_t n_samples = X.shape[0] # Create a new array which will be used to store nonzero # samples from the feature of interest self.samples = np.empty(n_samples, dtype=np.intp) cdef intp_t[::1] samples = self.samples cdef intp_t i, j cdef float64_t weighted_n_samples = 0.0 j = 0 for i in range(n_samples): # Only work with positively weighted samples if sample_weight is None or sample_weight[i] != 0.0: samples[j] = i j += 1 if sample_weight is not None: weighted_n_samples += sample_weight[i] else: weighted_n_samples += 1.0 # Number of samples is number of positively weighted samples self.n_samples = j self.weighted_n_samples = weighted_n_samples cdef intp_t n_features = X.shape[1] self.features = np.arange(n_features, dtype=np.intp) self.n_features = n_features self.feature_values = np.empty(n_samples, dtype=np.float32) self.constant_features = np.empty(n_features, dtype=np.intp) self.y = y self.sample_weight = sample_weight if missing_values_in_feature_mask is not None: self.criterion.init_sum_missing() return 0 cdef int node_reset( self, intp_t start, intp_t end, float64_t* weighted_n_node_samples ) except -1 nogil: """Reset splitter on node samples[start:end]. Returns -1 in case of failure to allocate memory (and raise MemoryError) or 0 otherwise. Parameters ---------- start : intp_t The index of the first sample to consider end : intp_t The index of the last sample to consider weighted_n_node_samples : ndarray, dtype=float64_t pointer The total weight of those samples """ self.start = start self.end = end self.criterion.init( self.y, self.sample_weight, self.weighted_n_samples, self.samples, start, end ) weighted_n_node_samples[0] = self.criterion.weighted_n_node_samples return 0 cdef int node_split( self, ParentInfo* parent_record, SplitRecord* split, ) except -1 nogil: """Find the best split on node samples[start:end]. This is a placeholder method. The majority of computation will be done here. It should return -1 upon errors. """ pass cdef void node_value(self, float64_t* dest) noexcept nogil: """Copy the value of node samples[start:end] into dest.""" self.criterion.node_value(dest) cdef inline void clip_node_value(self, float64_t* dest, float64_t lower_bound, float64_t upper_bound) noexcept nogil: """Clip the value in dest between lower_bound and upper_bound for monotonic constraints.""" self.criterion.clip_node_value(dest, lower_bound, upper_bound) cdef float64_t node_impurity(self) noexcept nogil: """Return the impurity of the current node.""" return self.criterion.node_impurity() cdef inline int node_split_best( Splitter splitter, Partitioner partitioner, Criterion criterion, SplitRecord* split, ParentInfo* parent_record, ) except -1 nogil: """Find the best split on node samples[start:end] Returns -1 in case of failure to allocate memory (and raise MemoryError) or 0 otherwise. """ cdef const int8_t[:] monotonic_cst = splitter.monotonic_cst cdef bint with_monotonic_cst = splitter.with_monotonic_cst # Find the best split cdef intp_t start = splitter.start cdef intp_t end = splitter.end cdef intp_t end_non_missing cdef intp_t n_missing = 0 cdef bint has_missing = 0 cdef intp_t n_searches cdef intp_t n_left, n_right cdef bint missing_go_to_left cdef intp_t[::1] samples = splitter.samples cdef intp_t[::1] features = splitter.features cdef intp_t[::1] constant_features = splitter.constant_features cdef intp_t n_features = splitter.n_features cdef float32_t[::1] feature_values = splitter.feature_values cdef intp_t max_features = splitter.max_features cdef intp_t min_samples_leaf = splitter.min_samples_leaf cdef float64_t min_weight_leaf = splitter.min_weight_leaf cdef uint32_t* random_state = &splitter.rand_r_state cdef SplitRecord best_split, current_split cdef float64_t current_proxy_improvement = -INFINITY cdef float64_t best_proxy_improvement = -INFINITY cdef float64_t impurity = parent_record.impurity cdef float64_t lower_bound = parent_record.lower_bound cdef float64_t upper_bound = parent_record.upper_bound cdef intp_t f_i = n_features cdef intp_t f_j cdef intp_t p cdef intp_t p_prev cdef intp_t n_visited_features = 0 # Number of features discovered to be constant during the split search cdef intp_t n_found_constants = 0 # Number of features known to be constant and drawn without replacement cdef intp_t n_drawn_constants = 0 cdef intp_t n_known_constants = parent_record.n_constant_features # n_total_constants = n_known_constants + n_found_constants cdef intp_t n_total_constants = n_known_constants _init_split(&best_split, end) partitioner.init_node_split(start, end) # Sample up to max_features without replacement using a # Fisher-Yates-based algorithm (using the local variables `f_i` and # `f_j` to compute a permutation of the `features` array). # # Skip the CPU intensive evaluation of the impurity criterion for # features that were already detected as constant (hence not suitable # for good splitting) by ancestor nodes and save the information on # newly discovered constant features to spare computation on descendant # nodes. while (f_i > n_total_constants and # Stop early if remaining features # are constant (n_visited_features < max_features or # At least one drawn features must be non constant n_visited_features <= n_found_constants + n_drawn_constants)): n_visited_features += 1 # Loop invariant: elements of features in # - [:n_drawn_constant[ holds drawn and known constant features; # - [n_drawn_constant:n_known_constant[ holds known constant # features that haven't been drawn yet; # - [n_known_constant:n_total_constant[ holds newly found constant # features; # - [n_total_constant:f_i[ holds features that haven't been drawn # yet and aren't constant apriori. # - [f_i:n_features[ holds features that have been drawn # and aren't constant. # Draw a feature at random f_j = rand_int(n_drawn_constants, f_i - n_found_constants, random_state) if f_j < n_known_constants: # f_j in the interval [n_drawn_constants, n_known_constants[ features[n_drawn_constants], features[f_j] = features[f_j], features[n_drawn_constants] n_drawn_constants += 1 continue # f_j in the interval [n_known_constants, f_i - n_found_constants[ f_j += n_found_constants # f_j in the interval [n_total_constants, f_i[ current_split.feature = features[f_j] partitioner.sort_samples_and_feature_values(current_split.feature) n_missing = partitioner.n_missing end_non_missing = end - n_missing if ( # All values for this feature are missing, or end_non_missing == start or # This feature is considered constant (max - min <= FEATURE_THRESHOLD) (( feature_values[end_non_missing - 1] <= feature_values[start] + FEATURE_THRESHOLD ) and n_missing == 0) ): # We consider this feature constant in this case. # Since finding a split among constant feature is not valuable, # we do not consider this feature for splitting. features[f_j], features[n_total_constants] = features[n_total_constants], features[f_j] n_found_constants += 1 n_total_constants += 1 continue f_i -= 1 features[f_i], features[f_j] = features[f_j], features[f_i] has_missing = n_missing != 0 criterion.init_missing(n_missing) # initialize even when n_missing == 0 # Evaluate all splits # If there are missing values, then we search twice for the most optimal split. # The first search will have all the missing values going to the right node. # The second search will have all the missing values going to the left node. # If there are no missing values, then we search only once for the most # optimal split. n_searches = 2 if has_missing else 1 for i in range(n_searches): missing_go_to_left = i == 1 criterion.missing_go_to_left = missing_go_to_left criterion.reset() p = start while p < end_non_missing: partitioner.next_p(&p_prev, &p) if p >= end_non_missing: continue if missing_go_to_left: n_left = p - start + n_missing n_right = end_non_missing - p else: n_left = p - start n_right = end_non_missing - p + n_missing # Reject if min_samples_leaf is not guaranteed if n_left < min_samples_leaf or n_right < min_samples_leaf: continue current_split.pos = p criterion.update(current_split.pos) # Reject if monotonicity constraints are not satisfied if ( with_monotonic_cst and monotonic_cst[current_split.feature] != 0 and not criterion.check_monotonicity( monotonic_cst[current_split.feature], lower_bound, upper_bound, ) ): continue # Reject if min_weight_leaf is not satisfied if ((criterion.weighted_n_left < min_weight_leaf) or (criterion.weighted_n_right < min_weight_leaf)): continue current_proxy_improvement = criterion.proxy_impurity_improvement() if current_proxy_improvement > best_proxy_improvement: best_proxy_improvement = current_proxy_improvement # sum of halves is used to avoid infinite value current_split.threshold = ( feature_values[p_prev] / 2.0 + feature_values[p] / 2.0 ) if ( current_split.threshold == feature_values[p] or current_split.threshold == INFINITY or current_split.threshold == -INFINITY ): current_split.threshold = feature_values[p_prev] current_split.n_missing = n_missing # if there are no missing values in the training data, during # test time, we send missing values to the branch that contains # the most samples during training time. if n_missing == 0: current_split.missing_go_to_left = n_left > n_right else: current_split.missing_go_to_left = missing_go_to_left best_split = current_split # copy # Evaluate when there are missing values and all missing values goes # to the right node and non-missing values goes to the left node. if has_missing: n_left, n_right = end - start - n_missing, n_missing p = end - n_missing missing_go_to_left = 0 if not (n_left < min_samples_leaf or n_right < min_samples_leaf): criterion.missing_go_to_left = missing_go_to_left criterion.update(p) if not ((criterion.weighted_n_left < min_weight_leaf) or (criterion.weighted_n_right < min_weight_leaf)): current_proxy_improvement = criterion.proxy_impurity_improvement() if current_proxy_improvement > best_proxy_improvement: best_proxy_improvement = current_proxy_improvement current_split.threshold = INFINITY current_split.missing_go_to_left = missing_go_to_left current_split.n_missing = n_missing current_split.pos = p best_split = current_split # Reorganize into samples[start:best_split.pos] + samples[best_split.pos:end] if best_split.pos < end: partitioner.partition_samples_final( best_split.pos, best_split.threshold, best_split.feature, best_split.n_missing ) criterion.init_missing(best_split.n_missing) criterion.missing_go_to_left = best_split.missing_go_to_left criterion.reset() criterion.update(best_split.pos) criterion.children_impurity( &best_split.impurity_left, &best_split.impurity_right ) best_split.improvement = criterion.impurity_improvement( impurity, best_split.impurity_left, best_split.impurity_right ) shift_missing_values_to_left_if_required(&best_split, samples, end) # Respect invariant for constant features: the original order of # element in features[:n_known_constants] must be preserved for sibling # and child nodes memcpy(&features[0], &constant_features[0], sizeof(intp_t) * n_known_constants) # Copy newly found constant features memcpy(&constant_features[n_known_constants], &features[n_known_constants], sizeof(intp_t) * n_found_constants) # Return values parent_record.n_constant_features = n_total_constants split[0] = best_split return 0 cdef inline int node_split_random( Splitter splitter, Partitioner partitioner, Criterion criterion, SplitRecord* split, ParentInfo* parent_record, ) except -1 nogil: """Find the best random split on node samples[start:end] Returns -1 in case of failure to allocate memory (and raise MemoryError) or 0 otherwise. """ cdef const int8_t[:] monotonic_cst = splitter.monotonic_cst cdef bint with_monotonic_cst = splitter.with_monotonic_cst # Draw random splits and pick the best cdef intp_t start = splitter.start cdef intp_t end = splitter.end cdef intp_t end_non_missing cdef intp_t n_missing = 0 cdef bint has_missing = 0 cdef intp_t n_left, n_right cdef bint missing_go_to_left cdef intp_t[::1] samples = splitter.samples cdef intp_t[::1] features = splitter.features cdef intp_t[::1] constant_features = splitter.constant_features cdef intp_t n_features = splitter.n_features cdef intp_t max_features = splitter.max_features cdef intp_t min_samples_leaf = splitter.min_samples_leaf cdef float64_t min_weight_leaf = splitter.min_weight_leaf cdef uint32_t* random_state = &splitter.rand_r_state cdef SplitRecord best_split, current_split cdef float64_t current_proxy_improvement = - INFINITY cdef float64_t best_proxy_improvement = - INFINITY cdef float64_t impurity = parent_record.impurity cdef float64_t lower_bound = parent_record.lower_bound cdef float64_t upper_bound = parent_record.upper_bound cdef intp_t f_i = n_features cdef intp_t f_j # Number of features discovered to be constant during the split search cdef intp_t n_found_constants = 0 # Number of features known to be constant and drawn without replacement cdef intp_t n_drawn_constants = 0 cdef intp_t n_known_constants = parent_record.n_constant_features # n_total_constants = n_known_constants + n_found_constants cdef intp_t n_total_constants = n_known_constants cdef intp_t n_visited_features = 0 cdef float32_t min_feature_value cdef float32_t max_feature_value _init_split(&best_split, end) partitioner.init_node_split(start, end) # Sample up to max_features without replacement using a # Fisher-Yates-based algorithm (using the local variables `f_i` and # `f_j` to compute a permutation of the `features` array). # # Skip the CPU intensive evaluation of the impurity criterion for # features that were already detected as constant (hence not suitable # for good splitting) by ancestor nodes and save the information on # newly discovered constant features to spare computation on descendant # nodes. while (f_i > n_total_constants and # Stop early if remaining features # are constant (n_visited_features < max_features or # At least one drawn features must be non constant n_visited_features <= n_found_constants + n_drawn_constants)): n_visited_features += 1 # Loop invariant: elements of features in # - [:n_drawn_constant[ holds drawn and known constant features; # - [n_drawn_constant:n_known_constant[ holds known constant # features that haven't been drawn yet; # - [n_known_constant:n_total_constant[ holds newly found constant # features; # - [n_total_constant:f_i[ holds features that haven't been drawn # yet and aren't constant apriori. # - [f_i:n_features[ holds features that have been drawn # and aren't constant. # Draw a feature at random f_j = rand_int(n_drawn_constants, f_i - n_found_constants, random_state) if f_j < n_known_constants: # f_j in the interval [n_drawn_constants, n_known_constants[ features[n_drawn_constants], features[f_j] = features[f_j], features[n_drawn_constants] n_drawn_constants += 1 continue # f_j in the interval [n_known_constants, f_i - n_found_constants[ f_j += n_found_constants # f_j in the interval [n_total_constants, f_i[ current_split.feature = features[f_j] # Find min, max as we will randomly select a threshold between them partitioner.find_min_max( current_split.feature, &min_feature_value, &max_feature_value ) n_missing = partitioner.n_missing end_non_missing = end - n_missing if ( # All values for this feature are missing, or end_non_missing == start or # This feature is considered constant (max - min <= FEATURE_THRESHOLD) (max_feature_value <= min_feature_value + FEATURE_THRESHOLD and n_missing == 0) ): # We consider this feature constant in this case. # Since finding a split with a constant feature is not valuable, # we do not consider this feature for splitting. features[f_j], features[n_total_constants] = features[n_total_constants], current_split.feature n_found_constants += 1 n_total_constants += 1 continue f_i -= 1 features[f_i], features[f_j] = features[f_j], features[f_i] has_missing = n_missing != 0 criterion.init_missing(n_missing) # Draw a random threshold current_split.threshold = rand_uniform( min_feature_value, max_feature_value, random_state, ) if has_missing: # If there are missing values, then we randomly make all missing # values go to the right or left. # # Note: compared to the BestSplitter, we do not evaluate the # edge case where all the missing values go to the right node # and the non-missing values go to the left node. This is because # this would indicate a threshold outside of the observed range # of the feature. However, it is not clear how much probability weight should # be given to this edge case. missing_go_to_left = rand_int(0, 2, random_state) else: missing_go_to_left = 0 criterion.missing_go_to_left = missing_go_to_left if current_split.threshold == max_feature_value: current_split.threshold = min_feature_value # Partition current_split.pos = partitioner.partition_samples( current_split.threshold ) if missing_go_to_left: n_left = current_split.pos - start + n_missing n_right = end_non_missing - current_split.pos else: n_left = current_split.pos - start n_right = end_non_missing - current_split.pos + n_missing # Reject if min_samples_leaf is not guaranteed if n_left < min_samples_leaf or n_right < min_samples_leaf: continue # Evaluate split # At this point, the criterion has a view into the samples that was partitioned # by the partitioner. The criterion will use the partition to evaluating the split. criterion.reset() criterion.update(current_split.pos) # Reject if min_weight_leaf is not satisfied if ((criterion.weighted_n_left < min_weight_leaf) or (criterion.weighted_n_right < min_weight_leaf)): continue # Reject if monotonicity constraints are not satisfied if ( with_monotonic_cst and monotonic_cst[current_split.feature] != 0 and not criterion.check_monotonicity( monotonic_cst[current_split.feature], lower_bound, upper_bound, ) ): continue current_proxy_improvement = criterion.proxy_impurity_improvement() if current_proxy_improvement > best_proxy_improvement: current_split.n_missing = n_missing # if there are no missing values in the training data, during # test time, we send missing values to the branch that contains # the most samples during training time. if has_missing: current_split.missing_go_to_left = missing_go_to_left else: current_split.missing_go_to_left = n_left > n_right best_proxy_improvement = current_proxy_improvement best_split = current_split # copy # Reorganize into samples[start:best.pos] + samples[best.pos:end] if best_split.pos < end: if current_split.feature != best_split.feature: partitioner.partition_samples_final( best_split.pos, best_split.threshold, best_split.feature, best_split.n_missing ) criterion.init_missing(best_split.n_missing) criterion.missing_go_to_left = best_split.missing_go_to_left criterion.reset() criterion.update(best_split.pos) criterion.children_impurity( &best_split.impurity_left, &best_split.impurity_right ) best_split.improvement = criterion.impurity_improvement( impurity, best_split.impurity_left, best_split.impurity_right ) shift_missing_values_to_left_if_required(&best_split, samples, end) # Respect invariant for constant features: the original order of # element in features[:n_known_constants] must be preserved for sibling # and child nodes memcpy(&features[0], &constant_features[0], sizeof(intp_t) * n_known_constants) # Copy newly found constant features memcpy(&constant_features[n_known_constants], &features[n_known_constants], sizeof(intp_t) * n_found_constants) # Return values parent_record.n_constant_features = n_total_constants split[0] = best_split return 0 cdef class BestSplitter(Splitter): """Splitter for finding the best split on dense data.""" cdef DensePartitioner partitioner cdef int init( self, object X, const float64_t[:, ::1] y, const float64_t[:] sample_weight, const uint8_t[::1] missing_values_in_feature_mask, ) except -1: Splitter.init(self, X, y, sample_weight, missing_values_in_feature_mask) self.partitioner = DensePartitioner( X, self.samples, self.feature_values, missing_values_in_feature_mask ) cdef int node_split( self, ParentInfo* parent_record, SplitRecord* split, ) except -1 nogil: return node_split_best( self, self.partitioner, self.criterion, split, parent_record, ) cdef class BestSparseSplitter(Splitter): """Splitter for finding the best split, using the sparse data.""" cdef SparsePartitioner partitioner cdef int init( self, object X, const float64_t[:, ::1] y, const float64_t[:] sample_weight, const uint8_t[::1] missing_values_in_feature_mask, ) except -1: Splitter.init(self, X, y, sample_weight, missing_values_in_feature_mask) self.partitioner = SparsePartitioner( X, self.samples, self.n_samples, self.feature_values, missing_values_in_feature_mask ) cdef int node_split( self, ParentInfo* parent_record, SplitRecord* split, ) except -1 nogil: return node_split_best( self, self.partitioner, self.criterion, split, parent_record, ) cdef class RandomSplitter(Splitter): """Splitter for finding the best random split on dense data.""" cdef DensePartitioner partitioner cdef int init( self, object X, const float64_t[:, ::1] y, const float64_t[:] sample_weight, const uint8_t[::1] missing_values_in_feature_mask, ) except -1: Splitter.init(self, X, y, sample_weight, missing_values_in_feature_mask) self.partitioner = DensePartitioner( X, self.samples, self.feature_values, missing_values_in_feature_mask ) cdef int node_split( self, ParentInfo* parent_record, SplitRecord* split, ) except -1 nogil: return node_split_random( self, self.partitioner, self.criterion, split, parent_record, ) cdef class RandomSparseSplitter(Splitter): """Splitter for finding the best random split, using the sparse data.""" cdef SparsePartitioner partitioner cdef int init( self, object X, const float64_t[:, ::1] y, const float64_t[:] sample_weight, const uint8_t[::1] missing_values_in_feature_mask, ) except -1: Splitter.init(self, X, y, sample_weight, missing_values_in_feature_mask) self.partitioner = SparsePartitioner( X, self.samples, self.n_samples, self.feature_values, missing_values_in_feature_mask ) cdef int node_split( self, ParentInfo* parent_record, SplitRecord* split, ) except -1 nogil: return node_split_random( self, self.partitioner, self.criterion, split, parent_record, )