def _find_best_split(self, feature):
"""Find the best threshold value to split this node on, using @feature.
Returns (less_than_threshold, split_err).
The @less_than_threshold is what you use to "decide", i.e.:
if example[feature] < less_than_threshold:
decide_left ...
else:
decide_right ...
Note that this method doesn't actually split anything: it just figures out
which threshold value would be best to split at.
"""
self._sort_by_features(feature)
left_output_stats = SummaryStats()
right_output_stats = SummaryStats()
assert len(self.examples) == len(self.examples_sorted_by_feature[feature])
# To begin, let's assume we push all examples into the right child node.
for example in self.examples:
right_output_stats.add(float(example["_OUTPUT"]))
# Now, move the examples one by one to the left child node.
# (Note the examples sorted by value -- it's as if we're adjusting the
# less_than_threshold.)
# After each example, calculate the goodness-of-split, and track the best.
best_threshold = None
best_err = None
last_feature_value = None
for example in self.examples_sorted_by_feature[feature]:
feature_value = example[feature]
output_value = float(example["_OUTPUT"])
# Speed optimization: skip over examples with same feature value.
if feature_value == last_feature_value:
left_output_stats.add(output_value)
right_output_stats.remove(output_value)
continue
last_feature_value = feature_value # remember for next iteration
left_count = left_output_stats.count()
right_count = right_output_stats.count()
# Edge-case: left or right child is empty
if left_count == 0 or right_count == 0:
left_output_stats.add(output_value)
right_output_stats.remove(output_value)
continue # not a true split
# Compute goodness-of-split: weighted average of the 2 output variances.
if left_count <= 1: left_err = 0
else: left_err = (left_count - 1) * left_output_stats.var()
if right_count <= 1: right_err = 0
else: right_err = (right_count - 1) * right_output_stats.var()
err = left_err + right_err
if best_err is None or err < best_err:
best_threshold = feature_value
best_err = err
left_output_stats.add(output_value)
right_output_stats.remove(output_value)
# to save memory, delete this sorted array (we'll never use it again anyway)
del self.examples_sorted_by_feature[feature]
return (best_threshold, best_err)
