def MakeChangePoint(series, split_index):
"""Makes a ChangePoint object for the given series at the given point.
Args:
series: A list of (x, y) pairs.
split_index: Index of the first point after the split.
Returns:
A ChangePoint object.
"""
assert 0 <= split_index < len(series)
x_values, y_values = zip(*series)
left, right = y_values[:split_index], y_values[split_index:]
left_median, right_median = math_utils.Median(left), math_utils.Median(
right)
ttest_results = ttest.WelchsTTest(left, right)
return ChangePoint(
x_value=x_values[split_index],
median_before=left_median,
median_after=right_median,
size_before=len(left),
size_after=len(right),
window_start=x_values[0],
window_end=x_values[-1], # inclusive bound
relative_change=math_utils.RelativeChange(left_median, right_median),
std_dev_before=math_utils.StandardDeviation(left),
t_statistic=ttest_results.t,
degrees_of_freedom=ttest_results.df,
p_value=ttest_results.p)
def _PassesThresholds(values, split_index, min_segment_size,
min_absolute_change, min_relative_change, min_steppiness,
multiple_of_std_dev):
"""Checks whether a point in a series appears to be an change point.
Args:
values: A list of numbers.
split_index: An index in the list of numbers.
min_segment_size: Threshold for size of segments before or after a point.
min_absolute_change: Minimum absolute median change threshold.
min_relative_change: Minimum relative median change threshold.
min_steppiness: Threshold for how similar to a step a change point must be.
multiple_of_std_dev: Threshold for change as multiple of std. deviation.
Returns:
A tuple of (bool, string) where the bool indicates whether the split index
passes the thresholds and the string being the reason it did not.
"""
left, right = values[:split_index], values[split_index:]
left_median, right_median = math_utils.Median(left), math_utils.Median(
right)
# 1. Segment size filter.
if len(left) < min_segment_size or len(right) < min_segment_size:
return (False, 'min_segment_size')
# 2. Absolute change filter.
absolute_change = abs(left_median - right_median)
if absolute_change < min_absolute_change:
return (False, 'min_absolute_change')
# 3. Relative change filter.
relative_change = math_utils.RelativeChange(left_median, right_median)
if relative_change < min_relative_change:
return (False, 'min_relative_change')
# 4. Multiple of standard deviation filter.
min_std_dev = min(math_utils.StandardDeviation(left),
math_utils.StandardDeviation(right))
if absolute_change < multiple_of_std_dev * min_std_dev:
return (False, 'min_std_dev')
# 5. Steppiness filter.
steppiness = find_step.Steppiness(values, split_index)
if steppiness < min_steppiness:
return (False, 'min_steppiness')
# Passed all filters!
return (True, 'passed')
def testRelativeChange_FromZero_ReturnsInf(self):
self.assertEqual(float('inf'), math_utils.RelativeChange(0, 1))
def testRelativeChange_NoChange_ReturnsZero(self):
self.assertEqual(0, math_utils.RelativeChange(7, 7))
def testRelativeChange(self):
# The relative difference is with respect to the first number, and the
# absolute value is taken. So 1 means doubling, and 0.5 means halving.
self.assertEqual(1, math_utils.RelativeChange(32, 64))
self.assertEqual(0.5, math_utils.RelativeChange(64, 32))
def _IsApproximatelyEqual(self, delta1, delta2): smaller = min(delta1, delta2) larger = max(delta1, delta2) return math_utils.RelativeChange(smaller, larger) <= _MAX_DELTA_DIFFERENCE
