From f75f356f2173a5fc08d839d46ab74697bde688b5 Mon Sep 17 00:00:00 2001 From: Denis Shchepakin <1842450+Sowiks@users.noreply.github.com> Date: Tue, 11 Nov 2025 00:00:49 -0800 Subject: [PATCH 1/4] Replacing signal_processing_algorithms with internal implementation --- otava/analysis.py | 178 ++-- otava/change_point_divisive/__init__.py | 16 + otava/change_point_divisive/base.py | 109 +++ otava/change_point_divisive/calculator.py | 198 +++++ otava/change_point_divisive/detector.py | 62 ++ .../significance_test.py | 77 ++ otava/series.py | 28 +- pyproject.toml | 2 +- tests/analysis_test.py | 47 +- tests/change_point_divisive_test.py | 122 +++ uv.lock | 797 ++++++++++-------- 11 files changed, 1182 insertions(+), 454 deletions(-) create mode 100644 otava/change_point_divisive/__init__.py create mode 100644 otava/change_point_divisive/base.py create mode 100644 otava/change_point_divisive/calculator.py create mode 100644 otava/change_point_divisive/detector.py create mode 100644 otava/change_point_divisive/significance_test.py create mode 100644 tests/change_point_divisive_test.py diff --git a/otava/analysis.py b/otava/analysis.py index 67396c8b..8221bea9 100644 --- a/otava/analysis.py +++ b/otava/analysis.py @@ -16,21 +16,28 @@ # under the License. from dataclasses import dataclass -from typing import Iterable, List, Reversible +from typing import List, Optional, Sequence, SupportsFloat, Tuple, TypeAlias import numpy as np from scipy.stats import ttest_ind_from_stats -from signal_processing_algorithms.e_divisive import EDivisive -from signal_processing_algorithms.e_divisive.base import SignificanceTester -from signal_processing_algorithms.e_divisive.calculators import cext_calculator -from signal_processing_algorithms.e_divisive.change_points import EDivisiveChangePoint -from signal_processing_algorithms.e_divisive.significance_test import ( - QHatPermutationsSignificanceTester, + +from otava.change_point_divisive.base import ( + BaseStats, + CandidateChangePoint, + ChangePoint, + GenericStats, + SignificanceTester, +) +from otava.change_point_divisive.calculator import PairDistanceCalculator +from otava.change_point_divisive.detector import ChangePointDetector +from otava.change_point_divisive.significance_test import ( + PermutationsSignificanceTester, + PermutationStats, ) @dataclass -class ComparativeStats: +class TTestStats(BaseStats): """ Keeps statistics of two series of data and the probability both series have the same distribution. @@ -40,7 +47,6 @@ class ComparativeStats: mean_2: float std_1: float std_2: float - pvalue: float def forward_rel_change(self, value_if_nan=0): """Relative change from left to right""" @@ -90,72 +96,22 @@ def to_json(self): } -@dataclass -class ChangePoint: - index: int - stats: ComparativeStats - - -class ExtendedSignificanceTester(SignificanceTester): - """ - Adds capability of exposing the means and deviations of both sides of the split - and the pvalue (strength) of the split. - """ - - pvalue: float - - def change_point(self, index: int, series: np.ndarray, windows: Iterable[int]) -> ChangePoint: - """ - Computes properties of the change point if the change point gets - inserted at the given index into the series array. - """ - ... - - def compare(self, left: np.ndarray, right: np.ndarray) -> ComparativeStats: - """ - Compares two sets of points for similarity / difference. - Computes basic stats and probability both sets come from the same distribution/ - """ - ... - - @staticmethod - def find_window(candidate: int, window_endpoints: Reversible[int]) -> (int, int): - start: int = next((x for x in reversed(window_endpoints) if x < candidate), None) - end: int = next((x for x in window_endpoints if x > candidate), None) - return start, end - - def is_significant( - self, candidate: EDivisiveChangePoint, series: np.ndarray, windows: Iterable[int] - ) -> bool: - try: - cp = self.change_point(candidate.index, series, windows) - return cp.stats.pvalue <= self.pvalue - except ValueError: - return False +# Generic Change Point List +GenCPList : TypeAlias = List[ChangePoint[GenericStats]] +# Permutation Change Point List +PermCPList : TypeAlias = List[ChangePoint[PermutationStats]] +# T-test Change Point List +TtestCPList : TypeAlias = List[ChangePoint[TTestStats]] -class TTestSignificanceTester(ExtendedSignificanceTester): +class TTestSignificanceTester(SignificanceTester): """ Uses two-sided Student's T-test to decide if a candidate change point splits the series into pieces that are significantly different from each other. This test is good if the data between the change points have normal distribution. It works well even with tiny numbers of points (<10). """ - - def __init__(self, pvalue: float): - self.pvalue = pvalue - - def change_point( - self, index: int, series: np.ndarray, window_endpoints: Reversible[int] - ) -> ChangePoint: - - (start, end) = self.find_window(index, window_endpoints) - left = series[start:index] - right = series[index:end] - stats = self.compare(left, right) - return ChangePoint(index, stats) - - def compare(self, left: np.ndarray, right: np.ndarray) -> ComparativeStats: + def compare(self, left: Sequence[SupportsFloat], right: Sequence[SupportsFloat]) -> TTestStats: if len(left) == 0 or len(right) == 0: raise ValueError @@ -170,10 +126,42 @@ def compare(self, left: np.ndarray, right: np.ndarray) -> ComparativeStats: ) else: p = 1.0 - return ComparativeStats(mean_l, mean_r, std_l, std_r, p) + return TTestStats(mean_1=mean_l, mean_2=mean_r, std_1=std_l, std_2=std_r, pvalue=p) + + def change_point( + self, candidate: CandidateChangePoint, series: Sequence[SupportsFloat], intervals: List[slice] + ) -> ChangePoint[TTestStats]: + """ + Computes properties of the change point if the Candidate Change Point based on the provided intervals. + + The method works for two cases: + 1. Divisive algorithm. + if the candidate is a new potential change point, i.e., its index is inside any interval, then + we split the interval by the candidate's index to get left and right subseries. + 2. Merge step in t-test algorithm. + if the candidate is an existing change point, i.e., it matches the end of two intervals, then + it's a potential weak change point, and we don't need to split the intervals anymore (just take + both intervals as left and right subseries). + + """ + for i, interval in enumerate(intervals): + if interval.stop == candidate.index: + left_interval = interval + right_interval = intervals[i + 1] + break + elif (interval.start is None or interval.start < candidate.index) and (interval.stop is None or candidate.index < interval.stop): + left_interval = slice(interval.start, candidate.index) + right_interval = slice(candidate.index, interval.stop) + break + else: + raise ValueError(f"Candidate Change Point at index={candidate.index} doesn't correspond to any interval in {intervals}.") + left = series[left_interval] + right = series[right_interval] + stats = self.compare(left, right) + return ChangePoint.from_candidate(candidate, stats) -def fill_missing(data: List[float]): +def fill_missing(data: Sequence[SupportsFloat]): """ Forward-fills None occurrences with nearest previous non-None values. Initial None values are back-filled with the nearest future non-None value. @@ -192,8 +180,8 @@ def fill_missing(data: List[float]): def merge( - change_points: List[ChangePoint], series: np.array, max_pvalue: float, min_magnitude: float -) -> List[ChangePoint]: + change_points: TtestCPList, series: Sequence[SupportsFloat], max_pvalue: float, min_magnitude: float +) -> TtestCPList: """ Removes weak change points recursively going bottom-up until we get only high-quality change points @@ -222,13 +210,13 @@ def merge( # We can't continue yet, because by removing a change_point # the adjacent change points changed their properties. # Recompute the adjacent change point stats: - window_endpoints = [0] + [cp.index for cp in change_points] + [len(series)] + intervals = tester.get_intervals(change_points) def recompute(index: int): if index < 0 or index >= len(change_points): return cp = change_points[index] - change_points[index] = tester.change_point(cp.index, series, window_endpoints) + change_points[index] = tester.change_point(cp.to_candidate(), series, intervals) recompute(weakest_cp_index) recompute(weakest_cp_index + 1) @@ -236,8 +224,8 @@ def recompute(index: int): return change_points -def split(series: np.array, window_len: int = 30, max_pvalue: float = 0.001, - new_points=None, old_cp=None) -> List[ChangePoint]: +def split(series: Sequence[SupportsFloat], window_len: int = 30, max_pvalue: float = 0.001, + new_points: Optional[int] = None, old_cp: Optional[TtestCPList] = None) -> TtestCPList: """ Finds change points by splitting the series top-down. @@ -259,13 +247,13 @@ def split(series: np.array, window_len: int = 30, max_pvalue: float = 0.001, assert "Window length must be at least 2", window_len >= 2 start = 0 step = int(window_len / 2) - indexes = [] + change_points = [] # N new_points are appended to the end of series. Typically N=1. # old_cp are the weak change points from before new points were added. # We now just compute e-e_divisive for the tail of the series, beginning at # max(old_cp[-1], a step that is over 2 window_len from the end) if new_points is not None and old_cp is not None: - indexes = [c.index for c in old_cp] + change_points = old_cp[:] steps_needed = new_points/window_len + 4 max_start = len(series) - steps_needed*window_len for c in old_cp: @@ -278,35 +266,31 @@ def split(series: np.array, window_len: int = 30, max_pvalue: float = 0.001, tester = TTestSignificanceTester(max_pvalue) while start < len(series): end = min(start + window_len, len(series)) - calculator = cext_calculator - algo = EDivisive(seed=None, calculator=calculator, significance_tester=tester) - pts = algo.get_change_points(series[start:end]) - new_indexes = [p.index + start for p in pts] - new_indexes.sort() - last_new_change_point_index = next(iter(new_indexes[-1:]), 0) + algo = ChangePointDetector(significance_tester=tester, calculator=PairDistanceCalculator) + new_change_points = algo.get_change_points(series, start, end) + last_new_change_point_index = new_change_points[-1].index if new_change_points else 0 start = max(last_new_change_point_index, start + step) # incremental Otava can duplicate an old cp - for i in new_indexes: - if i not in indexes: - indexes += [i] + for cp in new_change_points: + if cp not in change_points: + change_points += [cp] - window_endpoints = [0] + indexes + [len(series)] - return [tester.change_point(i, series, window_endpoints) for i in indexes] + intervals = tester.get_intervals(change_points) + return [tester.change_point(cp.to_candidate(), series, intervals) for cp in change_points] -def compute_change_points_orig(series: np.array, max_pvalue: float = 0.001) -> List[ChangePoint]: - calculator = cext_calculator - tester = QHatPermutationsSignificanceTester(calculator, pvalue=max_pvalue, permutations=100) - algo = EDivisive(seed=None, calculator=calculator, significance_tester=tester) - pts = algo.get_change_points(series) - return pts, None +def compute_change_points_orig(series: Sequence[SupportsFloat], max_pvalue: float = 0.001, seed: Optional[int] = None) -> Tuple[PermCPList, Optional[PermCPList]]: + tester = PermutationsSignificanceTester(alpha=max_pvalue, permurations=100, calculator=PairDistanceCalculator, seed=seed) + detector = ChangePointDetector(significance_tester=tester, calculator=PairDistanceCalculator) + change_points = detector.get_change_points(series=series) + return change_points, None def compute_change_points( - series: np.array, window_len: int = 50, max_pvalue: float = 0.001, min_magnitude: float = 0.0, - new_data=None, old_weak_cp=None -) -> List[ChangePoint]: + series: Sequence[SupportsFloat], window_len: int = 50, max_pvalue: float = 0.001, min_magnitude: float = 0.0, + new_data: Optional[int] = None, old_weak_cp: Optional[GenCPList] = None +) -> Tuple[GenCPList, Optional[GenCPList]]: first_pass_pvalue = max_pvalue * 10 if max_pvalue < 0.05 else (max_pvalue * 2 if max_pvalue < 0.5 else max_pvalue) weak_change_points = split(series, window_len, first_pass_pvalue, new_points=new_data, old_cp=old_weak_cp) return merge(weak_change_points, series, max_pvalue, min_magnitude), weak_change_points diff --git a/otava/change_point_divisive/__init__.py b/otava/change_point_divisive/__init__.py new file mode 100644 index 00000000..13a83393 --- /dev/null +++ b/otava/change_point_divisive/__init__.py @@ -0,0 +1,16 @@ +# Licensed to the Apache Software Foundation (ASF) under one +# or more contributor license agreements. See the NOTICE file +# distributed with this work for additional information +# regarding copyright ownership. The ASF licenses this file +# to you under the Apache License, Version 2.0 (the +# "License"); you may not use this file except in compliance +# with the License. You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, +# software distributed under the License is distributed on an +# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY +# KIND, either express or implied. See the License for the +# specific language governing permissions and limitations +# under the License. diff --git a/otava/change_point_divisive/base.py b/otava/change_point_divisive/base.py new file mode 100644 index 00000000..1ce21e83 --- /dev/null +++ b/otava/change_point_divisive/base.py @@ -0,0 +1,109 @@ +# Licensed to the Apache Software Foundation (ASF) under one +# or more contributor license agreements. See the NOTICE file +# distributed with this work for additional information +# regarding copyright ownership. The ASF licenses this file +# to you under the Apache License, Version 2.0 (the +# "License"); you may not use this file except in compliance +# with the License. You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, +# software distributed under the License is distributed on an +# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY +# KIND, either express or implied. See the License for the +# specific language governing permissions and limitations +# under the License. + +from dataclasses import dataclass, field, fields +from typing import Generic, List, Optional, TypeVar + +from numpy.typing import NDArray + + +@dataclass +class CandidateChangePoint: + '''Candidate for a change point. The point that maximizes Q-hat function on [start:end+1] slice''' + index: int + qhat: float = field(default=0.0, kw_only=True) + + +@dataclass +class BaseStats: + '''Abstract statistics class for change point. Implementation depends on the statistical test.''' + pvalue: float + + +GenericStats = TypeVar("GenericStats", bound=BaseStats) + + +@dataclass +class ChangePoint(CandidateChangePoint, Generic[GenericStats]): + '''Change point class, defined by index and signigicance test statistic.''' + stats: GenericStats + + def __eq__(self, other): + '''Helpful to identify new Change Points during divisive algorithm''' + return isinstance(other, self.__class__) and self.index == other.index + + @classmethod + def from_candidate(cls, candidate: CandidateChangePoint, stats: GenericStats) -> 'ChangePoint[GenericStats]': + return cls( + index=candidate.index, + qhat=candidate.qhat, + stats=stats, + ) + + def to_candidate(self) -> CandidateChangePoint: + '''Downgrades Change Point to a Candidate Change Point. Used to recompute stats for Weak Change Points.''' + data = {f.name: getattr(self, f.name) for f in fields(CandidateChangePoint)} + return CandidateChangePoint(**data) + + +class SignificanceTester(Generic[GenericStats]): + '''Abstract class for significance tester''' + + def __init__(self, alpha: float): + self.alpha = alpha + + def get_intervals(self, change_points: List[ChangePoint[GenericStats]]) -> List[slice]: + '''Returns list of slices of the series''' + intervals = [ + slice( + 0 if i == 0 else change_points[i - 1].index, + None if i == len(change_points) else change_points[i].index, + ) + for i in range(len(change_points) + 1) + ] + return [interval for interval in intervals if interval.start != interval.stop] + + def is_significant(self, point: ChangePoint[GenericStats]) -> bool: + '''Compares ChangePoint to level of significance alpha''' + return point.stats.pvalue <= self.alpha + + def change_point(self, candidate: CandidateChangePoint, series: NDArray, intervals: List[slice]) -> ChangePoint[GenericStats]: + '''Computes stats for a change point candidate and wraps it into ChangePoint class''' + ... + + +class Calculator: + '''Abstract class for calculator. Calculator provides an interface to get best change point candidate''' + def __init__(self, series: NDArray): + self.series = series + + def get_next_candidate(self, intervals: List[slice]) -> Optional[CandidateChangePoint]: + '''Returns list of existing change points to find next best change point candidate.''' + candidates = [ + self.get_candidate_change_point(interval=interval) + for interval in intervals + if len(self.series[interval]) > 1 + ] + if not candidates: + return + candidate = max(candidates, key=lambda point: point.qhat) + return candidate + + def get_candidate_change_point(self, interval: slice) -> CandidateChangePoint: + '''Given start and end indexes return best candidate for a change point. + Note that start and end are indexes of the first and last element, i.e. a slice [start:end+1].''' + ... diff --git a/otava/change_point_divisive/calculator.py b/otava/change_point_divisive/calculator.py new file mode 100644 index 00000000..f424115b --- /dev/null +++ b/otava/change_point_divisive/calculator.py @@ -0,0 +1,198 @@ +# Licensed to the Apache Software Foundation (ASF) under one +# or more contributor license agreements. See the NOTICE file +# distributed with this work for additional information +# regarding copyright ownership. The ASF licenses this file +# to you under the Apache License, Version 2.0 (the +# "License"); you may not use this file except in compliance +# with the License. You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, +# software distributed under the License is distributed on an +# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY +# KIND, either express or implied. See the License for the +# specific language governing permissions and limitations +# under the License. + + +import numpy as np +from numpy.typing import NDArray + +from otava.change_point_divisive.base import Calculator, CandidateChangePoint + + +class PairDistanceCalculator(Calculator): + def __init__(self, series: NDArray, power: int = 1): + super().__init__(series) + assert 0 < power < 2, f"power={power} isn't in (0, 2)" + self.power = power + self.V = None + self.H = None + + def _calculate_distances(self): + '''Precomputes `H` and `V` functions that are used for computation of `Q` function. + See more details about `Q` function in `get_candidate_change_point` method. + See more details about the use of `H` and `V` functions in `_get_A_B_C` method. + + Let matix `distances` be a matrix of all possible L1 (Manhattan) distances between + elements of 1d array `series`. If `D(i, j) = |series[i] - series[j]|` and `N = len(series)`, + then + + | D(0, 0) D(0, 1) … D(0, N - 1) | + | D(1, 0) D(1, 1) … D(1, N - 1) | + distances = | ⋮ ⋮ ⋱ ⋮ | . + | D(N - 1, 0) D(N - 1, 1) … D(N - 1, N - 1) | + + Note that the main diagonal of the matrix is filled with 0. + + + We define functions `V` and `H` as the following (V)ertical and (H)orizontal + cummulative sums: + V(start, τ, κ) = Σ distances[start:τ, τ], + H(start, τ, κ) = Σ distances[τ, τ:κ], + for `start < τ < κ <= N`. + Note that `V(start, τ, κ) = V(start, τ)` and `H(start, τ, κ) = H(τ, κ)`. + + + Vector V contains the following values of function `V(start, τ, κ)`: + V = [V(0, 1, κ) V(0, 2, κ), … V(0, N - 1, κ)]. + `V(0, 0, κ) = 0` so they are ommited. As noted, function `V(start, τ, κ)` + does not depend on `κ`. Therefore, vector V contains all values of function + `V(0, τ, κ)`. We can easily get values of function `V` for an arbitrary + value of `start` by + V(start, τ, κ) = V(0, τ, κ) - Σ distances[0 : start, τ]. + Note: The reason not all values of `V(start, τ, κ)` are precomputed is that + we do not need them all. The values of `start` will depend on critical + points we find. Precomuting them for all possible values is a waste. + + + Matrix H contains the following values of function `H(start, τ, κ)`: + + | H(start, 0, 2) H(start, 0, 3) … H(start, 0, N) | + | 0 H(start, 1, 3) … H(start, 1, N) | + H = | ⋮ ⋮ ⋱ ⋮ | . + | 0 0 … H(start, N - 2, N) | + + `H(start, x, x) = H(start, x - 1, x) = 0` for any `x` so they are ommited. + As noted, function `H(start, τ, κ)` does not depend on `start`. Therefore, + matrix H contains all possible values of function `H`. + Note: We precomputed all values of `H(start, τ, κ)` because all of them are needed + for the very first iteration (`start=0` and `end=N-1`).''' + self.distances = np.power(np.abs(self.series[:, None] - self.series[None, :]), self.power) + triu = np.triu(self.distances, k=1)[:-1, 1:] + self.V = triu.sum(axis=0) + self.H = triu.cumsum(axis=1) + + def _get_Q_vals(self, start: int, end: int) -> NDArray: + '''Computes matrices A, B, C where all possible values of function `Q` are + given by matrix Q = A - B - C. + See more details about `Q` function in `get_candidate_change_point` method. + + For any given `start` and `end` let + Q(τ, κ) = A(start, τ, κ) - B(start, τ, κ) - C(start, τ, κ), + where `start < τ < κ <= end + 1`. (For definitions of `A`, `B`, `C` see + formula of `Q` in `get_candidate_change_point` method.) All possible values of function + `A` are given by matrix + + | A(start, start + 1, start + 2) A(start, start + 1, start + 3) … A(start, start + 1, end + 1) | + | 0 A(start, start + 2, start + 3) … A(start, start + 2, end + 1) | + A = | ⋮ ⋮ ⋱ ⋮ | . + | 0 0 … A(start, end, end + 1) | + + Matrices B and C follow the same index-to-value pattern. + + Matrices A, B, and C are used to compute values of function `Q` recursively, without + recomputing the same sums over and over again. The recursive formulas were further + transformed to closed forms, so they can be computed using numpy cummulative sum + function to take advantage of numpy vectorized operations. (Note that each column + in matrices A, B, C can be repersented through np.cumsum). The formulas use + commulative sum of functions `H` and `V`, which definitions can be found in + `_calculate_distances` method. + + A(start, τ, κ) = 2 / (κ - s) * (Σt=start,τ-1 H(start, t, κ) - Σt=start+1,τ-1 V(start, t, κ)), + + B(start, τ, κ) = 2 * (κ - τ) / (κ - start) / (τ - start - 1) * Σt=start+1,τ-1 V(start, t, κ), + + C(start, τ, κ) = 2 * (τ - start) / (κ - start) / (κ - τ - 1) * Σt=τ,κ-2 H(start, t, κ).''' + if self.V is None or self.H is None: + self._calculate_distances() + + V = self.V[start : end] - self.distances[0 : start, start + 1 : end + 1].sum(axis=0) + H = self.H[start : end, start : end] + + taus = np.arange(start + 1, end + 1)[:, None] + kappas = np.arange(start + 2, end + 2)[None, :] + + A = np.zeros((end - start, end - start)) + A_coefs = 2 / (kappas - start) + A[1:, :] = np.cumsum(V)[:-1, None] + A = A_coefs * np.triu(np.cumsum(H, axis=0) - A, k=0) + + B = np.zeros((end - start, end - start)) + B_num = 2 * (kappas - taus) + B_den = (kappas - start) * (taus - start - 1) + B_mask = np.triu(np.ones_like(B_den, dtype=bool), k=0) + B_out = np.zeros_like(B_den, dtype=float) + B_coefs = np.divide(B_num, B_den, out=B_out, where=B_mask & (B_den != 0)) + B[1:, 1:] = B_coefs[1:, 1:] * np.cumsum(V)[:-1, None] + + C = np.zeros((end - start, end - start)) + C_num = 2 * (taus - start) + C_den = (kappas - start) * (kappas - taus - 1) + C_mask = np.triu(np.ones_like(C_den, dtype=bool), k=1) + C_out = np.zeros_like(C_den, dtype=float) + C_coefs = np.divide(C_num, C_den, out=C_out, where=C_mask & (C_den != 0)) + C[:-1, 1:] = C_coefs[:-1, 1:] * np.flipud(np.cumsum(np.flipud(H[1:, 1:]), axis=0)) + + # Element of matrix `Q_{i, j}` is equal to `Q(τ, κ) = Q(i + 1, j + 2) = QQ(sequence[start : i + 1], sequence[i + 1 : j + 2])`. + # So, critical point is `τ = i + 1`. + return A - B - C + + def get_candidate_change_point(self, interval: slice) -> CandidateChangePoint: + '''For a given `slice(start, stop)` finds potential critical point in subsequence series[slice], + i.e., from index `start` to `stop - 1` inclusive. For simplicity, we'll use `end = stop - 1`. + + + The potential critical point is defined as the following. + Suppose for given `start` and `end` the pair `(τ, κ)` maximizes function + Q(τ, κ) = QQ(series[start : τ], series[τ : κ]), + where `τ` and `κ` are such that both `series[start : τ]` and `series[τ : κ]` are non-empty. + Then `τ` is a potential critical point (i.e., the first element of `series[τ : κ]`). + Note: for `series[start:τ]` and `series[τ:κ]` to be non-empty, we have + start < τ < κ <= end + 1 = len(series). + Note: start < τ => sequence[0] cannot be a critical point. + + + Function `QQ` is defined as the following: + Let `Z` be a series `[Z_{start}, Z_{start + 1}, ..., Z_{end}]`, and `X` and `Y` + be a split of `Z`, i.e., + X = [Z_{start}, Z_{start + 1}, ..., Z_a] = [X_1, X_2, ..., X_n], + Y = [Z_{a + 1}, Z_{a + 2}, ..., Z_b] = [Y_1, Y_2, ..., Y_m], + then + QQ(X, Y) = 2 / (m + n) * Σi=1,n Σj=1,m |X_i - Y_j| + - 2 * m / (m + n) / (n - 1) * Σ1<=i List[ChangePoint[GenericStats]]: + if not isinstance(series, np.ndarray): + series = np.array(series[start : end], dtype=np.float64) + if not np.issubdtype(series.dtype, np.floating): + series = series.astype(np.float64, copy=False) + + calc = self.calculator(series) + change_points = [] + + while True: + intervals = self.tester.get_intervals(change_points) + candidate = calc.get_next_candidate(intervals) + if candidate is None: + break + change_point = self.tester.change_point(candidate, series, intervals) + if self.tester.is_significant(change_point): + # TODO: Consider BST vs sorted array + change_points.append(change_point) + # Could sort by either start or end for non-intersecting intervals + change_points.sort(key=lambda point: point.index) + else: + break + + if start is not None: + for cp in change_points: + cp.index += start + + return change_points diff --git a/otava/change_point_divisive/significance_test.py b/otava/change_point_divisive/significance_test.py new file mode 100644 index 00000000..b00769b6 --- /dev/null +++ b/otava/change_point_divisive/significance_test.py @@ -0,0 +1,77 @@ +# Licensed to the Apache Software Foundation (ASF) under one +# or more contributor license agreements. See the NOTICE file +# distributed with this work for additional information +# regarding copyright ownership. The ASF licenses this file +# to you under the Apache License, Version 2.0 (the +# "License"); you may not use this file except in compliance +# with the License. You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, +# software distributed under the License is distributed on an +# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY +# KIND, either express or implied. See the License for the +# specific language governing permissions and limitations +# under the License. + +from dataclasses import dataclass +from typing import List, Optional, Type + +import numpy as np +from numpy.typing import NDArray + +from otava.change_point_divisive.base import ( + BaseStats, + Calculator, + CandidateChangePoint, + ChangePoint, + SignificanceTester, +) + + +@dataclass +class PermutationStats(BaseStats): + '''Statistics for permutation significance test''' + permuted_qhats: NDArray + extreme_qhat_perm: int + n_perm: int + + +class PermutationsSignificanceTester(SignificanceTester): + def __init__(self, alpha: float, permurations: int, calculator: Type[Calculator], seed: Optional[int]): + '''alpha - significance level + permutations - number of permutations to run to test significance + calculator - Calculator class to perform permutations (and compute new qhat value) + ''' + super().__init__(alpha) + self.permutations = permurations + self.calculator = calculator + self.seed = seed + self.rng = np.random.default_rng(seed) + + def change_point(self, candidate: CandidateChangePoint, series: NDArray, intervals: List[slice]) -> ChangePoint[PermutationStats]: + '''Perform permutation test within candidate cluster''' + + # 1. Find permutated Qhats + qhats = np.empty(self.permutations) + for i in range(self.permutations): + # Permute points within each interval (cluster) + rand_series = series.copy() + for interval in intervals: + seg = rand_series[interval] + self.rng.shuffle(seg) + rand_calc = self.calculator(rand_series) + rand_candidate = rand_calc.get_next_candidate(intervals) + qhats[i] = rand_candidate.qhat + + # 2. Estimate p-value + extreme_qhat_perm = np.sum(qhats >= candidate.qhat) + pval = extreme_qhat_perm / (self.permutations + 1) + stats = PermutationStats( + pvalue=pval, + permuted_qhats=qhats, + extreme_qhat_perm=extreme_qhat_perm, + n_perm=self.permutations + ) + return ChangePoint.from_candidate(candidate, stats) diff --git a/otava/series.py b/otava/series.py index 69599625..a3e0a784 100644 --- a/otava/series.py +++ b/otava/series.py @@ -24,12 +24,13 @@ import numpy as np from otava.analysis import ( - ComparativeStats, TTestSignificanceTester, + TTestStats, compute_change_points, compute_change_points_orig, fill_missing, ) +from otava.change_point_divisive.base import ChangePoint as _ChangePoint @dataclass @@ -74,13 +75,10 @@ def to_json(self): @dataclass -class ChangePoint: +class ChangePoint(_ChangePoint[TTestStats]): """A change-point for a single metric""" - metric: str - index: int time: int - stats: ComparativeStats def forward_change_percent(self) -> float: return self.stats.forward_rel_change() * 100.0 @@ -490,8 +488,13 @@ def from_json(cls, analyzed_json): for metric, change_points in analyzed_json["change_points"].items(): new_list = list() for cp in change_points: - stat = ComparativeStats(cp["mean_before"], cp["mean_after"], cp["stddev_before"], - cp["stddev_after"], cp["pvalue"]) + stat = TTestStats( + mean_1=cp["mean_before"], + mean_2=cp["mean_after"], + std_1=cp["stddev_before"], + std_2=cp["stddev_after"], + pvalue=cp["pvalue"], + ) new_list.append( ChangePoint( index=cp["index"], time=cp["time"], metric=cp["metric"], stats=stat @@ -503,8 +506,13 @@ def from_json(cls, analyzed_json): for metric, change_points in analyzed_json.get("weak_change_points", {}).items(): new_list = list() for cp in change_points: - stat = ComparativeStats(cp["mean_before"], cp["mean_after"], cp["stddev_before"], - cp["stddev_after"], cp["pvalue"]) + stat = TTestStats( + mean_1=cp["mean_before"], + mean_2=cp["mean_after"], + std_1=cp["stddev_before"], + std_2=cp["stddev_after"], + pvalue=cp["pvalue"], + ) new_list.append( ChangePoint( index=cp["index"], time=cp["time"], metric=cp["metric"], stats=stat @@ -528,7 +536,7 @@ class SeriesComparison: series_2: AnalyzedSeries index_1: int index_2: int - stats: Dict[str, ComparativeStats] # keys: metric name + stats: Dict[str, TTestStats] # keys: metric name def compare( diff --git a/pyproject.toml b/pyproject.toml index 24e3b36e..fc78463f 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -38,7 +38,7 @@ dependencies = [ "dateparser>=1.0.0", "numpy==1.24.*", "python-dateutil>=2.8.1", - "signal-processing-algorithms==1.3.5", + "scipy==1.10.*", "ruamel.yaml==0.17.21", "requests>=2.25.1", "pystache>=0.6.0", diff --git a/tests/analysis_test.py b/tests/analysis_test.py index 2e1ed75b..5d02716e 100644 --- a/tests/analysis_test.py +++ b/tests/analysis_test.py @@ -16,9 +16,14 @@ # under the License. import numpy as np -from signal_processing_algorithms.e_divisive.change_points import EDivisiveChangePoint -from otava.analysis import TTestSignificanceTester, compute_change_points, fill_missing +from otava.analysis import ( + TTestSignificanceTester, + compute_change_points, + compute_change_points_orig, + fill_missing, +) +from otava.change_point_divisive.base import CandidateChangePoint def test_fill_missing(): @@ -61,15 +66,45 @@ def test_single_series(): assert indexes == [10] +def test_single_series_original(): + series = [ + 1.02, + 0.95, + 0.99, + 1.00, + 1.12, + 1.00, + 1.01, + 0.98, + 1.01, + 0.96, + 0.50, + 0.51, + 0.48, + 0.48, + 0.55, + 0.50, + 0.49, + 0.51, + 0.50, + 0.49, + ] + cps, _ = compute_change_points_orig(series, max_pvalue=0.0001, seed=1) + indexes = [c.index for c in cps] + assert indexes == [10] + + def test_significance_tester(): tester = TTestSignificanceTester(0.001) series = np.array([1.00, 1.02, 1.05, 0.95, 0.98, 1.00, 1.02, 1.05, 0.95, 0.98]) - cp = tester.change_point(5, series, [0, len(series)]) - assert not tester.is_significant(EDivisiveChangePoint(5), series, [0, len(series)]) + candidate = CandidateChangePoint(index=5, qhat=0.) + cp = tester.change_point(candidate, series, intervals=[slice(None, None)]) + assert not tester.is_significant(cp) assert 0.99 < cp.stats.pvalue < 1.01 series = np.array([1.00, 1.02, 1.05, 0.95, 0.98, 0.80, 0.82, 0.85, 0.79, 0.77]) - cp = tester.change_point(5, series, [0, len(series)]) - assert tester.is_significant(EDivisiveChangePoint(5), series, [0, len(series)]) + candidate = CandidateChangePoint(index=5, qhat=0.) + cp = tester.change_point(candidate, series, intervals=[slice(None, None)]) + assert tester.is_significant(cp) assert 0.00 < cp.stats.pvalue < 0.001 diff --git a/tests/change_point_divisive_test.py b/tests/change_point_divisive_test.py new file mode 100644 index 00000000..24335db1 --- /dev/null +++ b/tests/change_point_divisive_test.py @@ -0,0 +1,122 @@ +# Licensed to the Apache Software Foundation (ASF) under one +# or more contributor license agreements. See the NOTICE file +# distributed with this work for additional information +# regarding copyright ownership. The ASF licenses this file +# to you under the Apache License, Version 2.0 (the +# "License"); you may not use this file except in compliance +# with the License. You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, +# software distributed under the License is distributed on an +# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY +# KIND, either express or implied. See the License for the +# specific language governing permissions and limitations +# under the License. + +import numpy as np + +from otava.analysis import TTestSignificanceTester +from otava.change_point_divisive.calculator import PairDistanceCalculator +from otava.change_point_divisive.detector import ChangePointDetector +from otava.change_point_divisive.significance_test import PermutationsSignificanceTester + +SEQUENCE = np.array([ + 0.3, 2.4, 1.5, -0.9, -0.5, + 99.7, 98.3, 99.1, + 149.0, 149.7, 149.5, 149.1, 148.8, 150.0, +]) +CHANGE_POINTS_INDS = [5, 8] + + +def compute_Q_and_candidate_slow(sequence): + N = len(sequence) + Q = np.zeros((N - 1, N - 1)) + Q_max = 0 + candidate_ind = None + for tau in range(1, N): + for kappa in range(tau + 1, N + 1): + X, Y = sequence[: tau], sequence[tau : kappa] + n, m = len(X), len(Y) + + A = 0 + for x in X: + for y in Y: + A += abs(x - y) + A *= 2 / (m + n) + + B = 0 + for i in range(n - 1): + for k in range(i + 1, n): + B += abs(X[i] - X[k]) + B *= 2 * m / (m + n) / (n - 1) if n > 1 else 0 + + C = 0 + for j in range(m - 1): + for k in range(j, m): + C += abs(Y[j] - Y[k]) + C *= 2 * n / (m + n) / (m - 1) if m > 1 else 0 + + Q[tau - 1, kappa - 2] = A - B - C + # TODO: Figure out why tests are failing with the proper solution. + # See otava/change_point_divisive/calculator.py for details + # + # ============== Implementation from paper ====================== + # if Q[tau - 1, kappa - 2] > Q_max: + # + # ============== Current implementation ========================= + if kappa == N and Q[tau - 1, kappa - 2] > Q_max: + Q_max = Q[tau - 1, kappa - 2] + candidate_ind = tau + + return Q, Q_max, candidate_ind + + +def test_calculator_candidate(): + sequence = SEQUENCE.copy() + calc = PairDistanceCalculator(sequence) + Q = calc._get_Q_vals(start=0, end=len(sequence) - 1) + + test_Q, test_Q_max, test_candidate_ind = compute_Q_and_candidate_slow(sequence) + assert np.allclose(test_Q, Q) + + whole_interval = slice(None, None) + candidate = calc.get_candidate_change_point(whole_interval) + assert np.allclose(test_Q_max, candidate.qhat) + assert test_candidate_ind == candidate.index + + +def test_permutation_calculation(): + sequence = SEQUENCE.copy() + calc = PairDistanceCalculator(sequence) + whole_interval = slice(None, None) + candidate = calc.get_candidate_change_point(whole_interval) + + seed = 1 + st = PermutationsSignificanceTester(alpha=0.05, permurations=1, calculator=PairDistanceCalculator, seed=seed) + change_point = st.change_point(candidate=candidate, series=sequence, intervals=[whole_interval]) + + test_rng = np.random.default_rng(seed) + rand_sequence = sequence.copy() + test_rng.shuffle(rand_sequence) + _, rand_Q_max, rand_candidate_ind = compute_Q_and_candidate_slow(rand_sequence) + assert int(rand_Q_max >= candidate.qhat) == change_point.stats.extreme_qhat_perm + assert np.allclose(rand_Q_max, change_point.stats.permuted_qhats[0]) + + +def test_permutation_test(): + seed = 1 + sequence = SEQUENCE.copy() + st = PermutationsSignificanceTester(alpha=0.01, permurations=100, calculator=PairDistanceCalculator, seed=seed) + cpd = ChangePointDetector(significance_tester=st, calculator=PairDistanceCalculator) + cps = cpd.get_change_points(series=sequence) + assert [cp.index for cp in cps] == CHANGE_POINTS_INDS + + +def test_ttest(): + sequence = SEQUENCE.copy() + st = TTestSignificanceTester(alpha=0.01) + cpd = ChangePointDetector(significance_tester=st, calculator=PairDistanceCalculator) + cps = cpd.get_change_points(series=sequence) + assert [cp.index for cp in cps] == CHANGE_POINTS_INDS diff --git a/uv.lock b/uv.lock index a5beddfc..d80ca356 100644 --- a/uv.lock +++ b/uv.lock @@ -10,21 +10,22 @@ resolution-markers = [ [[package]] name = "apache-otava" -version = "0.6.1" +version = "0.7.0" source = { editable = "." } dependencies = [ { name = "configargparse" }, { name = "dateparser" }, { name = "google-cloud-bigquery", version = "3.30.0", source = { registry = 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+++++++++--------- 3 files changed, 12 insertions(+), 28 deletions(-) diff --git a/otava/change_point_divisive/calculator.py b/otava/change_point_divisive/calculator.py index f424115b..8f3835f7 100644 --- a/otava/change_point_divisive/calculator.py +++ b/otava/change_point_divisive/calculator.py @@ -185,14 +185,5 @@ def get_candidate_change_point(self, interval: slice) -> CandidateChangePoint: assert start < end, f"start={start} must be less than end={end}" Q = self._get_Q_vals(start, end) - # TODO: Figure out why tests are failing with the proper solution. - # Limiting κ=interval.stop solves the issue. However, this isn't a correct approach - # as specifically discussed in https://arxiv.org/abs/1306.4933 . Specifically, κ should vary. - # - # ============== Implementation from paper ====================== - # i, j = np.unravel_index(np.argmax(Q), Q.shape) - # return CandidateChangePoint(index=i + 1 + start, qhat=Q[i][j]) - # - # ============== Current implementation ========================= - i = np.argmax(Q[:, -1]) - return CandidateChangePoint(index=i + 1 + start, qhat=Q[i, -1]) + i, j = np.unravel_index(np.argmax(Q), Q.shape) + return CandidateChangePoint(index=i + 1 + start, qhat=Q[i][j]) diff --git a/tests/change_point_divisive_test.py b/tests/change_point_divisive_test.py index 24335db1..755da9f6 100644 --- a/tests/change_point_divisive_test.py +++ b/tests/change_point_divisive_test.py @@ -59,14 +59,7 @@ def compute_Q_and_candidate_slow(sequence): C *= 2 * n / (m + n) / (m - 1) if m > 1 else 0 Q[tau - 1, kappa - 2] = A - B - C - # TODO: Figure out why tests are failing with the proper solution. - # See otava/change_point_divisive/calculator.py for details - # - # ============== Implementation from paper ====================== - # if Q[tau - 1, kappa - 2] > Q_max: - # - # ============== Current implementation ========================= - if kappa == N and Q[tau - 1, kappa - 2] > Q_max: + if Q[tau - 1, kappa - 2] > Q_max: Q_max = Q[tau - 1, kappa - 2] candidate_ind = tau diff --git a/tests/tigerbeetle_test.py b/tests/tigerbeetle_test.py index 8c50a94f..b7971075 100644 --- a/tests/tigerbeetle_test.py +++ b/tests/tigerbeetle_test.py @@ -40,63 +40,63 @@ def test_tb_old_defaults(): series = _get_series() cps, weak_cps = compute_change_points(series, window_len=30, max_pvalue=0.01, min_magnitude=0.05) indexes = [c.index for c in cps] - assert indexes == [27, 71] + assert indexes == [15, 71] def test_tb_old_defaults_p05(): series = _get_series() cps, weak_cps = compute_change_points(series, window_len=30, max_pvalue=0.05, min_magnitude=0.05) indexes = [c.index for c in cps] - assert indexes == [16, 71] + assert indexes == [15, 71] def test_tb_old_defaults_p1(): series = _get_series() cps, weak_cps = compute_change_points(series, window_len=30, max_pvalue=0.1, min_magnitude=0.05) indexes = [c.index for c in cps] - assert indexes == [16, 71] + assert indexes == [10, 11, 15, 71, 363] def test_tb_old_defaults_p2(): series = _get_series() cps, weak_cps = compute_change_points(series, window_len=30, max_pvalue=0.2, min_magnitude=0.05) indexes = [c.index for c in cps] - assert indexes == [16, 71] + assert indexes == [10, 11, 15, 71] def test_tb_magnitude0_p2(): series = _get_series() cps, weak_cps = compute_change_points(series, window_len=30, max_pvalue=0.2, min_magnitude=0.0) indexes = [c.index for c in cps] - assert indexes == [16, 27, 29, 56, 58, 60, 61, 69, 71, 82, 83, 91, 95, 108, 114, 116, 117, 131, 138, 142, 148, 165, 167, 178, 187, 189, 190, 192, 206, 212, 213, 220, 241, 243, 244, 246, 247, 249, 260, 266, 268, 272, 274, 275, 278, 282, 284, 288, 295, 297, 311, 314, 325, 330, 347, 351] + assert indexes == [3, 6, 7, 10, 11, 13, 15, 16, 28, 29, 35, 37, 39, 41, 44, 48, 49, 56, 58, 61, 65, 66, 69, 71, 74, 76, 82, 95, 108, 117, 125, 126, 129, 131, 136, 137, 142, 148, 165, 169, 187, 190, 192, 197, 200, 212, 220, 241, 243, 246, 247, 249, 250, 260, 265, 266, 268, 278, 282, 288, 305, 306, 325, 330, 337, 338, 340, 347, 349, 363] def test_tb_magnitude0_p1(): series = _get_series() cps, weak_cps = compute_change_points(series, window_len=30, max_pvalue=0.1, min_magnitude=0.0) indexes = [c.index for c in cps] - assert indexes == [16, 27, 29, 56, 58, 61, 71, 82, 95, 113, 116, 117, 131, 138, 142, 148, 157, 165, 167, 178, 187, 189, 192, 206, 212, 213, 220, 246, 247, 249, 260, 266, 268, 272, 278, 282, 311, 312, 325, 330, 347, 351] + assert indexes == [3, 6, 10, 11, 15, 16, 28, 29, 35, 37, 39, 41, 44, 48, 49, 61, 71, 95, 117, 131, 142, 148, 165, 169, 192, 206, 212, 260, 265, 268, 278, 282, 288, 305, 363] def test_tb_magnitude0_p01(): series = _get_series() cps, weak_cps = compute_change_points(series, window_len=30, max_pvalue=0.01, min_magnitude=0.0) indexes = [c.index for c in cps] - assert indexes == [27, 61, 71, 82, 95, 131, 142, 148, 192, 212, 249, 260, 265, 353] + assert indexes == [15, 26, 61, 71, 95, 117, 131, 142, 148, 165, 169, 192, 212, 260] def test_tb_magnitude0_p001(): series = _get_series() cps, weak_cps = compute_change_points(series, window_len=30, max_pvalue=0.001, min_magnitude=0.0) indexes = [c.index for c in cps] - assert indexes == [71, 95, 113, 131, 142, 148, 192, 212, 260] + assert indexes == [15, 61, 71, 95, 117, 131, 142, 148, 192, 212, 260] def test_tb_magnitude0_p0001(): series = _get_series() cps, weak_cps = compute_change_points(series, window_len=30, max_pvalue=0.0001, min_magnitude=0.0) indexes = [c.index for c in cps] - assert indexes == [71, 95, 113, 131, 192, 212] + assert indexes == [71, 95, 117, 131, 142, 148, 192, 212] def test_tb_magnitude0_p00001(): From f8f81d873c23e7e8d7326360d73cbe4452f88e4c Mon Sep 17 00:00:00 2001 From: Denis Shchepakin <1842450+Sowiks@users.noreply.github.com> Date: Wed, 12 Nov 2025 00:24:08 -0800 Subject: [PATCH 3/4] Support for Python 3.8 and 3.9 --- otava/analysis.py | 8 ++++---- otava/change_point_divisive/base.py | 4 ++-- otava/series.py | 8 ++++---- 3 files changed, 10 insertions(+), 10 deletions(-) diff --git a/otava/analysis.py b/otava/analysis.py index 8221bea9..bfb2524f 100644 --- a/otava/analysis.py +++ b/otava/analysis.py @@ -16,7 +16,7 @@ # under the License. from dataclasses import dataclass -from typing import List, Optional, Sequence, SupportsFloat, Tuple, TypeAlias +from typing import List, Optional, Sequence, SupportsFloat, Tuple import numpy as np from scipy.stats import ttest_ind_from_stats @@ -97,11 +97,11 @@ def to_json(self): # Generic Change Point List -GenCPList : TypeAlias = List[ChangePoint[GenericStats]] +GenCPList = List[ChangePoint[GenericStats]] # Permutation Change Point List -PermCPList : TypeAlias = List[ChangePoint[PermutationStats]] +PermCPList = List[ChangePoint[PermutationStats]] # T-test Change Point List -TtestCPList : TypeAlias = List[ChangePoint[TTestStats]] +TtestCPList = List[ChangePoint[TTestStats]] class TTestSignificanceTester(SignificanceTester): diff --git a/otava/change_point_divisive/base.py b/otava/change_point_divisive/base.py index 1ce21e83..21812fca 100644 --- a/otava/change_point_divisive/base.py +++ b/otava/change_point_divisive/base.py @@ -15,7 +15,7 @@ # specific language governing permissions and limitations # under the License. -from dataclasses import dataclass, field, fields +from dataclasses import dataclass, fields from typing import Generic, List, Optional, TypeVar from numpy.typing import NDArray @@ -25,7 +25,7 @@ class CandidateChangePoint: '''Candidate for a change point. The point that maximizes Q-hat function on [start:end+1] slice''' index: int - qhat: float = field(default=0.0, kw_only=True) + qhat: float @dataclass diff --git a/otava/series.py b/otava/series.py index a3e0a784..5114eab9 100644 --- a/otava/series.py +++ b/otava/series.py @@ -262,13 +262,13 @@ def __compute_change_points( for c in weak_cps: weak_change_points[metric].append( ChangePoint( - index=c.index, time=series.time[c.index], metric=metric, stats=c.stats + index=c.index, qhat=0.0, time=series.time[c.index], metric=metric, stats=c.stats ) ) for c in change_points: result[metric].append( ChangePoint( - index=c.index, time=series.time[c.index], metric=metric, stats=c.stats + index=c.index, qhat=0.0, time=series.time[c.index], metric=metric, stats=c.stats ) ) # If you got an exception and are wondering about the next row... @@ -385,14 +385,14 @@ def append(self, time, new_data, attributes): for c in change_points: result[metric].append( ChangePoint( - index=c.index, time=self.__series.time[c.index], metric=metric, stats=c.stats + index=c.index, qhat=0.0, time=self.__series.time[c.index], metric=metric, stats=c.stats ) ) weak_change_points[metric] = [] for c in weak_cps: weak_change_points[metric].append( ChangePoint( - index=c.index, time=self.__series.time[c.index], metric=metric, stats=c.stats + index=c.index, qhat=0.0, time=self.__series.time[c.index], metric=metric, stats=c.stats ) ) fill_missing(self.__series.data[metric]) From 6aad9db88ae8a8263b51959955e5df52c079ee0a Mon Sep 17 00:00:00 2001 From: Denis Shchepakin <1842450+Sowiks@users.noreply.github.com> Date: Sat, 22 Nov 2025 20:55:08 -0800 Subject: [PATCH 4/4] Renamed variables, fixed typos, updated comments. Switched indexing to match slice object notations. --- otava/analysis.py | 78 +++++++++++++------ otava/change_point_divisive/base.py | 9 ++- otava/change_point_divisive/calculator.py | 55 ++++++------- otava/change_point_divisive/detector.py | 1 + .../significance_test.py | 8 +- tests/change_point_divisive_test.py | 8 +- 6 files changed, 95 insertions(+), 64 deletions(-) diff --git a/otava/analysis.py b/otava/analysis.py index bfb2524f..74f61444 100644 --- a/otava/analysis.py +++ b/otava/analysis.py @@ -134,11 +134,11 @@ def change_point( """ Computes properties of the change point if the Candidate Change Point based on the provided intervals. - The method works for two cases: - 1. Divisive algorithm. + The method works in both steps of the algorithm: + 1. Split step: if the candidate is a new potential change point, i.e., its index is inside any interval, then we split the interval by the candidate's index to get left and right subseries. - 2. Merge step in t-test algorithm. + 2. Merge step: if the candidate is an existing change point, i.e., it matches the end of two intervals, then it's a potential weak change point, and we don't need to split the intervals anymore (just take both intervals as left and right subseries). @@ -146,10 +146,19 @@ def change_point( """ for i, interval in enumerate(intervals): if interval.stop == candidate.index: + # Merge step left_interval = interval right_interval = intervals[i + 1] break elif (interval.start is None or interval.start < candidate.index) and (interval.stop is None or candidate.index < interval.stop): + # Split step + # Note: handles slices with omitted indexes: + # + # array[0 : i] == array[:i] == array[slice(None, i)] == array[slice(0, i)], + # i.e., interval.start == None and interval.start == 0 are equivalent. + # + # array[i: len(array)] == array[i:] == array[slice(i, None)] == array[slice(i, len(array))], + # i.e., interval.stop == None and interval.stop == len(array) are equivalent. left_interval = slice(interval.start, candidate.index) right_interval = slice(candidate.index, interval.stop) break @@ -183,9 +192,8 @@ def merge( change_points: TtestCPList, series: Sequence[SupportsFloat], max_pvalue: float, min_magnitude: float ) -> TtestCPList: """ - Removes weak change points recursively going bottom-up - until we get only high-quality change points - that meet the P-value and rel_change criteria. + Merge step of the change point detection process from "Hunter: Using Change Point Detection + to Hunt for Performance Regressions" by Fleming et al. (https://doi.org/10.1145/3578244.3583719). Parameters: :param max_pvalue: maximum accepted pvalue @@ -227,30 +235,16 @@ def recompute(index: int): def split(series: Sequence[SupportsFloat], window_len: int = 30, max_pvalue: float = 0.001, new_points: Optional[int] = None, old_cp: Optional[TtestCPList] = None) -> TtestCPList: """ - Finds change points by splitting the series top-down. - - Internally it uses the EDivisive algorithm from mongodb-signal-processing - that recursively splits the series in a way to maximize some measure of - dissimilarity (denoted qhat) between the chunks. - Splitting happens as long as the dissimilarity is statistically significant. - - Unfortunately this algorithms has a few downsides: - - the complexity is O(n^2), where n is the length of the series - - if there are too many change points and too much data, the change points in the middle - of the series may be missed - - This function tries to address these issues by invoking EDivisive on smaller - chunks (windows) of the input data instead of the full series and then merging the results. - Each window should be large enough to contain enough points to detect a change-point. - Consecutive windows overlap so that we won't miss changes happening between them. + Split step of the change point detection process from "Hunter: Using Change Point Detection + to Hunt for Performance Regressions" by Fleming et al. (https://doi.org/10.1145/3578244.3583719). """ - assert "Window length must be at least 2", window_len >= 2 + assert window_len >= 2, "Window length must be at least 2" start = 0 step = int(window_len / 2) change_points = [] # N new_points are appended to the end of series. Typically N=1. # old_cp are the weak change points from before new points were added. - # We now just compute e-e_divisive for the tail of the series, beginning at + # We now just identify change points in the tail of the series, beginning at # max(old_cp[-1], a step that is over 2 window_len from the end) if new_points is not None and old_cp is not None: change_points = old_cp[:] @@ -265,6 +259,7 @@ def split(series: Sequence[SupportsFloat], window_len: int = 30, max_pvalue: flo tester = TTestSignificanceTester(max_pvalue) while start < len(series): + # Sliding window series[start : end] end = min(start + window_len, len(series)) algo = ChangePointDetector(significance_tester=tester, calculator=PairDistanceCalculator) @@ -281,7 +276,14 @@ def split(series: Sequence[SupportsFloat], window_len: int = 30, max_pvalue: flo def compute_change_points_orig(series: Sequence[SupportsFloat], max_pvalue: float = 0.001, seed: Optional[int] = None) -> Tuple[PermCPList, Optional[PermCPList]]: - tester = PermutationsSignificanceTester(alpha=max_pvalue, permurations=100, calculator=PairDistanceCalculator, seed=seed) + """ + The original algorithm presented in "A Nonparametric Approach for Multiple Change Point + Analysis of Multivariate Data" by Matteson and James (https://doi.org/10.48550/arXiv.1306.4933). + + The algorithm recursively splits the series in a way to maximize some measure of dissimilarity (denoted qhat) + between the chunks. Splitting happens as long as the dissimilarity is statistically significant. + """ + tester = PermutationsSignificanceTester(max_pvalue=max_pvalue, permutations=100, calculator=PairDistanceCalculator, seed=seed) detector = ChangePointDetector(significance_tester=tester, calculator=PairDistanceCalculator) change_points = detector.get_change_points(series=series) return change_points, None @@ -291,6 +293,32 @@ def compute_change_points( series: Sequence[SupportsFloat], window_len: int = 50, max_pvalue: float = 0.001, min_magnitude: float = 0.0, new_data: Optional[int] = None, old_weak_cp: Optional[GenCPList] = None ) -> Tuple[GenCPList, Optional[GenCPList]]: + """ + Change Point detection algorithm described in "Hunter: Using Change Point Detection to Hunt for Performance + Regressions" by Fleming et al. (https://doi.org/10.1145/3578244.3583719). + + The algorithm consist of two steps: + 1. Split step: + - splitting a series into subseries via sliding windows + + - applying original change point detection algorithm to each window (https://doi.org/10.48550/arXiv.1306.4933) + with first-pass significance threshold max_pvalue (see clarification regarding this threshold below) + + - make a set union operation over all detected change points, so-called weak change points. They are "weak" + change points because the algorithm uses modified (relaxed) max_pvalue for this step. In the current + implementation the first-pass significance threshold is 10x of the original max_pvalue. For example, if we want + to detect all change points at significance threshold 0.001, a threshold of 0.01 will be used at this step. Since + it's a higher threshold for p-values, the algorithm will find more points. However, these points are just POTENTIAL + change points, because some of them are significant at 0.01 but not at 0.001. In statistical terms, the evidence + that they are change points is weak (only 0.01 compared to 0.001). Hence, the term "weak" change points. They will + be filtered down to the final change points (with correct significance threshold) at the next step (Merge step) + of the algorithm. For the reasoning on why change points cannot be computed right away (and the need for + [weak change points -> change points] process) read Fleming et al. paper. + + 2. Merge step: + - Filters out weak change points recursively going bottom-up, keeping only high-quality change points, i.e., the + ones that meet either a p-value threshold criteria or relative magnitude change criteria. + """ first_pass_pvalue = max_pvalue * 10 if max_pvalue < 0.05 else (max_pvalue * 2 if max_pvalue < 0.5 else max_pvalue) weak_change_points = split(series, window_len, first_pass_pvalue, new_points=new_data, old_cp=old_weak_cp) return merge(weak_change_points, series, max_pvalue, min_magnitude), weak_change_points diff --git a/otava/change_point_divisive/base.py b/otava/change_point_divisive/base.py index 21812fca..fbbf91b5 100644 --- a/otava/change_point_divisive/base.py +++ b/otava/change_point_divisive/base.py @@ -34,6 +34,7 @@ class BaseStats: pvalue: float +# Abstract variable type for statistics, corresponds to BaseStats class and its subclasses. GenericStats = TypeVar("GenericStats", bound=BaseStats) @@ -63,8 +64,8 @@ def to_candidate(self) -> CandidateChangePoint: class SignificanceTester(Generic[GenericStats]): '''Abstract class for significance tester''' - def __init__(self, alpha: float): - self.alpha = alpha + def __init__(self, max_pvalue: float): + self.max_pvalue = max_pvalue def get_intervals(self, change_points: List[ChangePoint[GenericStats]]) -> List[slice]: '''Returns list of slices of the series''' @@ -78,8 +79,8 @@ def get_intervals(self, change_points: List[ChangePoint[GenericStats]]) -> List[ return [interval for interval in intervals if interval.start != interval.stop] def is_significant(self, point: ChangePoint[GenericStats]) -> bool: - '''Compares ChangePoint to level of significance alpha''' - return point.stats.pvalue <= self.alpha + '''Compares ChangePoint to level of significance max_pvalue''' + return point.stats.pvalue <= self.max_pvalue def change_point(self, candidate: CandidateChangePoint, series: NDArray, intervals: List[slice]) -> ChangePoint[GenericStats]: '''Computes stats for a change point candidate and wraps it into ChangePoint class''' diff --git a/otava/change_point_divisive/calculator.py b/otava/change_point_divisive/calculator.py index 8f3835f7..cfc2d88d 100644 --- a/otava/change_point_divisive/calculator.py +++ b/otava/change_point_divisive/calculator.py @@ -23,19 +23,19 @@ class PairDistanceCalculator(Calculator): - def __init__(self, series: NDArray, power: int = 1): + def __init__(self, series: NDArray, power: float = 1.): super().__init__(series) assert 0 < power < 2, f"power={power} isn't in (0, 2)" self.power = power self.V = None self.H = None - def _calculate_distances(self): + def _calculate_pairwise_differences(self): '''Precomputes `H` and `V` functions that are used for computation of `Q` function. See more details about `Q` function in `get_candidate_change_point` method. See more details about the use of `H` and `V` functions in `_get_A_B_C` method. - Let matix `distances` be a matrix of all possible L1 (Manhattan) distances between + Let matrix `distances` be a matrix of all possible L1 (Manhattan) distances between elements of 1d array `series`. If `D(i, j) = |series[i] - series[j]|` and `N = len(series)`, then @@ -78,7 +78,7 @@ def _calculate_distances(self): As noted, function `H(start, τ, κ)` does not depend on `start`. Therefore, matrix H contains all possible values of function `H`. Note: We precomputed all values of `H(start, τ, κ)` because all of them are needed - for the very first iteration (`start=0` and `end=N-1`).''' + for the very first iteration (`start=0` and `end=N`).''' self.distances = np.power(np.abs(self.series[:, None] - self.series[None, :]), self.power) triu = np.triu(self.distances, k=1)[:-1, 1:] self.V = triu.sum(axis=0) @@ -91,14 +91,14 @@ def _get_Q_vals(self, start: int, end: int) -> NDArray: For any given `start` and `end` let Q(τ, κ) = A(start, τ, κ) - B(start, τ, κ) - C(start, τ, κ), - where `start < τ < κ <= end + 1`. (For definitions of `A`, `B`, `C` see + where `start < τ < κ <= end`. (For definitions of `A`, `B`, `C` see formula of `Q` in `get_candidate_change_point` method.) All possible values of function `A` are given by matrix - | A(start, start + 1, start + 2) A(start, start + 1, start + 3) … A(start, start + 1, end + 1) | - | 0 A(start, start + 2, start + 3) … A(start, start + 2, end + 1) | - A = | ⋮ ⋮ ⋱ ⋮ | . - | 0 0 … A(start, end, end + 1) | + | A(start, start + 1, start + 2) A(start, start + 1, start + 3) … A(start, start + 1, end) | + | 0 A(start, start + 2, start + 3) … A(start, start + 2, end) | + A = | ⋮ ⋮ ⋱ ⋮ | . + | 0 0 … A(start, end - 1, end) | Matrices B and C follow the same index-to-value pattern. @@ -108,7 +108,7 @@ def _get_Q_vals(self, start: int, end: int) -> NDArray: function to take advantage of numpy vectorized operations. (Note that each column in matrices A, B, C can be repersented through np.cumsum). The formulas use commulative sum of functions `H` and `V`, which definitions can be found in - `_calculate_distances` method. + `_calculate_pairwise_differences` method. A(start, τ, κ) = 2 / (κ - s) * (Σt=start,τ-1 H(start, t, κ) - Σt=start+1,τ-1 V(start, t, κ)), @@ -116,20 +116,20 @@ def _get_Q_vals(self, start: int, end: int) -> NDArray: C(start, τ, κ) = 2 * (τ - start) / (κ - start) / (κ - τ - 1) * Σt=τ,κ-2 H(start, t, κ).''' if self.V is None or self.H is None: - self._calculate_distances() + self._calculate_pairwise_differences() - V = self.V[start : end] - self.distances[0 : start, start + 1 : end + 1].sum(axis=0) - H = self.H[start : end, start : end] + V = self.V[start : end - 1] - self.distances[0 : start, start + 1 : end].sum(axis=0) + H = self.H[start : end - 1, start : end - 1] - taus = np.arange(start + 1, end + 1)[:, None] - kappas = np.arange(start + 2, end + 2)[None, :] + taus = np.arange(start + 1, end)[:, None] + kappas = np.arange(start + 2, end + 1)[None, :] - A = np.zeros((end - start, end - start)) + A = np.zeros((end - 1 - start, end - 1 - start)) A_coefs = 2 / (kappas - start) A[1:, :] = np.cumsum(V)[:-1, None] A = A_coefs * np.triu(np.cumsum(H, axis=0) - A, k=0) - B = np.zeros((end - start, end - start)) + B = np.zeros((end - 1 - start, end - 1 - start)) B_num = 2 * (kappas - taus) B_den = (kappas - start) * (taus - start - 1) B_mask = np.triu(np.ones_like(B_den, dtype=bool), k=0) @@ -137,7 +137,7 @@ def _get_Q_vals(self, start: int, end: int) -> NDArray: B_coefs = np.divide(B_num, B_den, out=B_out, where=B_mask & (B_den != 0)) B[1:, 1:] = B_coefs[1:, 1:] * np.cumsum(V)[:-1, None] - C = np.zeros((end - start, end - start)) + C = np.zeros((end - 1 - start, end - 1 - start)) C_num = 2 * (taus - start) C_den = (kappas - start) * (kappas - taus - 1) C_mask = np.triu(np.ones_like(C_den, dtype=bool), k=1) @@ -150,8 +150,8 @@ def _get_Q_vals(self, start: int, end: int) -> NDArray: return A - B - C def get_candidate_change_point(self, interval: slice) -> CandidateChangePoint: - '''For a given `slice(start, stop)` finds potential critical point in subsequence series[slice], - i.e., from index `start` to `stop - 1` inclusive. For simplicity, we'll use `end = stop - 1`. + '''For a given `slice(start, end)` finds potential critical point in subsequence series[slice], + i.e., from index `start` to `end - 1` inclusive. The potential critical point is defined as the following. @@ -160,29 +160,30 @@ def get_candidate_change_point(self, interval: slice) -> CandidateChangePoint: where `τ` and `κ` are such that both `series[start : τ]` and `series[τ : κ]` are non-empty. Then `τ` is a potential critical point (i.e., the first element of `series[τ : κ]`). Note: for `series[start:τ]` and `series[τ:κ]` to be non-empty, we have - start < τ < κ <= end + 1 = len(series). + start < τ < κ <= end = len(series). Note: start < τ => sequence[0] cannot be a critical point. Function `QQ` is defined as the following: Let `Z` be a series `[Z_{start}, Z_{start + 1}, ..., Z_{end}]`, and `X` and `Y` be a split of `Z`, i.e., - X = [Z_{start}, Z_{start + 1}, ..., Z_a] = [X_1, X_2, ..., X_n], - Y = [Z_{a + 1}, Z_{a + 2}, ..., Z_b] = [Y_1, Y_2, ..., Y_m], - then + X = [Z_{start}, Z_{start + 1}, ..., Z_{a - 1}] = [X_1, X_2, ..., X_n], + Y = [Z_{a}, Z_{a + 1}, ..., Z_{b - 1}] = [Y_1, Y_2, ..., Y_m], + where `start < a - 1 < b - 1 <= end`. + Then QQ(X, Y) = 2 / (m + n) * Σi=1,n Σj=1,m |X_i - Y_j| - 2 * m / (m + n) / (n - 1) * Σ1<=i 1, f"interval must be a non-empty slice, but array[{start}:{end}] was given." Q = self._get_Q_vals(start, end) i, j = np.unravel_index(np.argmax(Q), Q.shape) diff --git a/otava/change_point_divisive/detector.py b/otava/change_point_divisive/detector.py index d9ba3837..89453720 100644 --- a/otava/change_point_divisive/detector.py +++ b/otava/change_point_divisive/detector.py @@ -33,6 +33,7 @@ def __init__(self, significance_tester: SignificanceTester, calculator: Type[Cal self.calculator = calculator def get_change_points(self, series: Sequence[SupportsFloat], start: Optional[int] = None, end: Optional[int] = None) -> List[ChangePoint[GenericStats]]: + '''Finds change points in `series[start : end]`.''' if not isinstance(series, np.ndarray): series = np.array(series[start : end], dtype=np.float64) if not np.issubdtype(series.dtype, np.floating): diff --git a/otava/change_point_divisive/significance_test.py b/otava/change_point_divisive/significance_test.py index b00769b6..7e348c71 100644 --- a/otava/change_point_divisive/significance_test.py +++ b/otava/change_point_divisive/significance_test.py @@ -39,13 +39,13 @@ class PermutationStats(BaseStats): class PermutationsSignificanceTester(SignificanceTester): - def __init__(self, alpha: float, permurations: int, calculator: Type[Calculator], seed: Optional[int]): - '''alpha - significance level + def __init__(self, max_pvalue: float, permutations: int, calculator: Type[Calculator], seed: Optional[int]): + '''max_pvalue - significance level permutations - number of permutations to run to test significance calculator - Calculator class to perform permutations (and compute new qhat value) ''' - super().__init__(alpha) - self.permutations = permurations + super().__init__(max_pvalue) + self.permutations = permutations self.calculator = calculator self.seed = seed self.rng = np.random.default_rng(seed) diff --git a/tests/change_point_divisive_test.py b/tests/change_point_divisive_test.py index 755da9f6..34765bba 100644 --- a/tests/change_point_divisive_test.py +++ b/tests/change_point_divisive_test.py @@ -69,7 +69,7 @@ def compute_Q_and_candidate_slow(sequence): def test_calculator_candidate(): sequence = SEQUENCE.copy() calc = PairDistanceCalculator(sequence) - Q = calc._get_Q_vals(start=0, end=len(sequence) - 1) + Q = calc._get_Q_vals(start=0, end=len(sequence)) test_Q, test_Q_max, test_candidate_ind = compute_Q_and_candidate_slow(sequence) assert np.allclose(test_Q, Q) @@ -87,7 +87,7 @@ def test_permutation_calculation(): candidate = calc.get_candidate_change_point(whole_interval) seed = 1 - st = PermutationsSignificanceTester(alpha=0.05, permurations=1, calculator=PairDistanceCalculator, seed=seed) + st = PermutationsSignificanceTester(max_pvalue=0.05, permutations=1, calculator=PairDistanceCalculator, seed=seed) change_point = st.change_point(candidate=candidate, series=sequence, intervals=[whole_interval]) test_rng = np.random.default_rng(seed) @@ -101,7 +101,7 @@ def test_permutation_calculation(): def test_permutation_test(): seed = 1 sequence = SEQUENCE.copy() - st = PermutationsSignificanceTester(alpha=0.01, permurations=100, calculator=PairDistanceCalculator, seed=seed) + st = PermutationsSignificanceTester(max_pvalue=0.01, permutations=100, calculator=PairDistanceCalculator, seed=seed) cpd = ChangePointDetector(significance_tester=st, calculator=PairDistanceCalculator) cps = cpd.get_change_points(series=sequence) assert [cp.index for cp in cps] == CHANGE_POINTS_INDS @@ -109,7 +109,7 @@ def test_permutation_test(): def test_ttest(): sequence = SEQUENCE.copy() - st = TTestSignificanceTester(alpha=0.01) + st = TTestSignificanceTester(max_pvalue=0.01) cpd = ChangePointDetector(significance_tester=st, calculator=PairDistanceCalculator) cps = cpd.get_change_points(series=sequence) assert [cp.index for cp in cps] == CHANGE_POINTS_INDS