Change point detection aims to identify structural breaks in the probability distribution of a time series. Existing methods either assume a parametric model for within-segment distributions or are based on ranks or distances and thus fail in scenarios with a reasonably large dimensionality.
changeforest implements a classifier-based algorithm that consistently estimates
change points without any parametric assumptions, even in high-dimensional scenarios.
It uses the out-of-bag probability predictions of a random forest to construct a
classifier log-likelihood ratio that gets optimized using a computationally feasible two-step
method.
See [1] for details.
changeforest is available as rust crate, a Python package (on
PyPI and
conda-forge),
and an R package (on conda-forge
, linux and MacOS only). See below for their respective user guides.
To install from conda-forge (recommended), run
conda install -c conda-forge changeforestTo install from PyPI, run
pip install changeforestIn the following example, we perform random forest-based change point detection on
a simulated dataset with n=600 observations and covariance shifts at t=200, 400.
In [1]: import numpy as np
...:
...: Sigma = np.full((5, 5), 0.7)
...: np.fill_diagonal(Sigma, 1)
...:
...: rng = np.random.default_rng(12)
...: X = np.concatenate(
...: (
...: rng.normal(0, 1, (200, 5)),
...: rng.multivariate_normal(np.zeros(5), Sigma, 200, method="cholesky"),
...: rng.normal(0, 1, (200, 5)),
...: ),
...: axis=0,
...: )The simulated dataset X coincides with the change in covariance (CIC) setup
described in [1]. Observations in the first and last segments are independently drawn
from a standard multivariate Gaussian distribution. Observations in the second segment
are i.i.d. normal with mean zero and unit variance, but with a covariance of ρ = 0.7
between coordinates. This is a challenging scenario.
In [2]: from changeforest import changeforest
...:
...: result = changeforest(X, "random_forest", "bs")
...: result
Out[2]:
best_split max_gain p_value
(0, 600] 400 14.814 0.005
¦--(0, 400] 200 59.314 0.005
¦ ¦--(0, 200] 6 -1.95 0.67
¦ °--(200, 400] 393 -8.668 0.81
°--(400, 600] 412 -9.047 0.66
In [3]: result.split_points()
Out[3]: [200, 400]changeforest correctly identifies the change points at t=200 and t=400. The
changeforest function returns a BinarySegmentationResult. We use its plot method
to investigate the gain curves maximized by the change point estimates:
In [4]: result.plot().show()
For method="random_forest" and method="knn", the changeforest algorithm uses a two-step approach to
find an optimizer of the gain. This fits a classifier for three split candidates
at the segment's 1/4, 1/2 and 3/4 quantiles, computes approximate gain curves using
the resulting classifier log-likelihood ratios and selects the overall optimizer as a second guess.
We can investigate the gain curves from the optimizer using the plot method of OptimizerResult.
The initial guesses are marked in blue.
In [5]: result.optimizer_result.plot().show()
One can observe that the approximate gain curves are piecewise linear, with maxima around the true underlying change points.
The BinarySegmentationResult returned by changeforest is a tree-like object with attributes
start, stop, best_split, max_gain, p_value, is_significant, optimizer_result, model_selection_result, left, right and segments.
These can be interesting to investigate the output of the algorithm further.
The changeforest algorithm can be tuned with hyperparameters. See
here
for their descriptions and default values. In Python, the parameters can
be specified with the Control class,
which can be passed to changeforest. The following will build random forests with
50 trees:
In [6]: from changeforest import Control
...: changeforest(X, "random_forest", "bs", Control(random_forest_n_estimators=50))
Out[6]:
best_split max_gain p_value
(0, 600] 416 7.463 0.01
¦--(0, 416] 200 43.935 0.005
¦ ¦--(0, 200] 193 -14.993 0.945
¦ °--(200, 416] 217 -9.13 0.085
°--(416, 600] 591 -12.07 1 The changeforest algorithm still detects change points at t=200, but is slightly off
with t=416.
Due to the nature of the change, method="change_in_mean" is unable to detect any
change points at all:
In [7]: changeforest(X, "change_in_mean", "bs")
Out[7]:
best_split max_gain p_value
(0, 600] 589 8.625 To install from conda-forge, run
conda install -c conda-forge r-changeforestSee here for a detailed description
on installing the changeforest R package with conda.
In the following example, we perform random forest-based change point detection on
a simulated dataset with n=600 observations and covariance shifts at t=200, 400.
> library(MASS)
> set.seed(0)
> Sigma = matrix(0.7, nrow=5, ncol=5)
> diag(Sigma) = 1
> mu = rep(0, 5)
> X = rbind(
mvrnorm(n=200, mu=mu, Sigma=diag(5)),
mvrnorm(n=200, mu=mu, Sigma=Sigma),
mvrnorm(n=200, mu=mu, Sigma=diag(5))
)The simulated dataset X coincides with the change in covariance (CIC) setup
described in [1]. Observations in the first and last segments are independently drawn
from a standard multivariate Gaussian distribution. Observations in the second segment
are i.i.d. normal with mean zero and unit variance, but with a covariance of ρ = 0.7
between coordinates. This is a challenging scenario.
> library(changeforest)
> result = changeforest(X, "random_forest", "bs")
> result
name best_split max_gain p_value is_significant
1 (0, 600] 410 13.49775 0.005 TRUE
2 ¦--(0, 410] 199 61.47201 0.005 TRUE
3 ¦ ¦--(0, 199] 192 -22.47364 0.955 FALSE
4 ¦ °--(199, 410] 396 11.50559 0.190 FALSE
5 °--(410, 600] 416 -23.52932 0.965 FALSE
> result$split_points()
[1] 199 410changeforest correctly identifies the change point around t=200 but is slightly
off at t=410. The changeforest function returns an object of class binary_segmentation_result.
We use its plot method to investigate the gain curves maximized by the change point estimates:
> plot(result)
Change point estimates are marked in red.
For method="random_forest" and method="knn", the changeforest algorithm uses a two-step approach to
find an optimizer of the gain. This fits a classifier for three split candidates
at the segment's 1/4, 1/2 and 3/4 quantiles computes approximate gain curves using
the resulting classifier log-likelihood ratios and selects the overall optimizer as a second guess.
We can investigate the gain curves from the optimizer using the plot method of optimizer_result.
The initial guesses are marked in blue.
> plot(result$optimizer_result)
One can observe that the approximate gain curves are piecewise linear, with maxima around the true underlying change points.
The binary_segmentation_result object returned by changeforest is a tree-like object with attributes
start, stop, best_split, max_gain, p_value, is_significant, optimizer_result, model_selection_result, left, right and segments.
These can be interesting to investigate the output of the algorithm further.
The changeforest algorithm can be tuned with hyperparameters. See
here
for their descriptions and default values. In R, the parameters can
be specified with the Control class,
which can be passed to changeforest. The following will build random forests with
20 trees:
> changeforest(X, "random_forest", "bs", Control$new(random_forest_n_estimators=20))
name best_split max_gain p_value is_significant
1 (0, 600] 15 -6.592136 0.010 TRUE
2 ¦--(0, 15] 6 -18.186534 0.935 FALSE
3 °--(15, 600] 561 -4.282799 0.005 TRUE
4 ¦--(15, 561] 116 -8.084126 0.005 TRUE
5 ¦ ¦--(15, 116] 21 -17.780523 0.130 FALSE
6 ¦ °--(116, 561] 401 11.782002 0.005 TRUE
7 ¦ ¦--(116, 401] 196 22.792401 0.150 FALSE
8 ¦ °--(401, 561] 554 -16.338703 0.800 FALSE
9 °--(561, 600] 568 -5.230075 0.120 FALSE The changeforest algorithm still detects the change point around t=200 but also
returns false positives.
Due to the nature of the change, method="change_in_mean" is unable to detect any
change points at all:
> changeforest(X, "change_in_mean", "bs")
name best_split max_gain p_value is_significant
1 (0, 600] 498 17.29389 NA FALSE[1] M. Londschien, P. Bühlmann and S. Kovács (2023). "Random Forests for Change Point Detection" Journal of Machine Learning Research