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
pseudo-log-likelihood 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
bash
conda install -c conda-forge changeforest
To install from PyPI, run
bash
pip install changeforest
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.
python
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),
...: 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 segment 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.
```python In [2]: from changeforest import changeforest ...: ...: result = changeforest(X, "randomforest", "bs") ...: result Out[2]: bestsplit maxgain pvalue (0, 600] 412 19.603 0.005 ¦--(0, 412] 201 62.981 0.005 ¦ ¦--(0, 201] 194 -12.951 0.76 ¦ °--(201, 412] 211 -9.211 0.545 °--(412, 600] 418 -37.519 0.915
In [3]: result.split_points() Out[3]: [201, 412] ```
changeforest correctly identifies the change point around t=200 but is slightly
off at t=412. The changeforest function returns a BinarySegmentationResult.
We use its plot method to investigate the gain curves maximized by the change point estimates:
result.plot().show()
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 pseudo-log-likelihoods 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.
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
20 trees:
python
In [6]: from changeforest import Control
...: changeforest(X, "random_forest", "bs", Control(random_forest_n_estimators=20))
Out[6]:
best_split max_gain p_value
(0, 600] 592 -11.786 0.01
¦--(0, 592] 121 -6.26 0.015
¦ ¦--(0, 121] 13 -14.219 0.615
¦ °--(121, 592] 416 21.272 0.005
¦ ¦--(121, 416] 201 37.157 0.005
¦ ¦ ¦--(121, 201] 192 -17.54 0.65
¦ ¦ °--(201, 416] 207 -6.701 0.74
¦ °--(416, 592] 584 -44.054 0.935
°--(592, 600]
The changeforest algorithm still detects change points around t=200, 400 but also
returns two false positives.
Due to the nature of the change, method="change_in_mean" is unable to detect any
change points at all:
python
In [7]: changeforest(X, "change_in_mean", "bs")
Out[7]:
best_split max_gain p_value
(0, 600] 589 8.318
To install from conda-forge, run
bash
conda install -c conda-forge r-changeforest
See here for instructions on how to install 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.
```R
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 segment 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.
```R
library(changeforest)
result = changeforest(X, "randomforest", "bs") result name bestsplit maxgain pvalue 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$split_points() [1] 199 410 ```
changeforest correctly identifies the change point around t=200 but is slightly
off at t=410. The changeforest function returns an object of class binary_segmentation_result.
We use its plot method to investigate the gain curves maximized by the change point estimates:
```
plot(result) ```
Change point estimates are marked in red.
For method="random_forest" (and method="knn"), the changeforest algorithm uses a two-step approach to
find an optimizer of the gain. This fits a classifier for three split candidates
at the segment's 1/4, 1/2 and 3/4 quantiles computes approximate gain curves using
the resulting pseudo-log-likelihoods and selects the overall optimizer as a second guess.
We can investigate the gain curves from the optimizer using the plot method of optimizer_result.
The initial guesses are marked in blue.
result.optimizer_result.plot().show()
One can observe that the approximate gain curves are piecewise linear, with maxima around the true underlying change points.
The binary_segmentation_result object returned by changeforest is a tree-like object with attributes
start, stop, best_split, max_gain, p_value, is_significant, optimizer_result, model_selection_result, left, right and segments.
These can be interesting to investigate the output of the algorithm further.
The changeforest algorithm can be tuned with hyperparameters. See
here
for their descriptions and default values. In R, the parameters can
be specified with the Control class,
which can be passed to changeforest. The following will build random forests with
20 trees:
```R
changeforest(X, "randomforest", "bs", Control$new(randomforestnestimators=20)) name bestsplit maxgain pvalue issignificant 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:
```R
changeforest(X, "changeinmean", "bs") name bestsplit maxgain pvalue issignificant 1 (0, 600] 498 17.29389 NA FALSE ```
[1] M. Londschien, S. Kovács and P. Bühlmann (2022), "Random Forests for Change Point Detection", working paper.