Random Forests for Change Point Detection

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 a based on ranks or distances, and thus fail in scenarios with 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 as an R package (on conda-forge , linux and MacOS only). See below for their respective user guides.

Python

Installation

To install from conda-forge (recommended), simply run

conda install -c conda-forge changeforest

Example

The following example performs random forest based change point detection on the iris dataset. This includes three classes setosa, versicolor and virginica with 50 observations each. We interpret this as a simulated time series with change points at t = 50, 100.

In [1]: from changeforest import changeforest
   ...: from sklearn.datasets import fetch_openml
   ...:
   ...: iris = fetch_openml(data_id=61)["frame"].drop(columns="class").to_numpy()
   ...: result = changeforest(iris, "random_forest", "bs")
   ...: result
Out[1]:
                    best_split max_gain p_value
(0, 150]                    50   96.212    0.01
 ¦--(0, 50]                 34    -4.65       1
 °--(50, 150]              100   51.557    0.01
     ¦--(50, 100]           80   -3.068       1
     °--(100, 150]         134   -2.063       1

In [2]: result.split_points()
Out[2]: [50, 100]

changeforest also implements methods change_in_mean and knn. While random_forest and knn implement the TwoStepSearch optimizer as described in [1], for change_in_mean the optimizer GridSearch is used. Both random_forest and knn perform model selection via a pseudo-permutation test (see [1]). For change_in_mean split candidates are kept whenever max_gain > control.minimal_gain_to_split.

The iris dataset allows for rather simple classification due to large mean shifts between classes. As a result, both simple methods change_in_mean and knn correctly identify die true change points.

In [3]: result = changeforest(iris, "change_in_mean", "bs")
   ...: result.split_points()
Out[3]: [50, 100]

In [4]: result = changeforest(iris, "knn", "bs")
   ...: result.split_points()
Out[4]: [50, 100]

changeforest returns 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 further investigate the output of the algorithm. Here we plot the approximated gain curves of the first three segments:

In [5]: import matplotlib.pyplot as plt
   ...: result = changeforest(iris, "change_in_mean", "bs")
   ...: plt.plot(range(150), result.optimizer_result.gain_results[-1].gain)
   ...: plt.plot(range(50), result.left.optimizer_result.gain_results[-1].gain)
   ...: plt.plot(range(50, 150), result.right.optimizer_result.gain_results[-1].gain)
   ...: plt.legend([f"approx. gain for {x}" for x in ["(0, 150]", "(0, 50]", "(50, 150"]])
   ...: plt.show()

One can clearly observe that the approx. gain curves are piecewise linear, with maxima at the true underlying change points.

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 very few trees:

In [6]: from changeforest import Control
   ...: changeforest(iris, "random_forest", "bs", Control(random_forest_n_estimators=10))
Out[6]:
                    best_split max_gain p_value
(0, 150]                    50   96.071    0.01
 ¦--(0, 50]                 16   -3.788       1
 °--(50, 150]              100   46.544    0.01
     ¦--(50, 100]           66   -7.793    0.43
     °--(100, 150]         134   -9.329       1

R

To install from conda-forge, simply run

conda install -c conda-forge r-changeforest

Example

The following example performs random forest based change point detection on the iris dataset. This includes three classes setosa, versicolor and virginica with 50 observations each. We interpret this as a simulated time series with change points at t = 50, 100.

> library(changeforest)
> library(datasets)
> data(iris)
> X <- as.matrix(iris[, 1:4])
> changeforest(X, "random_forest", "bs")
                name best_split  max_gain p_value is_significant
1 (0, 150]                   50 96.173664    0.01           TRUE
2  ¦--(0, 50]                34 -5.262184    1.00          FALSE
3  °--(50, 150]             100 51.557473    0.01           TRUE
4      ¦--(50, 100]          80 -3.068934    1.00          FALSE
5      °--(100, 150]        134 -2.063508    1.00          FALSE

changeforest also implements methods change_in_mean and knn. While random_forest and knn implement the TwoStepSearch optimizer as described in [1], for change_in_mean the optimizer GridSearch is used. Both random_forest and knn perform model selection via a pseudo-permutation test (see [1]). For change_in_mean split candidates are kept whenever max_gain > control.minimal_gain_to_split.

The iris dataset allows for rather simple classification due to large mean shifts between classes. As a result, both change_in_mean and knn also correctly identify die true change points.

> result <- changeforest(X, "change_in_mean", "bs")
> result$split_points()
[1] [50, 100]
> result <- changeforest(X, "knn", "bs")
> result$split_points()
[1] [50, 100]

changeforest returns 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 further investigate the output of the algorithm. Here we plot the approximated gain curves of the first three segments:

> library(ggplot2)
> result <- changeforest(X, "random_forest", "bs")
> data = data.frame(
        t=1:150,
        gain=result$optimizer_result$gain_results[[3]]$gain,
        gain_left=c(result$left$optimizer_result$gain_results[[3]]$gain, rep(NA, 100)),
        gain_right=c(rep(NA, 50), result$right$optimizer_result$gain_results[[3]]$gain)
)

> ggplot(data=data) +
        geom_line(aes(x=t, y=gain), color="blue") + 
        geom_line(aes(x=t, y=gain_left), color="orange") + 
        geom_line(aes(x=t, y=gain_right), color="green") +
        labs(y = 'gain') + theme(legend.position="bottom")

One can clearly observe that the approx. gain curves are piecewise linear, with maxima at the true underlying change points.

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 very few trees:

> changeforest(X, "random_forest", "bs", Control(random_forest_n_estimators=10))
... TODO

References

[1] M. Londschien, S. Kovács and P. Bühlmann (2022), "Random Forests for Change Point Detection", working paper.