Rank-based cost function

Description

This cost function detects general distribution changes in multivariate signals, using a rank transformation [RALYFLevyLCappe15]. Formally, for a signal \(\{y_t\}_t\) on an interval \([a, b)\),

\[c_{rank}(a, b) = -(b - a) \bar{r}_{a..b}' \hat{\Sigma}_r^{-1} \bar{r}_{a..b}\]

where \(\bar{r}_{a..b}\) is the empirical mean of the sub-signal \(\{r_t\}_{t=a+1}^b\), and \(\hat{\Sigma}_r\) is the covariance matrix of the complete rank signal \(r\).

Usage

Start with the usual imports and create a signal.

import numpy as np
import matplotlib.pylab as plt
import ruptures as rpt
# creation of data
n, dim = 500, 3  # number of samples, dimension
n_bkps, sigma = 3, 5  # number of change points, noise standard deviation
signal, bkps = rpt.pw_constant(n, dim, n_bkps, noise_std=sigma)

Then create a CostRank instance and print the cost of the sub-signal signal[50:150].

c = rpt.costs.CostRank().fit(signal)
print(c.error(50, 150))

You can also compute the sum of costs for a given list of change points.

print(c.sum_of_costs(bkps))
print(c.sum_of_costs([10, 100, 200, 250, n]))

In order to use this cost class in a change point detection algorithm (inheriting from BaseEstimator), either pass a CostRank instance (through the argument 'custom_cost') or set model="rank".

c = rpt.costs.CostRank(); algo = rpt.Dynp(custom_cost=c)
# is equivalent to
algo = rpt.Dynp(model="rank")

Code explanation

class ruptures.costs.CostRank

Rank-based cost function

__init__()

Initialize self. See help(type(self)) for accurate signature.

error(start, end)

Return the approximation cost on the segment [start:end].

Parameters

• start (int) – start of the segment

• end (int) – end of the segment

Returns

segment cost

Return type

float

Raises

NotEnoughPoints – when the segment is too short (less than 'min_size' samples).

fit(signal)

Set parameters of the instance.

Parameters

signal (array) – signal. Shape (n_samples,) or (n_samples, n_features)

Returns

self

References

RALYFLevyLCappe15

A. Lung-Yut-Fong, C. Lévy-Leduc, and O. Cappé. Homogeneity and change-point detection tests for multivariate data using rank statistics. Journal de la Société Française de Statistique, 156(4):133–162, 2015.