example setting the penalty parameter?

[wqp89324]

Is there an example about how to set the pen parameter for Pelt?

[deepcharles]

Hello,

Finding a proper value for the pen paper heavily depends on the signal at hand. As a rule of thumb, the more noise, samples or dimensions, the larger this parameter should be.
For parametric changes (such as mean-shifts, scale-shifts,...), the Bayesian Information Criterion (BIC) is a good starting point. For instance, detecting mean-shifts with BIC yields:

T, d = signal.shape  # number of samples, dimension
sigma = ...  # noise standard deviation
bic = sigma*sigma*np.log(T)*d
algo = rpt.Pelt().fit(signal)
my_bkps = algo.predict(pen=bic)

However, BIC tends to produce too low penalty values. When that happens, the simplest procedure, is to test several values, as below:

pen_values = np.logspace(0, 3, 10)  # for instance
algo = rpt.Pelt().fit(signal)
bkps_list = [algo.predict(pen=pen) for pen in pen_values]
# then compare elements of bkps_list

Cheers,

Charles

[mylife126]

Hello thanks for sharing the BIC theory, however, could you please let me know why the way you calculate BIC is bic = sigmasigmanp.log(T)*d ? In the Wiki, i could not find such derivation. Thanks!

[deepcharles]

Hello,

There might be a mistake indeed. The formula should be

This is only valid for the cost function l2 (see Table 1 of this article).
To verify it, assume the signal is multivariate Gaussian with isotropic variance $sigma^2$, use the normal formula for BIC and get rid of all terms that does not depend on $K$, the number of change points.

[deepcharles]

If you would like to correct it in the docs, do not hesitate to make a pull request ;)

oh it is not in the docs yet, never mind then.

[DPTPaul]

Hello,

Thanks a lot for this very useful package!
I'm currently working on a signal and have no idea about the number of breakpoints.
I understand that BIC approximation can only be used with a l2 cost function. As I try to detect both mean and variance shifts, I would like to use a `rbf`` cost function.

Is there any trick to set a good penalty value (or at least a sense of scale)?