Feature: Double Mixture of Gaussians for dp_accounting

[jan-schuchardt]

Hi,

af761ba added "MixtureGaussianPrivacyLoss" to dp_accounting/pld/privacy_loss_mechanism.py, which enables privacy accounting for mechanisms that are dominated by a single Gaussian and a mixture of Gaussians.

For certain use cases, it might be nice to generalize this to mechanisms dominated by two mixture of Gaussians, each with different mixture weights and means/sensitivities.
For instance, such a "DoubleMixtureGaussianPrivacyLoss" can be used for efficient (albeit non-tight) accounting when considering substitutions of records, see Sections 6.2 & 6.3 in https://proceedings.mlr.press/v108/koskela20b.html.
It is also needed for tight accounting of group privacy under insertion/removal, see Theorem 3.8 in https://arxiv.org/abs/2403.04867.

I already had to implement this for my last project, see https://github.com/jan-schuchardt/group_amplification/blob/master/group_amplification/privacy_analysis/composition/pld/accounting.py.
So if you'd like, I could clean my code up a bit and create a pull request.

Let me know if you think that this would be useful addition :)

[arung54]

Hi Jan,

Thanks for offering to contribute! We would be interested in adding your accounting code, please go ahead and submit a PR when you feel the code is ready.

To anticipate some feedback on that PR - it seems like both DoubleMixtureLaplacePrivacyLoss and DoubleMixtureGaussianPrivacyLoss reuse many methods from MixtureGaussianPrivacyLoss - do you think it's possible to, as part of your cleanup, inherit these methods instead (e.g. from a new abstract class that all three could inherit the shared methods from)? This will make it easier to maintain the new code on our end after the PR is accepted :)

Thanks!
Arun

[jan-schuchardt]

Hi Arun,

I've created a draft pull request, see #277.
It would be great if you could have a look :)

Best,
Jan