[contributors wanted] Addition of new PDFs

[jonas-eschle]

Fill up the ranks of PDFs with the following. Please feel free to suggest more missing distributions and write in the comments if you want to implement one.

Available:

• Ipatia (or similarly named), we don't have the integral probably, but better without integral than no Ipatia
• Apollonis, shape for invariant mass fits, shuchong? -> in zfit-physics
• Multinomial (https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Multinomial)
• Multivariate Gauss either the TriL from TFP or the full cov (maybe a constructor that takes both args, and converts (see also impl of GaussianConstraint)) -> medium
• ExpModGauss, exponentially modified gaussian, a convolution of gauss + exp from TFP -> beginner friendly
• GeneralizedGauss, where the exponent is something else than squared from TFP -> beginner friendly
• Landau from ROOT, this package and this scipy PR -> medium @mmaehring
• LanGaus (convolution of Landau with Gaussian) -> medium
• Ipatia2/Hypathia (for zfit-physics) zfit snippet -> medium

Implementation finished:

• Chi2 distribution from TFP -> easy
• CMSShape (zfit-physics) (@iasonkrom)
• Voigtian (difficult to do correct, we tried the complex error function) (@iasonkrom)
  • implement somewhat simplified version from astropy
• Cruijff PDF (add to zfit physics, from numba-stas?)
• ErfExp PDF(add to zfit physics, from here)
• Gaussian with exponential tails from here ((@iasonkrom)
• Student's t from TFP -> beginner friendly @ikrommyd
• Q-Gaussian (generalized Gaussian, from numba-stats) -> easy through its relation to the Student's t distribution
• Novosibirsk (contribute to zfit-physics, from here or [from RooFit]
• Tsallis-Hagedorn, a model for the minimum bias pT distribution (zfit-physics) @ikrommyd -> medium
• Split normal distribution (@ikrommyd) -> easy with parameter transformation from TFP
• Berstein polynomial (from numba-stats?) -> medium
  (https://root.cern.ch/doc/master/classRooNovosibirsk.html)) -> beginner friendly, medium
• Gamma from TFP but use RooFit's parametrization @ikrommyd -> beginner friendly
• JohnsonSU (implementation from Matthieu or TensorFlow-Probability version?) -> beginner friendly

[ikrommyd]

• Voigtian
• Tsallis-Hagedorn, a model for the minimum bias pT distribution
• Q-Gaussian

[PasqualeAndreola]

As stated by @iasonkrom , I would be happy to see the Voigtian, too

[anjabeck]

Hi! I'd like to make a start on this. Just checking that noone is working on it already?

[ikrommyd]

Hi @anjabeck, I'm doing the Voigt, and I'm also gonna do the CMSShape and CBExGauss because I need them. You can start doing any other distribution if you want. I believe @jonas-eschle is happy to see PRs

[jonas-eschle]

Hi @anjabeck , you're very welcome to pick a PDF and start making a PR, I'll update the list

[ikrommyd]

@jonas-eschle I believe q-gaussian is different from the generalized normal? We should also add Student's t distribution which we can do from tensorflow-probability and then the q-gaussian is computed via a change of variables from the t-distribution. I updated the issue.

[ikrommyd]

@anjabeck would you be willing to do some more distributions for tf-probability?

[jonas-eschle]

@jonas-eschle I believe q-gaussian is different from the generalized normal? We should also add Student's t distribution which we can do from tensorflow-probability and then the q-gaussian is computed via a change of variables from the t-distribution. I updated the issue.

Agree, it's the student T that we can have to go fro the q-gaussian

[anjabeck]

@anjabeck would you be willing to do some more distributions for tf-probability?

I guess I'd rather try something new to learn stuff :)

[ikrommyd]

@anjabeck would you be willing to do some more distributions for tf-probability?

I guess I'd rather try something new to learn stuff :)

@anjabeck Do you want to take a shot at the Bernstein polynomials?

[ikrommyd]

@jonas-eschle would we want a guassian with different left/right sigmas or should we just leave it like that and a user will have to use the GeneralizedCB with very large fixed alphas? I think a double gaussian makes sense to add for ease of use. It was also part of probfit

[ikrommyd]

@jonas-eschle I also made some progress on Bernstein today. I have a working version on a notebook that gives the same results as numba_stats and RooBernstein but still not "properly" implemented in zfit.

[ikrommyd]

Hi @SengerM, we are interested here to add the Landau and LanGauss distribution to zfit. We basically want a tensorflow implementation that is auto-differentiable. As I was looking around, I came accross landaupy and also your scipy PR. As you seem to have done quite some research on this, do you have any recommendations on what approach to follow? I was thinking of following your vectorized numpy implementations and adjusting them to tensorflow (we also can't do in-place replacements in tensorflow tensors).

[SengerM]

Hello @ikrommyd , I don't have any specific recommendation as I don't have experience with Tensorflow. I can mention that landaupy and my scipy PR are different implementations:

• The landaupy implementation, based on the ROOT implementation, does not depend on any specific function, i.e. all the calculations are explicit +, -, * and /, except for some exponentials, logs and sqrts.
• The scipy PR implementation depends on numpy.polynomial.chebyshev.Chebyshev.

Because of this, it may be easier to follow the more explicit landaupy (ROOT) algorithm.

[ikrommyd]

Thanks for your response @SengerM.
Well my idea was to map your numpy API to tensorflow as they are fairly similar when it comes to vectorized operations.
We also have a Chebyshev polynomial implementation in zfit so I think either could work.
I was wondering if one route is faster and/or better than the other.
We've mapped ROOT code to tensorflow in the past and the workflow is generally in the lines of 1) make all c++ operations vectorized using numpy-like API in tensorflow. 2) all conditions are replaced with tf.where which is similar to np.where.

[mmaehring]

Hi @ikrommyd, I just wanted to ask if you've started the Landau implementation?
If not, I could give it a shot, though I'm rather inexperienced with tensorflow so I'll probably need some help along the way.

I already started an adaption of the ROOT version sometime ago and would continue from that point. The implementation adapts the ROOT code for the PDF and CDF starting in lines 21 and 336 respectively.

[ikrommyd]

Hi @mmaehring, I haven't started anything that is not done already. Please take a look at the above comments regarding the Landau.

[jonas-eschle]

@mmaehring feel free to open a PR in WIP and we can continue a more detailed discussion there, that's probably the easiest

[ikrommyd]

@jonas-eschle Regarding the multivariate normal, I would find anything other than the full covariance matrix version confusing in physics and I agree with scipy only having that version.
I think only that should go in zfit and we can of course use https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MultivariateNormalFullCovariance