Describe the bug There is a test suite, but the documentation does not explain how to run it.

Here is what works for me:

1. Install pytest.
2. Clone the source repository.
3. Run pytest in the root directory of the repository.

Your package offers support for simulating vine copulas. However, I don't see examples demonstrating how to simulate data from a vine copula given desired conditional dependency requirements.

Is this possible with the current API? If not, how would I use the vine copula generator to achieve this?

Otherwise, can examples show the difference between simulating Gaussian and vine copulas? I only see examples for the Gaussian copula.

Describe the bug

The documentation page on fPCA says:

PCA can be used to generate synthetic data for the high-dimensional vector $X$. For every instance $X_i$ in the data set, we compute the principal component scores $a_{i, 1}, \dots, a_{i, K}$. Because the principal components $v_1, \dots, v_K$ are orthogonal, the scores are necessarily uncorrelated and we may treat them as independent.

The claim that "because the principal components $v_1, \dots, v_K$ are orthogonal, the scores are necessarily uncorrelated" looks wrong to me. These scores are projections of the $X_i$ onto the elements of an orthonormal basis. That doesn't make them uncorrelated. There are lots of orthonormal bases one can project on, and for most of them the projections are not uncorrelated. You need some property of the distribution of $X$ to derive a zero correlation, for example a Gaussian distribution, for which the PCA basis yields approximately uncorrelated projections.

It would be helpful to add/explain what the different classes do Data Generators, Parametrizer, Transformers somewhere in the introduction or usage component of the documentation. Explain the different classes and what each is supposed to do. If it is similar to or inspired by well-known API of a different package, please point to it.

I think generators and transformers are obvious but I only sort of understand Parametrizers. It is also confusing in the sense that people might think this has something to do with parametric distributions when you mean it to be something different.

Is this API for Parametrizers inspired by some convention elsewhere? If so it would be helpful to point to that. For instance, the generators are very similar to statsmodel generators.

Hi, just letting you know I noticed a small error in the documentation.

At the bottom of this page https://dmey.github.io/synthia/examples/fpca.html

The error is in line [6] of the code, under "Plot the results".

You have: plot_profiles(ds_true, 'temperature_fl')

But I believe it should be: plot_profiles(ds_synth, 'temperature_fl')

you want to plot results, not the original here.

Cheers & thanks for the cool project!

What are other packages people might use to simulate data (e.g. statsmodels comes to mind) and how is this package different? Your package supports generating data for multivariate copula distributions and via fPCA. I understand what this entails but I think this could use further elaboration.

This package supports nonparametric distributions much more than the typical parametric data generators found in common packages and it would be useful to highlight these explicitly.

During fitting, category values are reindexed as integers starting from 0 and transformed to one-hot vectors. The opposite during generation. Any data type works for categories, including strings.

We can treat categorical data as discrete but first we need to pre-process categorical values by one hot encoding to remove the order. Re API we can change the current version from

# Assuming  an xarray datasets ds with X1 discrete and and X2 categorical 
generator.fit(ds, copula=syn.VineCopula(controls=ctrl), is_discrete={'X1': True, 'X2': False})

to something like

with X3 continuous 
g.fit(ds, copula=syn.VineCopula(controls=ctrl), types={'X1': 'disc', 'X2': 'cat', 'X3': 'cont'})

Introduces the option to specify and model discrete quantities as follows:

# Assuming  an xarray datasets ds with X1 discrete and and X2 continuous 
generator.fit(ds, copula=syn.VineCopula(controls=ctrl), is_discrete={'X1': True, 'X2': False})

This option is only supported for vine copulas