[MRG] Add Yeo-Johnson transform to PowerTransformer

[NicolasHug]

Reference Issues/PRs

Closes #10261

What does this implement/fix? Explain your changes.

This PR implements the Yeo-Johnson transform as part of the PowerTransformer class.

PowerTransformer currently only support Box-Cox which only works for positive values, Yeo-Johnson works for the whole real line.

Original paper : link.

TODO:

• Write transform
• Fix lambda param estimation
• Write inverse transform
• Write docs
• Write tests
• Update examples

Any other comments?

The lambda parameter estimation is a bit tricky and currently does not work. (should be OK now, see below). Unlike for Box-Cox there's no scipy built-in that we can rely on. I'm having a hard time finding decent guidelines, tried to implement likelihood maximization with the brent optimizer (just like for Box-Cox) but run into overflow issues.

The transform code seems to work though:

which is a reproduction of

From Quantile regression via vector generalized additive models by Thomas W. Yee.

Code for figure (hacky):

import numpy as np
from sklearn.preprocessing import PowerTransformer
import matplotlib.pyplot as plt

yj = PowerTransformer(method='yeo-johnson', standardize=False)
bc = PowerTransformer(method='box-cox', standardize=False)

X = np.arange(-4, 4, .1).reshape(-1, 1)
fig, axes = plt.subplots(ncols=2)

for lmbda in (0, .5, 1, 1.5, 2):
    X_pos = X[X > 0].reshape(-1, 1)
    bc.fit(X_pos)
    bc.lambdas_ = [lmbda]
    X_trans = bc.transform(X_pos)
    axes[0].plot(X_pos, X_trans, label=r'$\lambda = {}$'.format(lmbda))
    axes[0].set_title('Box-Cox')

    yj.fit(X)
    yj.lambdas_ = [lmbda]
    X_trans = yj.transform(X)
    axes[1].plot(X, X_trans, label=r'$\lambda = {}$'.format(lmbda))
    axes[1].set_title('Yeo-Johnson')

for ax in axes:
    ax.set(xlim=[-4, 4], ylim=[-5, 5], aspect='equal')
    ax.legend()
    ax.grid()

plt.show()

[NicolasHug]

Lambda param estimation should be fixed now, thanks @amueller.

Replication of this example with Yeo-Johnson instead of Box-Cox:

[amueller]

yeo?

[ogrisel]

Follow the white rabbit.

[amueller]

this took me a while.

[amueller]

We think it's working now, right? So we need a test for the optimization, and then documentation and adding it to an example?

[amueller]

space after #

[amueller]

do we need from __future__ import division?

[NicolasHug]

it's here already

[amueller]

thanks, was hard to see from the diff and I was lazy ;)

[amueller]

why is this needed? The default value shouldn't change, right? Or do we want to start a cycle to change the default to yeo-johnson?

[NicolasHug]

I find it clearer and explicit?

I don't know if we'll change the default but it should still be fine as PowerTransform hasn't been released yet AFAIK

[amueller]

good point. We should discuss before the release. I think yeo-johnson would make more sense.

[ogrisel]

The fact that Yeo-Johnson accepts negative values while Box-Cox does not makes me feel like we should use it by default. From a usability point of view, it's nicer to our users.

[NicolasHug]

I have the same feeling. Plus, it is designed to be a generalization of Box-Cox, even though that's not strictly the case.

[amueller]

+1

[NicolasHug]

shall I change the default then?

[amueller]

think so.

[NicolasHug]

Done

[ogrisel]

Why not:

del pt.lambdas_

[ogrisel]

Alternatively, create a new pt object from scratch to make the motivation of the test easier to read:

ground_truth_transform = PowerTransformer(method=method, standardize=False)
ground_truth_transform.lambdas_ = [lmbda]
X_inv = pt.inverse_transform(X)

estimated_transform = PowerTransformer(method=method, standardize=False)
X_inv_trans = estimated_transform.fit_transform(X_inv) 

[ogrisel]

Please also add an assertion that checks that X_inv_trans.mean(axis=0) is close to [0.] and X_inv_trans.std(axis=0) is close to [1.].

[ogrisel]

to make the test more explicit you can write: X = rng.normal(loc=0., scale=1., size=(n_samples, 1))

[amueller]

If we want this to be the default then this is a blocker, right?

[ogrisel]

To make sure that the location of the NaNs does not impact the estimation:

from sklearn.utils import shuffle
...

X = np.concatenate([X, np.full_like(X, np.nan)])
X = shuffle(X, random_state=0)

[NicolasHug]

Done

[ogrisel]

Could you add more values for lmbda for each method? E.g.:

[
 ('box-cox', .1),
 ('box-cox', .5),
 ('yeo-johnson', .1),
 ('yeo-johnson', .5),
 ('yeo-johnson', 1.),
]

[ogrisel]

I don't understand what "modeling problems where homoscedasticity is desired" mean in this context: to me heteroscedasticity is a property of the noise of the output variable that is not the same for different regions of the input space a conditional model.

It does not seem trivial how power transform can improve homoscedasticity.

[ogrisel]

Actually, this statement seems to be correct:

http://article.sapub.org/10.5923.j.ajms.20180801.02.html

It might be interesting to try to come up with a good example to show this corrective effect in a (maybe synthetic) linear regression problem. However, this is probably outside of the scope of the current PR.

[amueller]

tagged for 0.20 and added blocker label. I don't like that we keep adding stuff but if we want to make it default we should do it now.

[glemaitre]

Couple of opened comments.
If I am not wrong we should have something in the common estimator_checks which force the input to be positive to work with box-cox. We probably want to change this behavior with we change the default.

[glemaitre]

We can maybe have a bullet point list for each method referring to the reference section.

[glemaitre]

I would have expect func instead of fun :)

[glemaitre]

optim_function

[glemaitre]

probably transform_function is not so long to be called

[glemaitre]

we cannot just define the forward transform and take 1 / _yeo_johnson_transform for the inverse?

[NicolasHug]

The inverse here means f^{-1}, not 1 / f

[glemaitre]

n_samples instead

[glemaitre]

Uhm missing x most probably

[glemaitre]

Oh I see, can we pass x as an argument as well as in the optimize function?

[NicolasHug]

yes this is a nested function so x is implicitely passed anyway

[glemaitre]

Stupid question: is sig_sq the variance? If this is the case, you might want to call it var

[NicolasHug]

I was following the paper's notation. Should I use mean (or mean_) also then?

[NicolasHug]

I made a quick example to illustrate the use of Yeo-Johnson vs. Box-Cox + offset.

As Box-Cox only accepts positive data, one solution is to shift the data by a fixed offset value (typically min(data) + eps):

One thing we see is that the "after offset and Box-Cox" isn't as symmetric as the eo-Johnson and most importantly the values are much higher.

Is it worth adding this as an example @amueller? TBH I wouldn't be able to mathematically or intuitively explain those results.

[TomDLT]

Thanks for the added tests.
We might want to add them as common tests at some point, but it might be for another pull-request.

[TomDLT]

actually you should be able to use copy=False here, since a copy has already been done just before.

[glemaitre]

Couple of changes

[glemaitre]

Notes

[glemaitre]

Notes

[glemaitre]

only if self.method=='box-cox'

[glemaitre]

I am waiting to check the example in the documentation

[NicolasHug]

@glemaitre @ogrisel, I think the plot looks pretty OK now.

[jnothman]

I'm finding the plots in plot_map_data_to_normal relatively hard to navigate intuitively. It's not a blocker, but I think it needs to look more tabular: at the moment it takes some effort to see that each row is a different transformation; a label on the left of the row would be more helpful.

Also, having the transformations go from left to right and the datasets from top to bottom doesn't look like it would be infeasible, and would be more familiar from plot_cluster_comparison etc.

[jnothman]

Can I clarify why plot_all_scaling still only shows box-cox?

[NicolasHug]

Also, having the transformations go from left to right and the datasets from top to bottom doesn't look like it would be infeasible, and would be more familiar from plot_cluster_comparison etc.

Personally I find it easier to compare the transformations when they're stacked on each other, especially since the axes limits are uniform across the plots.

I don't have anything against having the transformation names on the left. It would also make sense to me to have one dataset per column (limiting the plot to 4 rows instead of 8), but that would make the plot wider which can be annoying on mobile.

Thanks for mentioning plot_all_scaling, I missed that one.

[NicolasHug]

Looks like 14e7c32 broke plot_all_scaling on master:

Traceback (most recent call last):
  File "examples/preprocessing/plot_all_scaling.py", line 71, in <module>
    dataset = fetch_california_housing()
  File "/home/nico/dev/sklearn/sklearn/datasets/california_housing.py", line 128, in fetch_california_housing
    cal_housing = joblib.load(filepath)
  File "/home/nico/dev/sklearn/sklearn/externals/joblib/numpy_pickle.py", line 578, in load
    obj = _unpickle(fobj, filename, mmap_mode)
  File "/home/nico/dev/sklearn/sklearn/externals/joblib/numpy_pickle.py", line 508, in _unpickle
    obj = unpickler.load()
  File "/usr/lib64/python3.6/pickle.py", line 1050, in load
    dispatch[key[0]](self)
  File "/usr/lib64/python3.6/pickle.py", line 1338, in load_global
    klass = self.find_class(module, name)
  File "/usr/lib64/python3.6/pickle.py", line 1388, in find_class
    __import__(module, level=0)
ModuleNotFoundError: No module named 'sklearn.externals._joblib.numpy_pickle'

Should I open an issue for this? I'm not sure if this comes from my env (I created a new one from scratch, still same). Doesn't the CI check that all the examples are passing?

[amueller]

@NicolasHug it's now "fixed" but you need to remove your scikit_learn_data folder in your home folder.

[NicolasHug]

Thanks, just updated plot_all_scaling

[ogrisel]

The matplotlib rendering of the 2 examples is good enough for now:

https://29575-843222-gh.circle-artifacts.com/0/doc/auto_examples/index.html#preprocessing

Merging. Thanks @NicolasHug for this nice contribution!

[amueller]

yay!

[ogrisel]

I agree with @jnothman (#11520 (comment)) that using a layout similar to the cluster comparison plot would improve the readability even further but I don't want to delay the release for this.

[GaelVaroquaux]

Yey!!