Adding explained variances to sparse pca #11527

jrmlhermitte · 2018-07-15T15:19:27Z

Adding explained variances for sparse PCA during a sprint.

I am unfamiliar with Sparse PCA. Based on conversation with @amueller

Reference Issues/PRs

Issue #11512

The variance computed from sparse PCA should match regular PCA. Printed variances here should match.

What does this implement/fix? Explain your changes.

Any other comments?

amueller · 2018-07-15T15:22:07Z

thanks :) You wanted someone else to pick this up now, right?

jrmlhermitte · 2018-07-15T15:40:44Z

The variances don't match. It's worth reading in more detail. See the gist I've linked above for comparing
variances. Can someone else help?

variances:

Non sparse variance:[18.840183  11.071763   6.3046103  3.954582   2.8560433  2.4977083]
Sparse variance:[2.506263e-03 0.000000e+00          nan 1.401298e-45 0.000000e+00
          nan]

thanks!

jrmlhermitte · 2018-07-16T18:45:18Z

ill give it another try. the variances should be easy...

jrmlhermitte · 2018-07-16T19:23:42Z

Added:

added a test to compare the resultant variance from normal PCA with sparse PCA (for orthogonal axes)
added def get_explained_variance(self, components, X): member of SparsePCA which computes the variance from principle components not assumed to be orthogonal
added a variance=False flat to fit for SparsePCA and SparsePCAMiniBatch. If True, will compute the variance and save to self.explained_variance_

Note:

Actual test on non-orthogonal axes was not done. It could be useful to compare this with a result computed with another function.

jrmlhermitte · 2018-07-16T19:24:52Z

sklearn/decomposition/sparse_pca.py

+            # subtract the previous projections
+            for j in range(i):
+                vecp = components[j].copy()
+                vec -= np.dot(unit_vecs[j], vec)*unit_vecs[j]


note, we dot the vec with the vec from the previous iteration (the projections should only get smaller and smaller)

GaelVaroquaux · 2018-07-17T20:19:53Z

Sparse PCA actually has a horrible bug.

#11585 fixes it. I don't know how it will interact with this PR.

jrmlhermitte · 2018-07-17T23:50:49Z

should be okay i think. The function computes Y from X - X.mean(axis=0) using the components, and computes the variance from this, corrected for non-orthogonal vectors supplied by components.

The test currently doesn't fit using sparse PCA. It takes in components computed from regular PCA and verifies that the variances match.

So long as the components are right, then this will be okay.
@amueller does that sound correct?

jeremiedbb · 2018-07-18T13:16:02Z

sklearn/decomposition/sparse_pca.py

@@ -98,7 +98,7 @@ def __init__(self, n_components=None, alpha=1, ridge_alpha=0.01,
        self.verbose = verbose
        self.random_state = random_state

-    def fit(self, X, y=None):
+    def fit(self, X, y=None, variance=False):


The fit method should not have any other param than X and y (and sometimes sample_weight). You have to make it a class attribute I guess.

edit: my bad, it can. However not in this case. It can only when the parameter's value depends on the data, meaning it can't be set before fitting. Here it should be a class attribute.

ok sounds good, moved to __init__

jeremiedbb · 2018-07-18T13:18:15Z

sklearn/decomposition/sparse_pca.py

@@ -109,6 +109,9 @@ def fit(self, X, y=None):

        y : Ignored

+        variance : bool, optional
+            If true, compute the explained variance
+


remove, see previous

moved this over to __init__ (for both)

jeremiedbb · 2018-07-18T13:21:17Z

sklearn/decomposition/sparse_pca.py

@@ -135,6 +138,9 @@ def fit(self, X, y=None):
                                               )
        self.components_ = Vt.T
        self.error_ = E
+        if variance:
+            self.explained_variance_ = \
+                self.get_explained_variance(self.components_, X)


if self.variance

I would name it with_explained_variance, although it's a bit long. But if it's a class attribute it should have a more informative name

I renamed to self.explained_variance_

jeremiedbb · 2018-07-18T13:22:43Z

sklearn/decomposition/sparse_pca.py

+        '''
+        # requires the mean to be subtracted
+        X = X - np.mean(X, axis=0)
+        # the number of samples


this might not be necessary after #11585 is merged.

Sounds good. I'll leave as is for now and rebase on that PR when merged (looks more important than this one right?)

It will probably be merged berfore. You can adapt you PR when it's done. Sounds good.

jeremiedbb · 2018-07-18T13:25:22Z

sklearn/decomposition/sparse_pca.py

@@ -185,6 +191,63 @@ def transform(self, X, ridge_alpha='deprecated'):
        U /= s
        return U

+    def get_explained_variance(self, components, X):
+        '''


Do we want this function to be used from outside ?
otherwise I think it should be private: _get_explained_variance

still in the optics to be a private function, you don't need to pass components to the function. You can directly access self.components_ inside the function.

renamed thanks!

jeremiedbb · 2018-07-18T13:33:48Z

sklearn/decomposition/sparse_pca.py

+        n_components = components.shape[0]
+        unit_vecs = components.copy()
+        unit_vecs = unit_vecs/np.linalg.norm(components, axis=1)[:, np.newaxis]
+


if #11585 is merged, components will be already normalized.
However there will be a deprecation cycle for that, so for a few releases you'll have to check if the attribute introduced in that PR, normalize, is false before computing it

ok, i think id rather wait and rebase, in case anything else changes, can you ping when done? (or feel free to take over if i take too long to respond!)

I checked for normalize_components and if False, subtract mean and warn. Would that work?
thanks!

jeremiedbb · 2018-07-18T13:39:03Z

sklearn/decomposition/sparse_pca.py

+        # we subtract the variance from components in the direction of previous
+        # axes
+        # the projection corrected vectors
+        proj_corrected_vecs = np.zeros_like(components)


too much verbose. I think you can remove first and last lines

removed verbosity to all lines mentioned

jeremiedbb · 2018-07-18T13:39:36Z

sklearn/decomposition/sparse_pca.py

+        # just the diagonal of the covariance of X projected to the new
+        # (component subtracted) basis
+        # Y in the new basis
+        Y = np.tensordot(X, proj_corrected_vecs.T, axes=(1, 0))


same, too much verbose

jeremiedbb · 2018-07-18T13:42:15Z

sklearn/decomposition/sparse_pca.py

@@ -265,7 +328,7 @@ def __init__(self, n_components=None, alpha=1, ridge_alpha=0.01,
        self.batch_size = batch_size
        self.shuffle = shuffle

-    def fit(self, X, y=None):
+    def fit(self, X, y=None, variance=False):


same comments as in SparsePCA

sklearn/decomposition/tests/test_sparse_pca.py

jeremiedbb · 2018-07-18T14:36:25Z

You also have to add explained_variance_ in the class docstring in attributes, and document it.

jeremiedbb · 2018-07-18T17:39:03Z

sklearn/decomposition/sparse_pca.py

@@ -77,6 +77,12 @@ class SparsePCA(BaseEstimator, TransformerMixin):
    n_iter_ : int
        Number of iterations run.

+    variance : bool, optional
+        If true, compute the explained variance
+


sorry for the miss leading. variance should be a parameter (I tend to use the word attribute for both as in C++...)

jeremiedbb · 2018-07-18T17:39:43Z

sklearn/decomposition/sparse_pca.py

@@ -135,6 +143,9 @@ def fit(self, X, y=None):
                                               )
        self.components_ = Vt.T
        self.error_ = E
+        if self.variance:
+            self.explained_variance_ = \
+                self._get_explained_variance(self.components_, X)


self._get_explained_variance(X)

jeremiedbb · 2018-07-18T17:42:16Z

sklearn/decomposition/sparse_pca.py

+        if self.variance:
+            self.explained_variance_ = \
+                self._get_explained_variance(self.components_, X)
+


self._get_explained_variance(X)

sklearn/decomposition/tests/test_sparse_pca.py

jeremiedbb · 2018-07-18T17:56:53Z

sklearn/decomposition/tests/test_sparse_pca.py

+    explained_variance = pca.explained_variance_
+    spca_lars.components_ = components
+    explained_variance_sparse = spca_lars.explained_variance_
+


hum, I misunderstood what you're doing.
You just want to assert that your function ̀_get_explained_variance returns the same result as in PCA if given same X and same components, right ?
Maybe you can add a comment before line 96 explaining that.

And I guess you have to do explained_variance_sparse = spca_lars._get_explained_variance_(Y)

Is it possible to make a test checking that the explained_variance_ computed with the components fitted by SparsePCA are correct ? maybe something like comparing explained_variance_ between PCA and SparsePCA with sparsity=0 ?

oops yes, it should be a function call. I also changed Y to X. i copied and pasted form a previous test. it could have been Y because maybe it was copied from another test that compared two feature vectors?

jeremiedbb · 2018-07-18T17:59:52Z

Also, you forgot to add variance in the init of MiniBatchSparsePCA. It should be in the super statement.

jeremiedbb · 2018-07-18T19:33:23Z

lgtm. Now I think we should wait #11585 to be merged.

jeremiedbb · 2018-07-18T19:39:30Z

sklearn/decomposition/sparse_pca.py

@@ -135,6 +143,8 @@ def fit(self, X, y=None):
                                               )
        self.components_ = Vt.T
        self.error_ = E
+        if self.variance:
+            self.explained_variance_ = self._get_explained_variance(X)


sorry one more thing. You should add

else: self.explained_variance_ = None

otherwise you'd get an attribute error if calling estimator.explained_variance afterwards.

and you can add a test which checks that when variance is False, explained_variance_ is not computed.

added thanks! one random question, i see in your PR, you added to "doc/whats_new/v0.20.rst"
should I be adding the same to a similar file? (and which?)

Yes you'll have to add it in the what's new. But I don't know if your PR will be in the 0.20 release. Let it as is for now and we'll fill the right what's new as soon as we know.

jeremiedbb · 2018-07-18T19:41:47Z

sklearn/decomposition/sparse_pca.py

@@ -77,6 +80,9 @@ class SparsePCA(BaseEstimator, TransformerMixin):
    n_iter_ : int
        Number of iterations run.

+    explained_variance_ : array, [n_components]
+        The explained variance versus component
+


add that it's only computed if variance is set to true

kimrants · 2018-07-20T14:06:24Z

When is this expected to be released? :)
Thanks!

jeremiedbb · 2018-07-20T14:11:03Z

We are waiting for another PR to be merged first.
Also it's not been reviewed by core devs yet.

So I can't tell but it will probably not be in the 0.20 release.

jrmlhermitte · 2018-07-21T14:34:48Z

I rebased and force pushed (but kept a local copy of my branch before rebase in case anything went wrong). Let me know what you think thanks!

jeremiedbb · 2018-07-23T11:42:58Z

sklearn/decomposition/sparse_pca.py

+        if not self.normalize_components:
+            X = X - np.mean(X, axis=0)
+            warnings.warn("normalize_components=False is a "
+                          "backward-compatible setting that implements a "


I wouldn't raise a warning here. The reason is that if someone calls SparsePCA with normalize_components=False, he will already get a warning in fit. No need for duplicate warning.

Instead, you could comment that this test should be removed in version 0.22.

sounds good! removed

jeremiedbb · 2018-07-23T11:47:47Z

sklearn/decomposition/sparse_pca.py

+        n_components = components.shape[0]
+        unit_vecs = components.copy()
+        unit_vecs = unit_vecs/np.linalg.norm(components, axis=1)[:, np.newaxis]
+


Correct me if I'm wrong but you should also normalize the components here, depending on normalize_components.

no, and this is tricky now. i will elaborate in a comment further below

jeremiedbb · 2018-07-23T11:54:09Z

sklearn/decomposition/sparse_pca.py

@@ -105,8 +112,9 @@ class SparsePCA(BaseEstimator, TransformerMixin):
    def __init__(self, n_components=None, alpha=1, ridge_alpha=0.01,
                 max_iter=1000, tol=1e-8, method='lars', n_jobs=1, U_init=None,
                 V_init=None, verbose=False, random_state=None,
-                 normalize_components=False):
+                 normalize_components=False, variance=False):


I'm wondering if we could make it True by default. Is _get_explained_variance computation intensive ? I mean versus SparsePCA.fit.

Also, I think variance is not enough informative. We could think of a better name. If I recall your first idea was with_variance. I think it's better than this one. Maybe core reviewers will have a better opinion on that.

made to True, I agree it makes sense

jeremiedbb · 2018-07-23T12:02:26Z

sklearn/decomposition/sparse_pca.py

+            ----------
+            X : 2D np.ndarray
+                The feature vector. Must be shape m x n where m is the number
+                of samples and n is the dimension of the incoming feature


Here I think the common accepted way is

X : ndarray, shape (n_samples, n_features)

done for all i can find, thanks!

jeremiedbb · 2018-07-23T12:04:29Z

sklearn/decomposition/sparse_pca.py

@@ -81,6 +81,9 @@ class SparsePCA(BaseEstimator, TransformerMixin):
           backward compatibility. It would be set to ``True`` from 0.22
           onwards.

+    variance : bool, optional
+        If true, this will compute the explained variance versus component.
+


Please state the default value
variance : boolean, optional (default=False)

done thanks!

jeremiedbb · 2018-07-23T12:04:55Z

sklearn/decomposition/sparse_pca.py

@@ -300,6 +365,9 @@ class MiniBatchSparsePCA(SparsePCA):
           backward compatibility. It would be set to ``True`` from 0.22
           onwards.

+    variance : bool, optional
+        If true, this will compute the explained variance versus component.
+


jeremiedbb · 2018-07-23T12:06:44Z

sklearn/decomposition/sparse_pca.py

@@ -96,6 +99,10 @@ class SparsePCA(BaseEstimator, TransformerMixin):
        Per-feature empirical mean, estimated from the training set.
        Equal to ``X.mean(axis=0)``.

+    explained_variance_ : array, [n_components]
+        The explained variance versus component


array, shape (n_components,)

jeremiedbb · 2018-07-23T12:09:50Z

sklearn/decomposition/sparse_pca.py

@@ -312,6 +380,10 @@ class MiniBatchSparsePCA(SparsePCA):
        Per-feature empirical mean, estimated from the training set.
        Equal to ``X.mean(axis=0)``.

+    explained_variance_ : array, [n_components]
+        The explained variance versus component.


array, shape (n_components,)

jeremiedbb · 2018-07-23T12:23:59Z

also it might be a good idea to test that explained_variance is the same whether normalize_components is True or False.

jeremiedbb · 2018-07-23T12:24:49Z

tests are failing because now warnings are raised as errors.
you can add
@pytest.mark.filterwarnings('ignore: msg')
where msg is a part of the warning message you want to catch. Here it could be 'normalize_components'

jrmlhermitte · 2018-07-24T03:44:18Z

Thanks @jeremiedbb for the input. I have made the changes, but I have a few questions:

The latest PR now normalizes the components. In normalizing the components, you lose the possibility to retrieve the variance. Is this a convention adopted by regular PCA? It doesn't seem to normalize them by default but I could be wrong. Anyway, this requires that the variance be computed internally before the components are normalized. (i.e. there is an ordering to when the functions should be called) I guess this should be fine since what computes the variance is a private function.
The normalize_components flag also does mean subtraction. Seems like PCA just did this by default though so it should do the same. This just requires being careful with writing the test (had to mean subtract the features before computing the variance)

jeremiedbb · 2018-07-25T11:13:27Z

In normalizing the components, you lose the possibility to retrieve the variance.

I don't understand what you mean. When you compute the explained variance, you begin with normalizing the components.

It doesn't seem to normalize them by default but I could be wrong.

Actually I think it does. In PCA, the components are computed using svd, which returns a unitary matrix.

Anyway, this requires that the variance be computed internally before the components are normalized.

Indeed, so I think you should call _get_explained_variance right after the component's normalization.

jeremiedbb · 2018-07-25T11:14:40Z

sklearn/decomposition/sparse_pca.py

        self.n_components = n_components
+        self._compute_variance = compute_variance


why the underscore ? this is not private.

jrmlhermitte · 2018-07-25T12:10:38Z

@jeremiedbb thanks. One way to compute the variance is to extract the diagonal of Y dot Y.T. This matrix is the matrix of components and it cannot be normalized.
in _get_explained_variance, the components are normalized just to subtract the projections from each component. Note that both the unit_vecs (which are normalized components) and the components matrices are used in this calculation (where components has not been normalized yet)

In SVD, I think it doesn't matter because we use the S matrix to compute the variance. Note that we don't have such an equivalent here.

This is explained on p 273 here.
An alternative to this approach is to perform QR decomposition. I could replace this for loop with that. I need to double check and test though later. Would that maybe be cleaner?

jeremiedbb · 2018-07-25T12:23:28Z

Thanks for the clarification. I missed that you needed both components and the corresponding unit vectors. So I think it's fine as it is.

I guess this should be fine since what computes the variance is a private function.

Agreed

jrmlhermitte · 2018-07-25T13:16:17Z

Great thanks! Do we need to ping anyone else to look at it now?

jeremiedbb · 2018-07-25T13:27:01Z

sklearn/decomposition/sparse_pca.py

@@ -361,6 +434,7 @@ def fit(self, X, y=None):
                          "compatibility mode will be removed in 0.22.",
                          DeprecationWarning)

+        self.n_samples = X.shape[0]


Where does that come from ?
you don't seem to use it anywhere.

oops yes this is vestigial code from a previous attempt

jeremiedbb · 2018-07-25T13:29:17Z

Sure !
you need to make the tests green first. Reviewers are reluctant when tests are red :)
(my last comment should make them green)

jrmlhermitte · 2018-07-25T18:26:37Z

ok thanks! submitted change, waiting..

jeremiedbb · 2018-07-25T19:25:05Z

Looks good !

@GaelVaroquaux @agramfort @glemaitre you might be interested in reviewing this, since you were recently involved in SparsePCA :)
(if not could you tag this as needs review ?)

jnothman · 2018-07-26T12:11:58Z

sklearn/decomposition/sparse_pca.py

@@ -81,9 +81,12 @@ class SparsePCA(BaseEstimator, TransformerMixin):
           backward compatibility. It would be set to ``True`` from 0.22
           onwards.

+    compute_variance : bool, optional (default=True)
+        If true, this will compute the explained variance versus component.


versus -> per

thanks, changed

jnothman · 2018-07-26T12:12:41Z

sklearn/decomposition/sparse_pca.py

        Per-feature empirical mean, estimated from the training set.
        Equal to ``X.mean(axis=0)``.

+    explained_variance_ : array, shape (n_components, )
+        The explained variance versus component


Versus -> per.
End the line with a full stop, please

you mean "."? Sorry not familiar with the word, thanks!

jnothman · 2018-07-26T12:13:00Z

sklearn/decomposition/sparse_pca.py

@@ -231,6 +245,57 @@ def transform(self, X, ridge_alpha='deprecated'):

        return U

+    def _get_explained_variance(self, X):
+        '''
+            Get the explained variance from the principal components of the


Descent please

ah yes, line too long, following doctstring convention of makinga new line with extra description, thanks

jnothman · 2018-07-26T13:33:14Z

sklearn/decomposition/sparse_pca.py

@@ -231,6 +245,57 @@ def transform(self, X, ridge_alpha='deprecated'):

        return U

+    def _get_explained_variance(self, X):


This seems to be a generalised approach? Perhaps pull this out into a module-level function taking X and components

yes, it should work for PCA as well (although not tested)
made a module, for discussion

jnothman · 2018-07-26T13:37:03Z

sklearn/decomposition/sparse_pca.py

+        n_samples = X.shape[0]
+        n_components = components.shape[0]
+        unit_vecs = components.copy()
+        components_norm = \


We tend to avoid this kind of line continuation and prefer breaking after a comma within parentheses

removed these awkward indents, thanks!

jnothman · 2018-07-26T13:39:49Z

sklearn/decomposition/tests/test_sparse_pca.py

+@pytest.mark.parametrize("norm_comp", [False, True])
+def test_fit_transform_variance(norm_comp):
+    '''
+        This function asserts that the variance computed by SparsePCA is the


We use comments rather than docstrings in tests (although mostly for historical reasons)

changed to comments, thanks!

jnothman · 2018-07-26T13:41:01Z

sklearn/decomposition/sparse_pca.py

@@ -300,18 +365,25 @@ class MiniBatchSparsePCA(SparsePCA):
           backward compatibility. It would be set to ``True`` from 0.22
           onwards.

+    compute_variance : bool, optional (default=True)


Do we need this to be a parameter? How costly is it relative to the sparse PCA?

i don't think it is, it's just vectorized products. it could be costly, when maybe running this in a loop though. i have removed it for now. we can perhaps add this in in a future issue if someone is discontent?

jrmlhermitte · 2018-07-30T18:54:15Z

@jeremiedbb what about the release notes, should I add some now?

jeremiedbb · 2018-07-30T20:45:28Z

Well there is no what's new for the 0.21 yet and I'm really not sure it will be reviewed (and approved) before the release.

You might have to let it as is until the release and then ping some guys for the review once they have a bit more time...

jrmlhermitte · 2018-08-14T00:51:12Z

ok sounds good thanks!

jrmlhermitte · 2018-09-15T19:15:57Z

rebased. just checking in

jnothman

Not a full review

sklearn/decomposition/sparse_pca.py

banilo · 2019-02-27T16:25:44Z

sklearn/decomposition/tests/test_sparse_pca.py

+    explained_variance = pca.explained_variance_
+
+    # force the components in spca_lars to be the same as in pca
+    spca_lars.components_ = pca.components_


How about a string version of that test that first applies QR-decomposition on spca_lars.components_ and then computes and compares the explained variances against PCA's output?

I assume by that you mean something like this:

# Force matrix to be orthogonal. sparse PCA must then be the same as PCA. X_orthogonal, R = np.linalg.qr(X) spca_lars.fit(X_orthogonal) pca.fit(X_orthogonal) explained_variance = pca.explained_variance_ explained_variance_sparse = _get_explained_variance( X_orthogonal, spca_lars.components_)

I would have assumed this to work but it does not. I will not add it. I don't have time to update it (I'm working in a completely different field). I suggest to either:

make correction here

add commit to this PR

we can close it and someone else continue it

make an issue to add this test

What do you think? I apologize for my latency. It is very hard for me to step into the open source world right now.
If i have free time I'll try to review and think about this later.

Yep, this goes into the direction I had in mind. Would be a nice option for a more careful test if feasible.

adrinjalali · 2019-03-02T18:35:01Z

sklearn/decomposition/sparse_pca.py

+
+    References
+    ----------
+    [1] Journal of Computational and Graphical Statistics, Volume 15, Number 2,


I think the rst syntax is .. [1]

jrmlhermitte · 2019-06-19T22:02:28Z

@adrinjalali I took a look and it looks like it needed to be rebased. looks like some things changed along the way.
Can we finish this or close this? This is growing stale. thanks

cmarmo · 2020-01-14T08:19:09Z

Can we finish this or close this? This is growing stale. thanks

@jrmlhermitte , it's up to you.... :) ... but it seems to me that with already one approval it is worth to finish it. Would you try to resolve conflicts and sync to master?
If you really feel that you haven't the time to work on it, we can put it in the sprint list: branching from your PR as your work will not get lost.

ogrisel · 2020-08-11T14:55:45Z

This was taken over by #16255 which was closed because the concept of component-wise explained variance is not well defined when the components are not orthogonal.

amueller added the help wanted label Jul 15, 2018

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feat(sparse_pca): Add explained variance to sparse PCA

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jrmlhermitte force-pushed the sparse_pca_variance branch from 84d7206 to 0d80178 Compare June 19, 2019 22:00

glemaitre self-requested a review June 20, 2019 14:23

Batalex mentioned this pull request Jan 28, 2020

[MRG] Adding explained variances to sparse pca #16255

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github-actions bot added the module:decomposition label Mar 2, 2020

cmarmo removed the help wanted label Jun 12, 2020

cmarmo added the Superseded PR has been replace by a newer PR label Jul 10, 2020

ogrisel closed this Aug 11, 2020

		self.n_components = n_components
		self._compute_variance = compute_variance

		@@ -231,6 +245,57 @@ def transform(self, X, ridge_alpha='deprecated'):

		return U

		def _get_explained_variance(self, X):

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Adding explained variances to sparse pca #11527

Adding explained variances to sparse pca #11527

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jrmlhermitte commented Jul 15, 2018

Reference Issues/PRs

What does this implement/fix? Explain your changes.

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amueller commented Jul 15, 2018

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jrmlhermitte commented Jul 16, 2018

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jeremiedbb commented Jul 18, 2018

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jeremiedbb commented Jul 18, 2018

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jeremiedbb commented Jul 18, 2018

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jeremiedbb Jul 18, 2018 •

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