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MNT Avoid catastrophic cancellation in mean_variance_axis #19766

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ogrisel merged 8 commits into from
Mar 31, 2021
Merged

MNT Avoid catastrophic cancellation in mean_variance_axis #19766

ogrisel merged 8 commits into from
Mar 31, 2021

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@jeremiedbb jeremiedbb commented Mar 25, 2021 •
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Fixes #19546

Fixes the unexpected lack of precision of the variance when input is sparse, with weights, and when the variance should actually be 0, as described here #19450 (comment)

With this PR the result is 0 as expected

import numpy as np
from scipy.sparse import csr_matrix
from sklearn.utils.sparsefuncs import mean_variance_axis
n_samples = 100
sw = np.random.rand(n_samples)
X = np.zeros(shape=(n_samples, 2))
X[:, 1] = 1.

mean_variance_axis(csr_matrix(X), axis=0, weights=sw)[1]
# array([0., 0.])

@jeremiedbb jeremiedbb mentioned this pull request Mar 25, 2021
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@ogrisel ogrisel self-requested a review March 26, 2021 14:41
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ogrisel commented Mar 26, 2021

Possibly related to #19546?

@jeremiedbb jeremiedbb changed the title MNT Improve precision of variance on sparse input with weights [WIP] MNT Improve precision of variance on sparse input with weights Mar 26, 2021
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jeremiedbb commented Mar 26, 2021

Possibly related to #19546?

Absolutely. It aims to solve the same issue. However, it turns out that it's still not as precise as the dense case. I'm digging further :)

@jeremiedbb jeremiedbb changed the title [WIP] MNT Improve precision of variance on sparse input with weights MNT Avoid catastrophic cancellation in mean_variance_axis Mar 29, 2021
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jeremiedbb commented Mar 29, 2021

I reworked the PR to focus on the catastrophic cancellation described in #19546, caused by variances[i] += (sum_weights[i] - sum_weights_nz[i]) * means[i]**2. The precision is now comparable the dense case one. Here are the results of the gist linked in #19546 with various rng.

## dtype=float64
_incremental_mean_and_var [100.] [0.]
csr_mean_variance_axis0 [100.] [7.2701421e-27]
incr_mean_variance_axis0 csr [100.] [7.2701421e-27]
csc_mean_variance_axis0 [100.] [7.2701421e-27]
incr_mean_variance_axis0 csc [100.] [7.2701421e-27]
## dtype=float32
_incremental_mean_and_var [100.00000577] [3.32692735e-11]
csr_mean_variance_axis0 [99.99997] [9.3132246e-10]
incr_mean_variance_axis0 csr [99.99997] [9.3132246e-10]
csc_mean_variance_axis0 [99.99997] [9.3132246e-10]
incr_mean_variance_axis0 csc [99.99997] [9.3132246e-10]

## dtype=float64
_incremental_mean_and_var [100.] [0.]
csr_mean_variance_axis0 [100.] [0.]
incr_mean_variance_axis0 csr [100.] [0.]
csc_mean_variance_axis0 [100.] [0.]
incr_mean_variance_axis0 csc [100.] [0.]
## dtype=float32
_incremental_mean_and_var [99.99999932] [4.66211111e-13]
csr_mean_variance_axis0 [99.99993] [4.7148196e-09]
incr_mean_variance_axis0 csr [99.99993] [4.7148196e-09]
csc_mean_variance_axis0 [99.99993] [4.7148196e-09]
incr_mean_variance_axis0 csc [99.99993] [4.7148196e-09]

## dtype=float64
_incremental_mean_and_var [100.] [2.01948392e-28]
csr_mean_variance_axis0 [100.] [1.81753553e-27]
incr_mean_variance_axis0 csr [100.] [1.81753553e-27]
csc_mean_variance_axis0 [100.] [1.81753553e-27]
incr_mean_variance_axis0 csc [100.] [1.81753553e-27]
## dtype=float32
_incremental_mean_and_var [99.99999692] [9.51546741e-12]
csr_mean_variance_axis0 [100.] [0.]
incr_mean_variance_axis0 csr [100.] [0.]
csc_mean_variance_axis0 [100.] [0.]
incr_mean_variance_axis0 csc [100.] [0.]

ogrisel
ogrisel approved these changes Mar 29, 2021
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Very nice fix @jeremiedbb! I assume this code has changed too much in main to consider a backport for 0.24.2, but this is fine with me.

@ogrisel ogrisel added this to the 1.0 milestone Mar 29, 2021
thomasjpfan
thomasjpfan reviewed Mar 30, 2021
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sklearn/utils/sparsefuncs_fast.pyx
np.ndarray[floating, ndim=1] sum_weights_nz = \
np.zeros(shape=n_features, dtype=dtype)

np.ndarray[np.uint64_t, ndim=1] counts = np.full(
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A more explicit name:

Suggested change
np.ndarray[np.uint64_t, ndim=1] counts = np.full(
np.ndarray[np.uint64_t, ndim=1] counts_nan = np.full(

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sum_weights is the sum of all weights where X is not nan
sum_weights_nan is the sum of weights where X is nan
sum_weights_nz is the sum of weights where X is non zero

Following the same scheme:
counts is the number of elements which are not nan
counts_nz is the number of elements which are non zero

I'd rather keep that. Maybe you missed that the increment is negative (counts[col_ind] -= 1).
Let me try to reorder the code such that the match is clearer (and remove sum_weights_nan, we actually need only 2 out the 3 arrays).

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@thomasjpfan thomasjpfan Mar 30, 2021 •
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Yes I was mistaken with the suggestion. I was thinking about the negation of it, so it the suggestion should have been counts_non_nan.

If we do not change the name, I think we should at least put a comment above counts to say that it is the number of elements which are not nan.

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I added comments to describe the different arrays

@jeremiedbb jeremiedbb mentioned this pull request Mar 30, 2021
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ogrisel commented Mar 30, 2021

@thomasjpfan merge?

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LGTM!

Maybe @ogrisel should look this over one more time because removing sum_weights_nan is a semi-significant change from his last approval.

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I gave it another look and LGTM. Let's merge!

@ogrisel ogrisel merged commit 57d3668 into scikit-learn:main Mar 31, 2021
@glemaitre glemaitre mentioned this pull request Apr 22, 2021
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Weighted variance computation for sparse data is not numerically stable

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