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[MRG] Implement Sinkhorn in log-domain for WDA #336

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Merged
rflamary merged 4 commits into from
Jan 21, 2022
Merged

[MRG] Implement Sinkhorn in log-domain for WDA #336

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65ba51a
[MRG] Implement Sinkhorn in log-domain for WDA
Jan 17, 2022
76bdbfd
Add feature to RELEASES and contributor name
Jan 18, 2022
71b0ef6
Merge branch 'master' into log-sinkhorn-wda
rflamary Jan 20, 2022
1c72560
Add 'sinkhorn_method' parameter to WDA
Jan 20, 2022
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[MRG] Implement Sinkhorn in log-domain for WDA 
* for small values of the regularization parameter (reg) the current implementation runs into numerical issues (nans and infs)

* this can be resolved by using log-domain implementation of the sinkhorn algorithm
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Jakub Zadrożny committed Jan 17, 2022
commit 65ba51ae79c89c5fb0e1f2163a6999d3cfcd8d62
23 changes: 16 additions & 7 deletions ot/dr.py
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Original file line number Diff line number Diff line change
Expand Up @@ -30,16 +30,25 @@ def dist(x1, x2):
return x1p2.reshape((-1, 1)) + x2p2.reshape((1, -1)) - 2 * np.dot(x1, x2.T)


def logsumexp(M, axis):
r"""Log-sum-exp reduction compatible with autograd (no numpy implementation)
"""
amax = np.amax(M, axis=axis, keepdims=True)
return np.log(np.sum(np.exp(M - amax), axis=axis)) + np.squeeze(amax, axis=axis)
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def sinkhorn(w1, w2, M, reg, k):
r"""Sinkhorn algorithm with fixed number of iteration (autograd)
r"""Sinkhorn algorithm in log-domain with fixed number of iteration (autograd)
"""
K = np.exp(-M / reg)
ui = np.ones((M.shape[0],))
vi = np.ones((M.shape[1],))
Mr = -M / reg
ui = np.zeros((M.shape[0],))
vi = np.zeros((M.shape[1],))
log_w1 = np.log(w1)
log_w2 = np.log(w2)
for i in range(k):
vi = w2 / (np.dot(K.T, ui))
ui = w1 / (np.dot(K, vi))
G = ui.reshape((M.shape[0], 1)) * K * vi.reshape((1, M.shape[1]))
vi = log_w2 - logsumexp(Mr + ui[:, None], 0)
ui = log_w1 - logsumexp(Mr + vi[None, :], 1)
G = np.exp(ui[:, None] + Mr + vi[None, :])
return G


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22 changes: 22 additions & 0 deletions test/test_dr.py
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Expand Up @@ -60,6 +60,28 @@ def test_wda():
np.testing.assert_allclose(np.sum(Pwda**2, 0), np.ones(p))


@pytest.mark.skipif(nogo, reason="Missing modules (autograd or pymanopt)")
def test_wda_low_reg():

n_samples = 100 # nb samples in source and target datasets
np.random.seed(0)

# generate gaussian dataset
xs, ys = ot.datasets.make_data_classif('gaussrot', n_samples)

n_features_noise = 8

xs = np.hstack((xs, np.random.randn(n_samples, n_features_noise)))

p = 2

Pwda, projwda = ot.dr.wda(xs, ys, p, reg=0.01, maxiter=10)

projwda(xs)

np.testing.assert_allclose(np.sum(Pwda**2, 0), np.ones(p))


@pytest.mark.skipif(nogo, reason="Missing modules (autograd or pymanopt)")
def test_wda_normalized():

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