Merge pull request #108 from kilianFatras/master

[MRG] Fix log and nbiter bug in gromov_wasserstein and gromov_wasserstein2

Author: rflamary

ot/gromov.py

@@ -276,7 +276,6 @@ def gromov_wasserstein(C1, C2, p, q, loss_fun, log=False, armijo=False, **kwargs
     - p  : distribution in the source space
     - q  : distribution in the target space
     - L  : loss function to account for the misfit between the similarity matrices
-    - H  : entropy
 
     Parameters
     ----------
@@ -343,6 +342,83 @@ def df(G):
         return cg(p, q, 0, 1, f, df, G0, armijo=armijo, C1=C1, C2=C2, constC=constC, **kwargs)
 
 
+def gromov_wasserstein2(C1, C2, p, q, loss_fun, log=False, armijo=False, **kwargs):
+    """
+    Returns the gromov-wasserstein discrepancy between (C1,p) and (C2,q)
+
+    The function solves the following optimization problem:
+
+    .. math::
+        GW = \min_T \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}
+
+    Where :
+    - C1 : Metric cost matrix in the source space
+    - C2 : Metric cost matrix in the target space
+    - p  : distribution in the source space
+    - q  : distribution in the target space
+    - L  : loss function to account for the misfit between the similarity matrices
+
+    Parameters
+    ----------
+    C1 : ndarray, shape (ns, ns)
+        Metric cost matrix in the source space
+    C2 : ndarray, shape (nt, nt)
+        Metric cost matrix in the target space
+    p : ndarray, shape (ns,)
+        Distribution in the source space.
+    q :  ndarray, shape (nt,)
+        Distribution in the target space.
+    loss_fun :  str
+        loss function used for the solver either 'square_loss' or 'kl_loss'
+    max_iter : int, optional
+        Max number of iterations
+    tol : float, optional
+        Stop threshold on error (>0)
+    verbose : bool, optional
+        Print information along iterations
+    log : bool, optional
+        record log if True
+    armijo : bool, optional
+        If True the steps of the line-search is found via an armijo research. Else closed form is used.
+        If there is convergence issues use False.
+
+    Returns
+    -------
+    gw_dist : float
+        Gromov-Wasserstein distance
+    log : dict
+        convergence information and Coupling marix
+
+    References
+    ----------
+    .. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,
+        "Gromov-Wasserstein averaging of kernel and distance matrices."
+        International Conference on Machine Learning (ICML). 2016.
+
+    .. [13] Mémoli, Facundo. Gromov–Wasserstein distances and the
+        metric approach to object matching. Foundations of computational
+        mathematics 11.4 (2011): 417-487.
+
+    """
+
+    constC, hC1, hC2 = init_matrix(C1, C2, p, q, loss_fun)
+
+    G0 = p[:, None] * q[None, :]
+
+    def f(G):
+        return gwloss(constC, hC1, hC2, G)
+
+    def df(G):
+        return gwggrad(constC, hC1, hC2, G)
+    res, log_gw = cg(p, q, 0, 1, f, df, G0, log=True, armijo=armijo, C1=C1, C2=C2, constC=constC, **kwargs)
+    log_gw['gw_dist'] = gwloss(constC, hC1, hC2, res)
+    log_gw['T'] = res
+    if log:
+        return log_gw['gw_dist'], log_gw
+    else:
+        return log_gw['gw_dist']
+
+
 def fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5, armijo=False, log=False, **kwargs):
     """
     Computes the FGW transport between two graphs see [24]
@@ -506,84 +582,6 @@ def df(G):
         return log['fgw_dist']
 
 
-def gromov_wasserstein2(C1, C2, p, q, loss_fun, log=False, armijo=False, **kwargs):
-    """
-    Returns the gromov-wasserstein discrepancy between (C1,p) and (C2,q)
-
-    The function solves the following optimization problem:
-
-    .. math::
-        GW = \min_T \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}
-
-    Where :
-    - C1 : Metric cost matrix in the source space
-    - C2 : Metric cost matrix in the target space
-    - p  : distribution in the source space
-    - q  : distribution in the target space
-    - L  : loss function to account for the misfit between the similarity matrices
-    - H  : entropy
-
-    Parameters
-    ----------
-    C1 : ndarray, shape (ns, ns)
-        Metric cost matrix in the source space
-    C2 : ndarray, shape (nt, nt)
-        Metric cost matrix in the target space
-    p : ndarray, shape (ns,)
-        Distribution in the source space.
-    q :  ndarray, shape (nt,)
-        Distribution in the target space.
-    loss_fun :  str
-        loss function used for the solver either 'square_loss' or 'kl_loss'
-    max_iter : int, optional
-        Max number of iterations
-    tol : float, optional
-        Stop threshold on error (>0)
-    verbose : bool, optional
-        Print information along iterations
-    log : bool, optional
-        record log if True
-    armijo : bool, optional
-        If True the steps of the line-search is found via an armijo research. Else closed form is used.
-        If there is convergence issues use False.
-
-    Returns
-    -------
-    gw_dist : float
-        Gromov-Wasserstein distance
-    log : dict
-        convergence information and Coupling marix
-
-    References
-    ----------
-    .. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,
-        "Gromov-Wasserstein averaging of kernel and distance matrices."
-        International Conference on Machine Learning (ICML). 2016.
-
-    .. [13] Mémoli, Facundo. Gromov–Wasserstein distances and the
-        metric approach to object matching. Foundations of computational
-        mathematics 11.4 (2011): 417-487.
-
-    """
-
-    constC, hC1, hC2 = init_matrix(C1, C2, p, q, loss_fun)
-
-    G0 = p[:, None] * q[None, :]
-
-    def f(G):
-        return gwloss(constC, hC1, hC2, G)
-
-    def df(G):
-        return gwggrad(constC, hC1, hC2, G)
-    res, log = cg(p, q, 0, 1, f, df, G0, log=True, armijo=armijo, C1=C1, C2=C2, constC=constC, **kwargs)
-    log['gw_dist'] = gwloss(constC, hC1, hC2, res)
-    log['T'] = res
-    if log:
-        return log['gw_dist'], log
-    else:
-        return log['gw_dist']
-
-
 def entropic_gromov_wasserstein(C1, C2, p, q, loss_fun, epsilon,
                                 max_iter=1000, tol=1e-9, verbose=False, log=False):
     """

ot/optim.py

@@ -134,7 +134,7 @@ def solve_linesearch(cost, G, deltaG, Mi, f_val,
     return alpha, fc, f_val
 
 
-def cg(a, b, M, reg, f, df, G0=None, numItermax=200,
+def cg(a, b, M, reg, f, df, G0=None, numItermax=200, numItermaxEmd=100000,
        stopThr=1e-9, stopThr2=1e-9, verbose=False, log=False, **kwargs):
     """
     Solve the general regularized OT problem with conditional gradient
@@ -172,6 +172,8 @@ def cg(a, b, M, reg, f, df, G0=None, numItermax=200,
         initial guess (default is indep joint density)
     numItermax : int, optional
         Max number of iterations
+    numItermaxEmd : int, optional
+        Max number of iterations for emd
     stopThr : float, optional
         Stop threshol on the relative variation (>0)
     stopThr2 : float, optional
@@ -238,7 +240,7 @@ def cost(G):
         Mi += Mi.min()
 
         # solve linear program
-        Gc = emd(a, b, Mi)
+        Gc = emd(a, b, Mi, numItermax=numItermaxEmd)
 
         deltaG = Gc - G
 

test/test_gromov.py

@@ -44,10 +44,14 @@ def test_gromov():
 
     gw, log = ot.gromov.gromov_wasserstein2(C1, C2, p, q, 'kl_loss', log=True)
 
+    gw_val = ot.gromov.gromov_wasserstein2(C1, C2, p, q, 'kl_loss', log=False)
+
     G = log['T']
 
     np.testing.assert_allclose(gw, 0, atol=1e-1, rtol=1e-1)
 
+    np.testing.assert_allclose(gw, gw_val, atol=1e-1, rtol=1e-1)  # cf log=False
+
     # check constratints
     np.testing.assert_allclose(
         p, G.sum(1), atol=1e-04)  # cf convergence gromov

test/test_optim.py

@@ -37,6 +37,39 @@ def df(G):
     np.testing.assert_allclose(b, G.sum(0))
 
 
+def test_conditional_gradient2():
+    n = 4000  # nb samples
+
+    mu_s = np.array([0, 0])
+    cov_s = np.array([[1, 0], [0, 1]])
+
+    mu_t = np.array([4, 4])
+    cov_t = np.array([[1, -.8], [-.8, 1]])
+
+    xs = ot.datasets.make_2D_samples_gauss(n, mu_s, cov_s)
+    xt = ot.datasets.make_2D_samples_gauss(n, mu_t, cov_t)
+
+    a, b = np.ones((n,)) / n, np.ones((n,)) / n
+
+    # loss matrix
+    M = ot.dist(xs, xt)
+    M /= M.max()
+
+    def f(G):
+        return 0.5 * np.sum(G**2)
+
+    def df(G):
+        return G
+
+    reg = 1e-1
+
+    G, log = ot.optim.cg(a, b, M, reg, f, df, numItermaxEmd=200000,
+                         verbose=True, log=True)
+
+    np.testing.assert_allclose(a, G.sum(1))
+    np.testing.assert_allclose(b, G.sum(0))
+
+
 def test_generalized_conditional_gradient():
 
     n_bins = 100  # nb bins