add sgd

Author: Kilian Fatras

README.md

@@ -22,6 +22,7 @@ It provides the following solvers:
 * Linear OT [14] and Joint OT matrix and mapping estimation [8].
 * Wasserstein Discriminant Analysis [11] (requires autograd + pymanopt).
 * Gromov-Wasserstein distances and barycenters ([13] and regularized [12])
+* Stochastic Optimization for Large-scale Optimal Transport (semi-dual problem [18] and dual problem [19])
 
 Some demonstrations (both in Python and Jupyter Notebook format) are available in the examples folder.
 
@@ -149,6 +150,7 @@ The contributors to this library are:
 * [Stanislas Chambon](https://slasnista.github.io/)
 * [Antoine Rolet](https://arolet.github.io/)
 * Erwan Vautier (Gromov-Wasserstein)
+* [Kilian Fatras](https://kilianfatras.github.io/) (Stochastic optimization)
 
 This toolbox benefit a lot from open source research and we would like to thank the following persons for providing some code (in various languages):
 
@@ -213,3 +215,9 @@ You can also post bug reports and feature requests in Github issues. Make sure t
 [15] Peyré, G., & Cuturi, M. (2018). [Computational Optimal Transport](https://arxiv.org/pdf/1803.00567.pdf) .
 
 [16] Agueh, M., & Carlier, G. (2011). [Barycenters in the Wasserstein space](https://hal.archives-ouvertes.fr/hal-00637399/document). SIAM Journal on Mathematical Analysis, 43(2), 904-924.
+
+[17] Blondel, M., Seguy, V., & Rolet, A. (2018). [Smooth and Sparse Optimal Transport](https://arxiv.org/pdf/1710.06276.pdf). Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (AISTATS).
+
+[18] Genevay, A., Cuturi, M., Peyré, G. & Bach, F. (2016) [Stochastic Optimization for Large-scale Optimal Transport](arXiv preprint arxiv:1605.08527). Advances in Neural Information Processing Systems (2016).
+
+[19] Seguy, V., Bhushan Damodaran, B., Flamary, R., Courty, N., Rolet, A.& Blondel, M. [Large-scale Optimal Transport and Mapping Estimation](https://arxiv.org/pdf/1711.02283.pdf). International Conference on Learning Representation (2018)

examples/plot_stochastic.py

@@ -18,9 +18,9 @@
 
 
 #############################################################################
-# COMPUTE TRANSPORTATION MATRIX
+# COMPUTE TRANSPORTATION MATRIX FOR SEMI-DUAL PROBLEM
 #############################################################################
-
+print("------------SEMI-DUAL PROBLEM------------")
 #############################################################################
 # DISCRETE CASE
 # Sample two discrete measures for the discrete case
@@ -48,12 +48,12 @@
 # Call the "SAG" method to find the transportation matrix in the discrete case
 # ---------------------------------------------
 #
-# Define the method "SAG", call ot.transportation_matrix_entropic and plot the
+# Define the method "SAG", call ot.solve_semi_dual_entropic and plot the
 # results.
 
 method = "SAG"
-sag_pi = ot.stochastic.transportation_matrix_entropic(a, b, M, reg, method,
-                                                      numItermax, lr)
+sag_pi = ot.stochastic.solve_semi_dual_entropic(a, b, M, reg, method,
+                                             numItermax, lr)
 print(sag_pi)
 
 #############################################################################
@@ -68,8 +68,9 @@
 n_source = 7
 n_target = 4
 reg = 1
-numItermax = 500000
+numItermax = 100000
 lr = 1
+log = True
 
 a = ot.utils.unif(n_source)
 b = ot.utils.unif(n_target)
@@ -85,12 +86,13 @@
 # case
 # ---------------------------------------------
 #
-# Define the method "ASGD", call ot.transportation_matrix_entropic and plot the
+# Define the method "ASGD", call ot.solve_semi_dual_entropic and plot the
 # results.
 
 method = "ASGD"
-asgd_pi = ot.stochastic.transportation_matrix_entropic(a, b, M, reg, method,
-                                                       numItermax, lr)
+asgd_pi, log = ot.stochastic.solve_semi_dual_entropic(a, b, M, reg, method,
+                                                   numItermax, lr, log)
+print(log['alpha'], log['beta'])
 print(asgd_pi)
 
 #############################################################################
@@ -100,7 +102,7 @@
 #
 # Call the Sinkhorn algorithm from POT
 
-sinkhorn_pi = ot.sinkhorn(a, b, M, 1)
+sinkhorn_pi = ot.sinkhorn(a, b, M, reg)
 print(sinkhorn_pi)
 
 
@@ -113,7 +115,7 @@
 # ----------------
 
 pl.figure(4, figsize=(5, 5))
-ot.plot.plot1D_mat(a, b, sag_pi, 'OT matrix SAG')
+ot.plot.plot1D_mat(a, b, sag_pi, 'semi-dual : OT matrix SAG')
 pl.show()
 
 
@@ -122,7 +124,76 @@
 # -----------------
 
 pl.figure(4, figsize=(5, 5))
-ot.plot.plot1D_mat(a, b, asgd_pi, 'OT matrix ASGD')
+ot.plot.plot1D_mat(a, b, asgd_pi, 'semi-dual : OT matrix ASGD')
+pl.show()
+
+
+##############################################################################
+# Plot Sinkhorn results
+# ---------------------
+
+pl.figure(4, figsize=(5, 5))
+ot.plot.plot1D_mat(a, b, sinkhorn_pi, 'OT matrix Sinkhorn')
+pl.show()
+
+#############################################################################
+# COMPUTE TRANSPORTATION MATRIX FOR DUAL PROBLEM
+#############################################################################
+print("------------DUAL PROBLEM------------")
+#############################################################################
+# SEMICONTINOUS CASE
+# Sample one general measure a, one discrete measures b for the semicontinous
+# case
+# ---------------------------------------------
+#
+# Define one general measure a, one discrete measures b, the points where
+# are defined the source and the target measures and finally the cost matrix c.
+
+n_source = 7
+n_target = 4
+reg = 1
+numItermax = 100000
+lr = 0.1
+batch_size = 3
+log = True
+
+a = ot.utils.unif(n_source)
+b = ot.utils.unif(n_target)
+
+rng = np.random.RandomState(0)
+X_source = rng.randn(n_source, 2)
+Y_target = rng.randn(n_target, 2)
+M = ot.dist(X_source, Y_target)
+
+#############################################################################
+#
+# Call the "SGD" dual method to find the transportation matrix in the semicontinous
+# case
+# ---------------------------------------------
+#
+# Call ot.solve_dual_entropic and plot the results.
+
+sgd_dual_pi, log = ot.stochastic.solve_dual_entropic(a, b, M, reg, batch_size,
+                                                  numItermax, lr, log)
+print(log['alpha'], log['beta'])
+print(sgd_dual_pi)
+
+#############################################################################
+#
+# Compare the results with the Sinkhorn algorithm
+# ---------------------------------------------
+#
+# Call the Sinkhorn algorithm from POT
+
+sinkhorn_pi = ot.sinkhorn(a, b, M, reg)
+print(sinkhorn_pi)
+
+##############################################################################
+# Plot  SGD results
+# -----------------
+
+pl.figure(4, figsize=(5, 5))
+ot.plot.plot1D_mat(a, b, sgd_dual_pi, 'dual : OT matrix SGD')
 pl.show()