diff options
-rw-r--r-- | ot/da.py | 17 |
1 files changed, 15 insertions, 2 deletions
@@ -643,7 +643,7 @@ def OT_mapping_linear(xs, xt, reg=1e-6, ws=None, The function estimate the optimal linear operator that align the two empirical distributions. This is equivalent to estimating the closed form mapping between two Gaussian distribution :math:`N(\mu_s,\Sigma_s)` - and :math:`N(\mu_t,\Sigma_t)` as proposed in [14]. + and :math:`N(\mu_t,\Sigma_t)` as proposed in [14] and discussed in remark 2.29 in [15]. The linear operator from source to target :math:`M` @@ -692,6 +692,9 @@ def OT_mapping_linear(xs, xt, reg=1e-6, ws=None, .. [14] Knott, M. and Smith, C. S. "On the optimal mapping of distributions", Journal of Optimization Theory and Applications Vol 43, 1984 + + .. [15] Peyré, G., & Cuturi, M. (2017). "Computational Optimal + Transport", 2018. """ @@ -1290,7 +1293,8 @@ class LinearTransport(BaseTransport): The function estimate the optimal linear operator that align the two empirical distributions. This is equivalent to estimating the closed form mapping between two Gaussian distribution :math:`N(\mu_s,\Sigma_s)` - and :math:`N(\mu_t,\Sigma_t)` as proposed in [14]. + and :math:`N(\mu_t,\Sigma_t)` as proposed in [14] and discussed in + remark 2.29 in [15]. The linear operator from source to target :math:`M` @@ -1314,6 +1318,15 @@ class LinearTransport(BaseTransport): log : bool, optional record log if True + References + ---------- + + .. [14] Knott, M. and Smith, C. S. "On the optimal mapping of + distributions", Journal of Optimization Theory and Applications + Vol 43, 1984 + + .. [15] Peyré, G., & Cuturi, M. (2017). "Computational Optimal + Transport", 2018. """ |