diff options
Diffstat (limited to 'ot/sliced.py')
| -rw-r--r-- | ot/sliced.py | 7 |
1 files changed, 4 insertions, 3 deletions
diff --git a/ot/sliced.py b/ot/sliced.py index d3dc3f2..7c09111 100644 --- a/ot/sliced.py +++ b/ot/sliced.py @@ -17,7 +17,7 @@ from .utils import list_to_array def get_random_projections(d, n_projections, seed=None, backend=None, type_as=None): r""" - Generates n_projections samples from the uniform on the unit sphere of dimension d-1: :math:`\mathcal{U}(\mathcal{S}^{d-1})` + Generates n_projections samples from the uniform on the unit sphere of dimension :math:`d-1`: :math:`\mathcal{U}(\mathcal{S}^{d-1})` Parameters ---------- @@ -67,11 +67,12 @@ def sliced_wasserstein_distance(X_s, X_t, a=None, b=None, n_projections=50, p=2, Computes a Monte-Carlo approximation of the p-Sliced Wasserstein distance .. math:: - \mathcal{SWD}_p(\mu, \nu) = \underset{\theta \sim \mathcal{U}(\mathbb{S}^{d-1})}{\mathbb{E}}[\mathcal{W}_p^p(\theta_\# \mu, \theta_\# \nu)]^{\frac{1}{p}} + \mathcal{SWD}_p(\mu, \nu) = \underset{\theta \sim \mathcal{U}(\mathbb{S}^{d-1})}{\mathbb{E}}\left(\mathcal{W}_p^p(\theta_\# \mu, \theta_\# \nu)\right)^{\frac{1}{p}} + where : - - :math:`\theta_\# \mu` stands for the pushforwars of the projection :math:`\mathbb{R}^d \ni X \mapsto \langle \theta, X \rangle` + - :math:`\theta_\# \mu` stands for the pushforwards of the projection :math:`X \in \mathbb{R}^d \mapsto \langle \theta, X \rangle` Parameters |