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| author | Hicham Janati <hicham.janati@inria.fr> | 2019-06-24 16:19:31 +0200 |
|---|---|---|
| committer | Hicham Janati <hicham.janati@inria.fr> | 2019-06-24 16:19:31 +0200 |
| commit | 632bc9a8ec8a227d90db9635a34bb364d128cccb (patch) | |
| tree | 21728e7790ee51f48ff6432f84fc58cdea3521b2 /ot/unbalanced.py | |
| parent | adf9d046445bf142a29d914352f397b36f7905c0 (diff) | |
update docstrings + init
Diffstat (limited to 'ot/unbalanced.py')
| -rw-r--r-- | ot/unbalanced.py | 28 |
1 files changed, 14 insertions, 14 deletions
diff --git a/ot/unbalanced.py b/ot/unbalanced.py index 918dda4..484ce95 100644 --- a/ot/unbalanced.py +++ b/ot/unbalanced.py @@ -19,7 +19,7 @@ def sinkhorn_unbalanced(a, b, M, reg, alpha, method='sinkhorn', numItermax=1000, The function solves the following optimization problem: .. math:: - W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma) + alpha KL(\gamma 1, a) + alpha KL(\gamma^T 1, b) + W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma) + \alpha KL(\gamma 1, a) + \alpha KL(\gamma^T 1, b) s.t. \gamma\geq 0 @@ -43,9 +43,9 @@ def sinkhorn_unbalanced(a, b, M, reg, alpha, method='sinkhorn', numItermax=1000, M : np.ndarray (ns, nt) loss matrix reg : float - Regularization term > 0 + Entropy regularization term > 0 alpha : float - Regulatization term > 0 + Marginal relaxation term > 0 method : str method used for the solver either 'sinkhorn', 'sinkhorn_stabilized' or 'sinkhorn_epsilon_scaling', see those function for specific parameters @@ -128,7 +128,7 @@ def sinkhorn_unbalanced2(a, b, M, reg, alpha, method='sinkhorn', The function solves the following optimization problem: .. math:: - W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma) + alpha KL(\gamma 1, a) + alpha KL(\gamma^T 1, b) + W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma) + \alpha KL(\gamma 1, a) + \alpha KL(\gamma^T 1, b) s.t. \gamma\geq 0 @@ -152,9 +152,9 @@ def sinkhorn_unbalanced2(a, b, M, reg, alpha, method='sinkhorn', M : np.ndarray (ns,nt) loss matrix reg : float - Regularization term > 0 - alpha: float - Regularization term > 0 + Entropy regularization term > 0 + alpha : float + Marginal relaxation term > 0 method : str method used for the solver either 'sinkhorn', 'sinkhorn_stabilized' or 'sinkhorn_epsilon_scaling', see those function for specific parameters @@ -239,7 +239,7 @@ def sinkhorn_knopp_unbalanced(a, b, M, reg, alpha, numItermax=1000, The function solves the following optimization problem: .. math:: - W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma) + alpha KL(\gamma 1, a) + alpha KL(\gamma^T 1, b) + W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma) + \alpha KL(\gamma 1, a) + \alpha KL(\gamma^T 1, b) s.t. \gamma\geq 0 @@ -263,9 +263,9 @@ def sinkhorn_knopp_unbalanced(a, b, M, reg, alpha, numItermax=1000, M : np.ndarray (ns,nt) loss matrix reg : float - Regularization term > 0 - alpha: float - Regularization term > 0 + Entropy regularization term > 0 + alpha : float + Marginal relaxation term > 0 numItermax : int, optional Max number of iterations stopThr : float, optional @@ -410,7 +410,7 @@ def barycenter_unbalanced(A, M, reg, alpha, weights=None, numItermax=1000, where : - - :math:`W_{reg}(\cdot,\cdot)` is the unbalanced entropic regularized Wasserstein distance (see ot.unbalanced.sinkhorn_unbalanced) + - :math:`Wu_{reg}(\cdot,\cdot)` is the unbalanced entropic regularized Wasserstein distance (see ot.unbalanced.sinkhorn_unbalanced) - :math:`\mathbf{a}_i` are training distributions in the columns of matrix :math:`\mathbf{A}` - reg and :math:`\mathbf{M}` are respectively the regularization term and the cost matrix for OT - alpha is the marginal relaxation hyperparameter @@ -423,9 +423,9 @@ def barycenter_unbalanced(A, M, reg, alpha, weights=None, numItermax=1000, M : np.ndarray (d,d) loss matrix for OT reg : float - Regularization term > 0 + Entropy regularization term > 0 alpha : float - Regularization term > 0 + Marginal relaxation term > 0 weights : np.ndarray (n,) Weights of each histogram a_i on the simplex (barycentric coodinates) numItermax : int, optional |