diff options
Diffstat (limited to 'ot/da.py')
| -rw-r--r-- | ot/da.py | 123 |
1 files changed, 102 insertions, 21 deletions
@@ -14,7 +14,6 @@ def indices(a, func): return [i for (i, val) in enumerate(a) if func(val)] - def sinkhorn_lpl1_mm(a,labels_a, b, M, reg, eta=0.1,numItermax = 10,numInnerItermax = 200,stopInnerThr=1e-9,verbose=False,log=False): """ Solve the entropic regularization optimal transport problem with nonconvex group lasso regularization @@ -49,15 +48,15 @@ def sinkhorn_lpl1_mm(a,labels_a, b, M, reg, eta=0.1,numItermax = 10,numInnerIter samples in the target domain M : np.ndarray (ns,nt) loss matrix - reg: float + reg : float Regularization term for entropic regularization >0 - eta: float, optional + eta : float, optional Regularization term for group lasso regularization >0 - numItermax: int, optional + numItermax : int, optional Max number of iterations - numInnerItermax: int, optional + numInnerItermax : int, optional Max number of iterations (inner sinkhorn solver) - stopInnerThr: float, optional + stopInnerThr : float, optional Stop threshold on error (inner sinkhorn solver) (>0) verbose : bool, optional Print information along iterations @@ -67,9 +66,9 @@ def sinkhorn_lpl1_mm(a,labels_a, b, M, reg, eta=0.1,numItermax = 10,numInnerIter Returns ------- - gamma: (ns x nt) ndarray + gamma : (ns x nt) ndarray Optimal transportation matrix for the given parameters - log: dict + log : dict log dictionary return only if log==True in parameters @@ -145,7 +144,10 @@ def joint_OT_mapping_linear(xs,xt,mu=1,eta=0.001,bias=False,verbose=False,verbos The problem consist in solving jointly an optimal transport matrix :math:`\gamma` and a linear mapping that fits the barycentric mapping - :math:`n_s\gamma X_t` + :math:`n_s\gamma X_t`. + + One can also estimate a mapping with constant bias (see supplementary + material of [8]) using the bias optional argument. The algorithm used for solving the problem is the block coordinate descent that alternates between updates of G (using conditionnal gradient) @@ -158,19 +160,19 @@ def joint_OT_mapping_linear(xs,xt,mu=1,eta=0.001,bias=False,verbose=False,verbos samples in the source domain xt : np.ndarray (nt,d) samples in the target domain - mu: float,optional + mu : float,optional Weight for the linear OT loss (>0) - eta: float, optional + eta : float, optional Regularization term for the linear mapping L (>0) - bias: bool,optional + bias : bool,optional Estimate linear mapping with constant bias - numItermax: int, optional + numItermax : int, optional Max number of BCD iterations - stopThr: float, optional + stopThr : float, optional Stop threshold on relative loss decrease (>0) - numInnerItermax: int, optional + numInnerItermax : int, optional Max number of iterations (inner CG solver) - stopInnerThr: float, optional + stopInnerThr : float, optional Stop threshold on error (inner CG solver) (>0) verbose : bool, optional Print information along iterations @@ -180,11 +182,11 @@ def joint_OT_mapping_linear(xs,xt,mu=1,eta=0.001,bias=False,verbose=False,verbos Returns ------- - gamma: (ns x nt) ndarray + gamma : (ns x nt) ndarray Optimal transportation matrix for the given parameters - L: (d x d) ndarray + L : (d x d) ndarray Linear mapping matrix (d+1 x d if bias) - log: dict + log : dict log dictionary return only if log==True in parameters @@ -291,10 +293,89 @@ def joint_OT_mapping_linear(xs,xt,mu=1,eta=0.001,bias=False,verbose=False,verbos def joint_OT_mapping_kernel(xs,xt,mu=1,eta=0.001,kerneltype='gaussian',sigma=1,bias=False,verbose=False,verbose2=False,numItermax = 100,numInnerItermax = 10,stopInnerThr=1e-6,stopThr=1e-5,log=False,**kwargs): - """Joint Ot and mapping estimation (uniform weights and ) + """Joint OT and nonlinear mapping estimation with kernels as proposed in [8] + + The function solves the following optimization problem: + + .. math:: + \min_{\gamma,L\in\mathcal{H}}\quad \|L(X_s) -n_s\gamma X_t\|^2_F + \mu<\gamma,M>_F + \eta \|L\|^2_\mathcal{H} + + s.t. \gamma 1 = a + + \gamma^T 1= b + + \gamma\geq 0 + where : + + - M is the (ns,nt) squared euclidean cost matrix between samples in Xs and Xt (scaled by ns) + - :math:`L` is a ns x d linear operator on a kernel matrix that approximates the barycentric mapping + - a and b are uniform source and target weights + + The problem consist in solving jointly an optimal transport matrix + :math:`\gamma` and the nonlinear mapping that fits the barycentric mapping + :math:`n_s\gamma X_t`. + + One can also estimate a mapping with constant bias (see supplementary + material of [8]) using the bias optional argument. + + The algorithm used for solving the problem is the block coordinate + descent that alternates between updates of G (using conditionnal gradient) + abd the update of L using a classical kernel least square solver. + + + Parameters + ---------- + xs : np.ndarray (ns,d) + samples in the source domain + xt : np.ndarray (nt,d) + samples in the target domain + mu : float,optional + Weight for the linear OT loss (>0) + eta : float, optional + Regularization term for the linear mapping L (>0) + bias : bool,optional + Estimate linear mapping with constant bias + kerneltype : str,optional + kernel used by calling function ot.utils.kernel (gaussian by default) + sigma : float, optional + Gaussian kernel bandwidth. + numItermax : int, optional + Max number of BCD iterations + stopThr : float, optional + Stop threshold on relative loss decrease (>0) + numInnerItermax : int, optional + Max number of iterations (inner CG solver) + stopInnerThr : float, optional + Stop threshold on error (inner CG solver) (>0) + verbose : bool, optional + Print information along iterations + log : bool, optional + record log if True + + + Returns + ------- + gamma : (ns x nt) ndarray + Optimal transportation matrix for the given parameters + L : (ns x d) ndarray + Nonlinear mapping matrix (ns+1 x d if bias) + log : dict + log dictionary return only if log==True in parameters + + + References + ---------- + + .. [8] M. Perrot, N. Courty, R. Flamary, A. Habrard, "Mapping estimation for discrete optimal transport", Neural Information Processing Systems (NIPS), 2016. + + See Also + -------- + ot.lp.emd : Unregularized OT + ot.optim.cg : General regularized OT + """ - ns,nt,d=xs.shape[0],xt.shape[0],xt.shape[1] + ns,nt=xs.shape[0],xt.shape[0] K=kernel(xs,xs,method=kerneltype,sigma=sigma) if bias: |