Auxillary objects for Sinkhorn solvers

This section includes auxillary classes that are needed to fully define a Sinkhorn transport problem, such as cost functions, schedule for the entropic regularization parameter (aka epsilon scaling), and minor parameters.

Transport cost functions

class MultiScaleOT.THierarchicalCostFunctionProvider

Abstract base class of cost function object. Does not expose a constructor.

getCost(self: MultiScaleOT.THierarchicalCostFunctionProvider, layer: int, xId: int, yId: int) → float

Computes lower bound on cost between points with numbers <xId> and <yId> at layer <layer>.

getCostAsym(self: MultiScaleOT.THierarchicalCostFunctionProvider, xLayer: int, xId: int, yLayer: int, yId: int) → float

Computes lower bound on cost between points with numbers <xId> at layer <xLayer> and <yId> at layer <yLayer>.

getCostEff(self: MultiScaleOT.THierarchicalCostFunctionProvider, layer: int, xId: int, yId: int) → float

Computes lower bound on effective cost (i.e. cost reduced by dual variables) between points with numbers <xId> and <yId> at layer <layer>.

getCostEffAsym(self: MultiScaleOT.THierarchicalCostFunctionProvider, xLayer: int, xId: int, yLayer: int, yId: int) → float

Computes lower bound on effective cost (i.e. cost reduced by dual variables) between points with numbers <xId> at layer <xLayer> and <yId> at layer <yLayer>.

setLayerBottom(self: MultiScaleOT.THierarchicalCostFunctionProvider, layerBottom: int) → None

Sets number of layer which should be considered as finest level.

class MultiScaleOT.THierarchicalCostFunctionProvider_SquaredEuclidean

Represents the squared Euclidean distance cost function.

__init__(self: MultiScaleOT.THierarchicalCostFunctionProvider_SquaredEuclidean, MultiScaleSetupX: MultiScaleOT.TMultiScaleSetup, MultiScaleSetupY: MultiScaleOT.TMultiScaleSetup, HKmode: bool = False, HKscale: float = 1.0) → None

Parameters:

• MultiScaleSetupX – TMultiScaleSetup instance describing first marginal

• MultiScaleSetupY – TMultiScaleSetup instance describing second marginal

• HKmode – whether Hellinger–Kantorovich mode should be activated

• HKscale – trade-off weight between transport and mass change. Maximal transport distance is HKscale*pi/2.

setHKscale(self: MultiScaleOT.THierarchicalCostFunctionProvider_SquaredEuclidean, arg0: float) → None

setScale(self: MultiScaleOT.THierarchicalCostFunctionProvider_SquaredEuclidean, arg0: float) → None

class MultiScaleOT.THierarchicalCostFunctionProvider_PEuclidean

Represents the Euclidean distance cost function to power p.

__init__(self: MultiScaleOT.THierarchicalCostFunctionProvider_PEuclidean, MultiScaleSetupX: MultiScaleOT.TMultiScaleSetup, MultiScaleSetupY: MultiScaleOT.TMultiScaleSetup, p: float = 2.0) → None

Parameters:

• MultiScaleSetupX – TMultiScaleSetup instance describing first marginal

• MultiScaleSetupY – TMultiScaleSetup instance describing second marginal

• p – exponent for distance

Epsilon scaling

class MultiScaleOT.TEpsScalingHandler

Class for setting up and managing a schedule for epsilon scaling.

get(self: MultiScaleOT.TEpsScalingHandler) → list

setupExplicit(self: MultiScaleOT.TEpsScalingHandler, epsLists: list) → None

setupGeometricMultiLayerA(self: MultiScaleOT.TEpsScalingHandler, nLayers: int, epsStart: float, epsTarget: float, epsSteps: int, boxScale: float, layerExponent: float, layerCoarsest: int, overlap: bool) → int

setupGeometricMultiLayerB(self: MultiScaleOT.TEpsScalingHandler, nLayers: int, epsBase: float, layerFactor: float, layerSteps: int, stepsFinal: int) → int

setupGeometricSingleLayer(self: MultiScaleOT.TEpsScalingHandler, nLayers: int, epsStart: float, epsTarget: float, epsSteps: int) → int

Minor parameters of Sinkhorn algorithm

class MultiScaleOT.TSinkhornSolverParameters

Bundle all smaller parameters of the Sinkhorn solver objects.

__init__(self: MultiScaleOT.TSinkhornSolverParameters, maxIterations: int = 100000, innerIterations: int = 100, maxAbsorptionLoops: int = 100, absorption_scalingBound: float = 1000.0, absorption_scalingLowerBound: float = 1000.0, truncation_thresh: float = 1e-20, refineKernel: bool = False, generateFinalKernel: bool = True) → None