PythonOT/POT

Features

• Exact Solvers - Provides exact solvers and specialized 1D solvers to calculate precise optimal transport plans.
• Gromov-Wasserstein Distance Computations - Implements solvers for estimating distances and transport plans between distributions in different metric spaces based on relational geometry.
• Optimal Transport Libraries - Provides a comprehensive collection of solvers for computing Wasserstein, Gromov-Wasserstein, and Fused Gromov-Wasserstein distances.
• Optimal Transport Solvers - Provides a comprehensive suite of mathematical solvers for computing optimal transport matrices between discrete probability distributions.
• Wasserstein Distance Estimators - Provides solvers to calculate the minimum cost of transforming one probability distribution into another.
• Cross-Framework Tensor Dispatch - Provides an abstraction layer that allows tensor operations to run across multiple backends including PyTorch, TensorFlow, and JAX.
• Differentiable Optimization Layers - Implements mathematical optimization algorithms as differentiable layers for gradient-based updates in neural networks.
• Differentiable Transport Solvers - Implements optimal transport algorithms as differentiable layers for seamless integration into gradient-based machine learning workflows.
• Sinkhorn Solvers - Provides fast approximation of transport plans using iterative Sinkhorn solvers.
• Optimal Transport Layers - Integrates differentiable optimal transport solvers directly into graph neural network architectures as layers.
• Hardware Acceleration Backends - Integrates with hardware acceleration backends to enable GPU-powered solver execution and automatic differentiation.
• Tensor Computation Backends - Integrates with various tensor backends to enable automatic differentiation and high-performance hardware acceleration for transport operations.
• Transport Solver Integration - Incorporates differentiable transport solvers directly into neural network workflows for gradient-based optimization.
• Discrete Solvers - Solves optimal transport problems for discrete distributions using linear programming and entropic regularization.
• Entropic Solvers - Uses entropy regularization and the Sinkhorn algorithm to approximate optimal transport plans.
• Regularized Solvers - Ships transport solvers that incorporate regularization terms via conditional gradient methods for improved speed.
• Unbalanced Transport Solvers - Computes optimal transport plans between distributions with different total masses using the Sinkhorn algorithm.
• Wasserstein Barycenter Analysis - Computes representative average distributions, known as barycenters, based on weighted optimal transport distance.
• Entropic Regularization - Accelerates optimal transport computations by adding an entropy term to the objective function.
• Optimal Transport Solvers - Computes optimal transport matrices to minimize mass movement costs between discrete distributions.
• Graph Topology Alignment - Matches structured graphs by measuring the distance between their internal geometries and associated node features.
• Distributional Alignment - Implements mathematical utilities to align data distributions across different metric spaces to improve model generalization.
• Distributional Domain Alignment - Aligns probability distributions across different domains using optimal transport to transport labels and improve model generalization.
• GPU Acceleration Backends - Provides a backend-agnostic interface to execute complex optimal transport solvers on GPU hardware.
• Tensor Backend Switching - Executes transport solvers across multiple tensor libraries like PyTorch and JAX through a common backend-agnostic interface.
• Computational Backend Integrations - Implements interfaces to delegate heavy mathematical operations to high-performance external tensor libraries for acceleration.
• Differentiable Tensor Backends - Functions as a differentiable tensor framework that integrates with multiple libraries for GPU acceleration.
• Gromov-Wasserstein Metrics - Measures distance between distributions in different metric spaces by analyzing internal relational geometry.
• Partial Gromov-Wasserstein Distances - Provides solvers for measuring distance between different metric spaces where only a portion of the mass is transported.
• Partial Wasserstein Distances - Calculates optimal transport plans and distances when only a specified fraction of the probability mass is transported.
• Distribution Alignment Toolkits - Provides a comprehensive suite of tools for mapping and aligning probability distributions using various transport mappings.
• Fused Gromov-Wasserstein Distances - Implements metrics that combine Wasserstein and Gromov distances to align graphs using both topology and node features.
• Graph Barycenters - Computes representative average structures between multiple graphs while preserving topology and attributes.
• Fused Gromov-Wasserstein Distances - Combines structural relational costs with node feature similarities to measure distance between graphs.
• Gromov-Wasserstein Graph Distances - Provides solvers to compute the Gromov-Wasserstein divergence to minimize distances between graph topologies.
• Metric Space Alignments - Aligns probability distributions across different metric spaces by comparing internal distance matrices.
• Relational - Compares relational structures and internal geometries of distributions rather than using absolute coordinates.
• Optimal Transport Distances - Calculates the minimum cost required to transform one probability distribution into another.
• Optimal Transport Plan Computations - Calculates optimal transport coupling matrices to determine the most efficient way to move mass between probability distributions.
• Semi-Relaxed Optimal Transport - Provides transport solvers that allow node reweighting to minimize divergence between structured datasets.
• Sliced Wasserstein Distances - Estimates high-dimensional distances by averaging the Wasserstein costs of multiple one-dimensional linear projections.
• Transport Map Estimations - Computes functional transformations, or transport maps, that push one probability distribution onto another.
• Wasserstein Barycenters - Computes representative central distributions between probability measures using linear programming or entropic regularization.
• Gromov-Wasserstein Barycenters - Provides computations for barycenters based on the Gromov-Wasserstein distance for distributions in different metric spaces.
• Unbalanced Barycenters - Computes regularized Wasserstein barycenters for probability distributions that do not share the same total mass.
• Fused-Cost Objectives - Features cost objectives that combine structural relational data and feature distances for complex dataset alignment.
• Sparse Transport Solvers - Includes algorithms designed to generate sparse transport plans through specific regularization techniques.
• Dimensionality Reduction - Simplifies complex datasets by reducing dimensionality while preserving the underlying Wasserstein distance structure.
• Wasserstein Discriminant Analysis - Uses linear projection techniques based on Wasserstein distances to maximize separation between class distributions.
• Gaussian Transport Plans - Computes specific optimal transport plans and densities tailored for Gaussian Mixture Models.
• GMM Distribution Mappings - Transforms data between Gaussian Mixture Models using barycentric projections or sampling based on an optimal coupling.
• Graph Dictionary Learning - Learns representative atoms for graph-structured data capturing both node attributes and connectivity.
• Multi-Source Domain Adaptation - Aligns multiple source data distributions to a single target domain using optimal transport maps.
• Partial Transport Solvers - Finds optimal transport plans for scenarios where only a fixed portion of the total mass is moved.
• Smooth Transport Solvers - Produces smooth transport plans using regularization techniques such as KL divergence or L2 norm.
• Stochastic Transport Solvers - Provides solvers that utilize stochastic optimization to compute transportation matrices for probability measures.
• Transport Regularizations - Applies entropic, quadratic, or group Lasso regularization to ensure uniqueness and sparsity in transport plans.
• Labeled Graph Barycenters - Calculates average graphs for labeled data using Fused Gromov-Wasserstein distance to preserve features and structure.
• Linear Transport Mappings - Estimates parametric linear mappings between two distributions to approximate optimal transport plans for data transformation.
• High-Dimensional Distribution Analysis - Analyzes complex high-dimensional probability distributions using slicing and projection techniques to reduce complexity.
• Domain Adaptation Techniques - Provides algorithmic techniques for adapting data distributions to reduce shift and improve model performance.
• Brenier Potentials - Computes strongly convex potentials to approximate the optimal transport map between two distributions.
• Co-Optimal Transport Alignments - Aligns two dimensions of a data matrix simultaneously by solving co-optimal transport problems.
• Circular Wasserstein Distances - Calculates optimal transport distances between probability distributions while accounting for circular periodicity.
• Partial - Combines structural and feature costs to match only a fraction of the total mass between distributions.
• Graph Analysis Frameworks - Provides algorithms for subgraph matching, graph dictionary learning, and computing barycenters of labeled graphs.
• Subgraph Matching - Identifies matching sub-structures within graphs by combining structural adjacency and node features.
• Quantized Distance Computations - Approximates transport distances by partitioning distributions or graphs into representative clusters for efficiency.
• Subgraph Matching - Identifies similar sub-structures between graphs by computing distances between adjacency matrices.
• Low-Rank Coupling Approximations - Reduces computational complexity of large transport plans using factored low-rank coupling approximations.
• Large-Scale Transport Solvers - Processes massive datasets using stochastic solvers and differentiable losses to maintain computational efficiency.
• Monge Map Approximations - Provides numerical approximations of Monge maps that push one probability distribution onto another.
• Monge Mapping Estimators - Approximates the optimal Monge map between distributions using Gaussian solutions, kernels, or barycentric mapping.
• Marginal Constraint Relaxations - Handles unbalanced transport by replacing strict mass constraints with penalization terms.
• Optimal Transport Cost Functions - Provides mathematical objectives to measure discrepancy by combining feature and structural costs in optimal transport.
• Projective Distance Estimations - Estimates distances between high-dimensional distributions by averaging transport costs of 1D projections.
• Spherical Sliced Discrepancies - Measures the discrepancy between probability distributions on a spherical domain using random projections.
• Barycenter Debiasing - Implements post-processing and refinement to remove regularization bias from Sinkhorn barycenters.
• Debiased Barycenters - Removes systematic bias introduced by entropic regularization to produce more accurate barycenter representations.
• Stochastic Distance Estimators - Approximates distances between probability distributions using sampling and stochastic processes to improve scalability.
• Entropic Dual Variables - Computes entropic dual variables used as potential functions to train neural networks via stochastic continuous distributions.
• Lazy Tensor Evaluations - Employs lazy tensor evaluation to minimize memory overhead when processing large-scale mathematical computations.

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