Optimal transport aligns source and target distributions for linear regression in 2D.
problem Domain adaptation for linear regression in 2D with limited target data.
method Combining K-means and optimal transport for estimating geometric transformations.
result Optimal transport recovers geometric transformations like rotations, translations, and homotheties.
TSC uses HMC and adaptive transport maps to optimize forward KL for variational inference.
problem Variational inference underestimates uncertainty when minimizing reverse KL.
method TSC uses Hamiltonian Monte Carlo and adaptive transport maps to optimize KL(p||q).
result TSC achieves competitive performance in training variational autoencoders on large-scale data.
Unbalanced minibatch Optimal Transport improves domain adaptation performance.
problem Optimal transport distances are computationally expensive for large datasets.
method Use unbalanced minibatch Optimal Transport to estimate distances over subsets of data.
result Unbalanced Optimal Transport leads to better domain adaptation results.
Paper proposes a probabilistic alignment method for domain adaptation.
problem Latent distribution mismatch and miscalibrated uncertainty in adapting large-scale models.
method Bayesian latent transport framework with PAC-Bayesian regularization.
result Reduction in latent manifold discrepancy and improved uncertainty calibration.
A novel unsupervised domain adaptation method using hierarchical optimal transport.
problem Unsupervised domain adaptation between source and target domains.
method Hierarchical optimal transport, leveraging class labels for structure formation in the source domain and learning probability measures in the target domain.
result The proposed HOT-DA method outperforms state-of-the-art approaches on various datasets.
Study investigates duality and dual optimizers for various transport problems.
problem Existence and characterization of dual optimizers for adapted transport problems.
method Minimal assumptions, including causal and bicausal settings, are considered.
result No-arbitrage assumption leads to multicausal couplings and equivalent robust superhedging price computation.
FEAT estimates free energy using adaptive transports.
problem Estimating free energy across scientific domains.
method Uses learned transports and stochastic interpolants.
result Provides consistent, minimum-variance estimators.
Proposes m-POT to improve m-OT's misspecified mappings issue.
problem Misspecified mappings in mini-batch optimal transport.
method Partial optimal transport (POT) between mini-batch empirical measures.
result m-POT alleviates incorrect mappings compared to current methods.
Optimal transport between Gaussian Mixture Models improves domain adaptation efficiency.
problem Adapting machine learning models to new data distributions with minimal access.
method Optimal transport between Gaussian Mixture Models (GMMs) for domain adaptation.
result Our methods are more efficient and scalable with sample size and dimensions.
Adaptive optimal transport priors improve few-shot learning robustness.
problem Limited supervision and distribution shifts in few-shot learning.
method Prototype-Guided Distributionally Robust Optimization (PG-DRO) framework.
result PG-DRO achieves stronger robust generalization in few-shot scenarios.
Optimal transport method rejects new classes and adjusts class ratios for open set domain adaptation.
problem Handling new classes in target domains with distribution shifts.
method Two-step optimal transport approach: reject new classes first, then adjust class ratios.
result Outperforms state-of-the-art methods in open set domain adaptation.
Optimal transport aligns rotated linear regression models across domains.
problem Aligning rotated linear regression models across domains with differing statistical properties.
method Combines K-means clustering, OT, and SVD to estimate rotation angle and adapt regression model.
result Optimal transport map recovers underlying rotation in R2. New method reduces label and data shifts between domains using optimal transport.
problem Label shift between source and target domains in domain adaptation.
method Developed theory and LDROT method to mitigate label and data shifts.
result Theoretical and experimental validation of LDROT's effectiveness.
Optimal transport for functional data using Hilbert-Schmidt operators.
problem Optimal transport for distributions on function spaces with partially represented stochastic maps.
method Regularization technique to restrict transport maps to Hilbert-Schmidt operators, developing an efficient algorithm.
result Existence, uniqueness, and consistency of the Hilbert-Schmidt operator estimate for the transport map.
Optimal transport aligns source and target distributions for domain adaptation.
problem Unsupervised domain adaptation with joint class-conditional and label shifts.
method Minimizes importance weighted loss and Wasserstein distance for aligned marginals and class-conditional distributions.
result Our method outperforms competitors on various domain adaptation tasks.
InfoOT improves data alignment by maximizing mutual information.
problem Optimal transport's limitations in handling clusters, outliers, and new data.
method InfoOT extends optimal transport by maximizing mutual information while minimizing distances.
result InfoOT outperforms optimal transport in domain adaptation, cross-domain retrieval, and single-cell alignment.
Adaptive algorithm improves nonlinear data assimilation for non-Gaussian systems.
problem Challenges of non-Gaussian statistics in data assimilation.
method Triangular measure transport with P-spline basis functions and an information criterion.
result Automatic selection of parsimonious parametrization for efficient adaptation.
Paper improves bike-sharing demand prediction by adapting to changing patterns.
problem Improving bike-sharing demand prediction under temporal domain shifts.
method Gen-ROTDA, a robust optimal transport-guided residual domain adaptation framework.
result Gen-ROTDA achieves the lowest MAE and is the best OT-family method on average.
New framework for domain adaptation using hierarchical optimal transport.
problem Improving domain adaptation when source and target data distributions differ.
method Proposes a new theoretical framework and hierarchical Wasserstein distance.
result Provides more explicit generalization bounds and aligns specific structures for successful adaptation.
In this paper, we propose a new feature selection method for unsupervised domain adaptation based on the emerging optimal transportation theory. We build upon a recent theoretical analysis of optimal transport in domain adaptation and show that it can directly suggest a feature selection procedure leveraging the shift …
Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation, sentence similarities to deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground metric" is limited. In this work, we develop a nonlinear generalization of (discrete) …
Estimates optimal transport maps with known cost functions.
problem Ensuring optimal transport maps correspond to real-world usefulness.
method Differentiable neural ground costs with known Monge map forms.
result General approach for incorporating prior information.
New scalable methods for unbalanced optimal transport improve efficiency and applicability.
problem Scalable algorithms for unbalanced optimal transport remain underexplored.
method Analysis of semi-dual formulation and adaptive gradient methods.
result SGD methods achieve a convergence rate of O(n/εT) for large-scale applications.
A new method computes high-dimensional optimal transport using flow neural networks.
problem Computing optimal transport for high-dimensional data.
method Optimizing a flow model to minimize transport cost between two arbitrary distributions.
result Trained optimal transport flow enables downstream tasks like DRE and domain adaptation.
We show that a certain entropy-like function is convex, under an optimal transport problem that is adapted to Ricci flow. We use this to reprove the monotonicity of Perelman's reduced volume.
Adaptive, sparse graphs improve learning performance.
problem Inappropriate kNN for varying sampling density or noise.
method Quadratically regularised optimal transport.
result Graphs outperform kNN in learning applications.
Paper tackles MSDA with GMMs and OT, improving over prior art.
problem Adapting multiple heterogeneous source measures to a target measure.
method Optimal Transport between Gaussian Mixture Models, with novel barycenter calculation.
result Improves image classification and fault diagnosis benchmarks.
This thesis tackles Optimal Transport on incomparable spaces, proposing new tools and properties.
problem How to apply Optimal Transport between graphs and structured data in different metric spaces?
method Study of Gromov-Wasserstein distance and development of new Optimal Transport tools.
result Mathematical properties and algorithmic solutions for transport problems on incomparable spaces.
Method predicts how probability distributions evolve over time.
problem Predicting how systems described by probability distributions evolve under different conditions.
method Wasserstein Parallel Transport
result Wasserstein Parallel Transport provides counterfactual comparisons of distributional dynamics.
Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When the entropy regularization is added to the problem, the transportation plan can be…
A new method aligns source and target distributions by tuning their weights.
problem Domain adaptation on unlabeled target datasets using labeled source datasets.
method Weighted Joint Distribution Optimal Transport (WJDOT) method that finds alignment between source and target distributions and re-weighting of source distributions.
result Achieves state-of-the-art performance on simulated and real-life datasets.
Paper introduces a novel map learning algorithm for domain translation and adaptation.
problem Learning a map between related data spaces that can be applied to out-of-sample data and satisfies application-specific constraints.
method Utilizes normalizing flows to parameterize a map that minimizes a probability distance and application-specific regularizers, solving a modified optimal transport problem.
result The proposed method (parOT) outperforms existing optimal transport approaches in domain adaptation and translation tasks.
We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension. Unlike plug-in rules that simply replace the true distributions by their empirical counterparts, our method promotes couplings with low transport rank, a new struct…
Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework called SPOT (Scalable Push-forward of Optimal Transport). Specifically, we approxima…
Unbalanced COOT improves feature alignment robustly to outliers.
problem Optimal transport methods are sensitive to outliers in real-world data.
method COOT infers alignment between features and samples, unbalanced COOT adds robustness.
result Unbalanced COOT is robust to noise in real-world datasets.
FVI method calculates bicausal OT with neural networks, outperforming other methods.
problem Computing bicausal optimal transport with adapted coupling structures.
method FVI method using multilayer neural networks to approximate value functions.
result FVI method outperforms linear programming and Sinkhorn methods in scalability.
New robust method for optimal transportation improves statistical inference.
problem Sensitivity to outliers and undefinedness in optimal transportation methods.
method Robust optimal transportation with a tuning parameter λ, leading to robust Wasserstein distance.
result The robust method provides statistical guarantees and improves machine learning applications.
New bounds show empirical EOT adapts to simpler measure.
problem Statistical performance of empirical EOT estimators.
method Novel statistical bounds, empirical process theory, dual formulation.
result Empirical EOT and its unregularized version follow lower complexity adaptation.
New bounds for PDA using partial optimal transport improve domain alignment.
problem Scarcity of labeled target data with abundant source data.
method Derive theoretical bounds based on partial optimal transport.
result Theoretical bounds support partial Wasserstein distance for domain alignment.
Neural framework for conditional OT maps learns from categorical and continuous variables.
problem Learning conditional optimal transport maps between complex distributions.
method Hypernetwork generates adaptive transport layer parameters based on conditioning variables.
result Our method outperforms simpler conditioning methods in comprehensive ablation studies.
Paper tackles adapting multiple domains to a target domain using distillation and dictionary learning.
problem Adapting multiple heterogeneous labeled source domains to an unlabeled target domain.
method Combines Multi-Source Domain Adaptation and Dataset Distillation with Dataset Dictionary Learning.
result Achieves state-of-the-art adaptation performance even with minimal labeled data.
Improves domain adaptation by aligning source and target distributions and mitigating noisy labels.
problem Improving performance on target images with different acquisition conditions.
method Combines optimal transport, MixUp regularization, and robust loss for noisy labels.
result Improves domain adaptation performance on various benchmarks and real-world problems.
Multi-language speech datasets are scarce and often have small sample sizes in the medical domain. Robust transfer of linguistic features across languages could improve rates of early diagnosis and therapy for speakers of low-resource languages when detecting health conditions from speech. We utilize out-of-domain, unp…
In this paper, we propose to tackle the problem of reducing discrepancies between multiple domains referred to as multi-source domain adaptation and consider it under the target shift assumption: in all domains we aim to solve a classification problem with the same output classes, but with labels' proportions differing…
Optimal transport adapted for contaminated probabilities, showing equivalence under specific conditions.
problem Adapting optimal transport for ε-contaminated sets. method Generalized optimal transport problems with lower probabilities, showing equivalence under ε-contaminations. result Monge's and Kantorovich's problems coincide under ε-contaminated sets, but not always. Geometric approach for unsupervised word embedding alignment.
problem Learning alignment between word embeddings of source and target languages.
method Formulates alignment as domain adaptation on the manifold of doubly stochastic matrices, employing Riemannian conjugate gradient algorithm.
result Empirically outperforms state-of-the-art methods on bilingual lexicon induction tasks.
Paper develops fast method for computing optimal transport.
problem Efficient computation of optimal transport distance between distributions.
method Entropy-regularized extragradient method for first-order optimization.
result Achieves state-of-the-art runtime guarantees and good numerical performance.
New proof of energy functional monotonicity via geodesics in measure space.
problem Proving monotonicity of energy functional in generalized Ricci flow.
method Defining adapted cost functional, geodesics, and entropy functional.
result Monotonicity of cost along backwards heat flow and energy functional along generalized Ricci flow.