We extend Sobolev transport to unbalanced measures on graphs.
problem Optimal transport struggles with measures of different total mass and high computational complexity.
method We propose a scalable unbalanced Sobolev transport (UST) for measures on graphs.
result UST admits a closed-form formula for fast computation and is negative definite.
We present a methodology for clustering N objects which are described by multivariate time series, i.e. several sequences of real-valued random variables. This clustering methodology leverages copulas which are distributions encoding the dependence structure between several random variables. To take fully into account …
FairPOT balances fairness and AUC performance by selectively transforming risk scores.
problem Balancing fairness and AUC performance in high-stakes domains.
method FairPOT uses proportional optimal transport to selectively transform risk scores.
result FairPOT consistently improves fairness with minimal AUC degradation or even positive gains.
Proposes a method to create fair ITRs that balance value and fairness.
problem Fairness issues in ITRs that can lead to unfair advantages or disadvantages.
method Optimal transport theory to transform optimal ITRs into fair ITRs.
result Established a theoretical upper bound on value loss for improved trade-off ITRs.
Study examines active travel in Chicago communities, revealing mixed perceptions.
problem Transport disadvantage and lack of active mobility in underserved communities.
method Focus groups, qualitative discourse analysis, quantitative text-mining (topic modeling, sentiment analysis).
result Residents view active travel as both necessity and symbol of privilege, influenced by local culture.
Study shows caste's reduced importance in predicting women's work status and type.
problem Social disadvantage and caste impact women's work status and type in India.
method Interpreted machine learning models using feature attribution.
result Caste is less influential in predicting work for younger women compared to older women.
Algorithms are increasingly used to aid, or in some cases supplant, human decision-making, particularly for decisions that hinge on predictions. As a result, two additional features in addition to prediction quality have generated interest: (i) to facilitate human interaction and understanding with these algorithms, we…
Improves AUC for disadvantaged groups by adding features.
problem Reducing cross-group differences in AUC for classification models.
method Feature augmentation to improve AUC for disadvantaged groups.
result Significantly improves AUC for disadvantaged groups.
The purpose of this thesis is to use the language of orbifold groupoids to describe the geometry and topology of orbifolds, highlighting advantages and disadvantages of this language as they arise.
Study highlights fairness issues in travel behavior prediction models.
problem Ethical challenges in travel behavior analysis using machine learning.
method Operationalized computational fairness by equality of opportunity; compared DNN and DCM; introduced absolute correlation regularization.
result Both DNN and DCM predict disparities across social groups, with DNN outperforming DCM in prediction disparities.
Proposes FairDRL-ST for fair spatio-temporal mobility prediction.
problem Fairness concerns in spatio-temporal AI applications.
method Disentangled representation learning, adversarial learning.
result Achieves fairness in spatio-temporal mobility prediction without performance loss.
Algorithmic fairness is a field of study that addresses the systematic disadvantage of marginalized groups in machine learning systems.
problem Modern machine learning systems increasingly determine access to economic and social opportunities, leading to structural inequalities and prejudices.
method Statistical and structural approaches to algorithmic fairness.
result The field of algorithmic fairness emerged to address the systematic disadvantage of marginalized groups in machine learning systems.
AI helps Vancouver identify where off-street parking saves time and space.
problem On-street parking inefficiencies and associated costs in Vancouver.
method Developed AI models for on-street and off-street parking, comparing time costs.
result Many areas off-street parking saves time and space, aligning with city goals.
Paper defines and solves a problem in representation learning to ensure fairness with high confidence.
problem Learning fair representations with high confidence guarantees for all downstream tasks.
method Formally defines the problem, introduces FRG framework, proves high probability fairness, and demonstrates effectiveness empirically.
result FRG framework provides high-confidence guarantees for limiting unfairness across all downstream models and tasks.
Bayesian model identifies health disparities in disease progression.
problem Health disparities bias disease progression models.
method Interpretable Bayesian model accounting for three disparities.
result Model identifies and corrects for health disparities.
PyCFRL helps ensure fair reinforcement learning policies from offline data.
problem Ensuring fairness in reinforcement learning policies for disadvantaged groups.
method Sequential data preprocessing to learn counterfactually fair policies.
result PyCFRL implements a novel algorithm for fair RL policy learning.
Proposes learning regularization strength directly from data.
problem Computational expense and data reduction in grid search for deep learning hyperparameters.
method Modified Evidence Lower Bound (ELBo) objective for model selection on full training set.
result Comparable heldout accuracy to grid search with less compute time.
Stability proved for martingale and weak transport problems.
problem Stability of martingale and weak optimal transport problems.
method Established stability through unconventional topology considering temporal structure of martingales.
result Proved stability of martingale and weak transport problems.
New methods estimate transport-growth pairs in unbalanced optimal transport.
problem Statistical guarantees for Monge-type estimation in unbalanced optimal transport remain limited.
method Developed two estimators for transport-growth pairs under different setups.
result Achieved minimax optimal rate for estimation of transport-growth pairs.
This paper will serve as an introduction to the body of work on robust subspace recovery. Robust subspace recovery involves finding an underlying low-dimensional subspace in a dataset that is possibly corrupted with outliers. While this problem is easy to state, it has been difficult to develop optimal algorithms due t…
Novel approach learns optimal transport using convex neural networks.
problem Learning optimal transport between distributions from samples.
method Solving a minimax optimization to learn two convex functions, representing the optimal transport map.
result The approach finds optimal transport mappings that are independent of initialization and can handle discontinuous distributions.
Introduces statistical optimal transport for probabilistic lectures.
problem No specific problem stated; focuses on introduction.
method Lecture-based introduction to statistical optimal transport.
result Provides an introduction to statistical optimal transport.
Study shows how optimal transport behaves in higher dimensions.
problem Characterizing optimal transport in higher dimensions with Euclidean distance.
method Investigates the small regularization limit of entropic optimal transport.
result The limiting transport plan is supported on transport rays and uniquely minimizes a relative entropy functional.
A concise discussion of the axiomatic approach to the concept of parallel transport is presented. Attention is drawn to a bijective map between the sets of connections and (axiomatically defined) parallel transports. The transports along paths are pointed as a generalization of the (axiomatically defined) parallel tran…
The axiomatic approach to parallel transport theory is partially discussed. Bijective correspondences between the sets of connections, (axiomatically defined) parallel transports, and transports along paths satisfying some additional conditions, are constructed. In particular, the equivalence between the concepts "conn…
New framework uses cohomology to analyze probabilistic distortions and arbitrage.
problem Analyzing probabilistic distortions and arbitrage in categorical filtrations.
method Transport cohomological framework, simplicial structure, loop effects, holonomy.
result Nontrivial probabilistic distortions and obstructions generated by loops.
The importance of counterparty credit risk to the derivative contracts was demonstrated consistently throughout the financial crisis of 2008. Accurate valuation of Credit value adjustment (CVA) is essential to reflect the economic values of these risks. In the present article, we reviewed several different approaches f…
NOT learns optimal transport plans, kernel costs improve performance.
problem NOT algorithm learns non-optimal plans with weak quadratic costs.
method Introduced kernel weak quadratic costs to improve NOT's performance.
result Kernel costs provide improved theoretical and practical guarantees.
New algorithm solves unbalanced optimal transport on trees in quasi-linear time.
problem Efficiently solving unbalanced optimal transport problems on trees.
method Proposed an algorithm that solves a more general unbalanced optimal transport problem exactly in quasi-linear time on a tree metric.
result Solves unbalanced optimal transport on trees in quasi-linear time (less than one second for a tree with one million nodes).
A review of the parallel transport (translation) in fibre bundles is presented. The connections between transports along paths and parallel transports in fibre bundles are examined. It is proved that the latter ones are special cases of the former.
New metric for probability measures connects physics and geometry.
problem Developing a new metric for probability measures.
method Transport Hessian metric, formulated dynamical systems.
result Connections to physics equations and mathematical models.
Using McCann's transportation map, we establish a transport inequality on compact manifolds with positive Ricci curvature. This inequality contains the sharp spectral comparison estimates.
A new algorithm for parallel transport on shape spaces is presented and compared to existing methods.
problem Statistical analysis of shape data, especially in time series and optimization.
method Pole ladder algorithm for parallel transport on Kendall shape spaces, compared to integration methods.
result The pole ladder algorithm is a more efficient method for parallel transport.
Extends optimal transport to dynamic and martingale settings.
problem Dynamic and martingale relaxation of optimal transport problems.
method Extends Benamou-Brenier formula to weak optimal transport and introduces barycentric optimal transport.
result Relates barycentric optimal transport to martingale Benamou-Brenier formula.
Fairness constraints can improve accuracy from biased data.
problem Learning from biased training data can produce biased and suboptimal classifiers.
method Examined fairness-constrained ERM and other recovery methods.
result Equal Opportunity fairness constraint combined with ERM provably recovers Bayes Optimal Classifier under various bias models.
Review of modern computational optimal transport methods for biomedical applications.
problem Efficient computation of optimal transport for big data.
method Regularization-based and projection-based computational methods.
result Advancements in computational optimal transport methods for biomedical research.
Paper relaxes optimal transport using convex functions for data science.
problem Optimal transport problem on finite spaces.
method Relaxation via strictly convex functions (Kullback-Leibler divergence, Bregman divergences). Gradient descent iterative process.
result Mathematical foundations and iterative process for the relaxed optimal transport problem.
Study optimal transport on simplex boundary, proving transport map and potential regularity.
problem Regularity of transport map and potential on simplex boundary.
method Boundary regularity results for optimal transport maps, exploiting simplex symmetries.
result Regularity properties of transport map and its convex potential.
Bayesian approach to optimal transport with stochastic costs.
problem Inferring optimal transport plans with uncertain costs.
method Bayesian framework and Hamiltonian Monte Carlo (HMC) sampling.
result Inference of optimal transport plans under stochastic cost functions.
This paper generalizes Sinkhorn algorithm for unbalanced optimal transport.
problem Handling distributions with different total mass and robustness to outliers.
method Alternates between standard Sinkhorn updates and pointwise application of a contractive function.
result Defines Sinkhorn divergences that are differentiable, positive, definite, convex, and robust.
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.
New method uses kernel Stein discrepancy for measure transport without strict continuity constraints.
problem Minimizing Kullback-Leibler divergence for posterior approximation.
method Proposes minimizing kernel Stein discrepancy instead of Kullback-Leibler divergence.
result Demonstrates consistency and competitiveness of the new method.
A new framework SPOT efficiently solves large scale optimal transport problems.
problem Heavy computational burden in optimal transport limits its use.
method Implicit generative learning framework (SPOT) approximates optimal transport plan and solves it using stochastic gradient algorithms.
result SPOT efficiently solves optimal transport problems and can recover the density of the plan.
A new model corrects inhomogeneity in Optimal Transport with Boundary.
problem Inhomogeneity in UROT models for Optimal Transport with Boundary.
method Proposed a modified entropic regularization term to make UROT models homogeneous.
result Homogeneous UROT model preserves properties of standard UROT while correcting inhomogeneity.
Paper investigates optimal transport map estimation in infinite-dimensional spaces.
problem Estimating optimal transport maps in infinite-dimensional spaces is challenging.
method Characterizes γ-smoothness for optimal transport maps and develops a polynomial-rate estimator. result Shows polynomial-order minimax risk for optimal transport map estimation.
Survey of linking information geometry and optimal transport.
problem Connecting two geometric frameworks for probability measures.
method Exploration of interactions and links between information geometry and optimal transport.
result Outstanding questions for both disciplines.
This paper introduces a new process for portfolio rebalancing that is more equitable than existing methods.
problem Improving portfolio rebalancing processes in finance to be more equitable.
method Introduces a new market-invariant process for portfolio rebalancing, proving its superiority over existing methods.
result The market-invariant process is more equitable than the banker and linear processes, as demonstrated by empirical results.
New optimal transport method handles mass creation and destruction.
problem Optimal re-balancing of portfolios with mass creation or destruction.
method Formalizes an optimal transport problem with mass-change factor.
result Existence of optimal transport plans and maps established.