Aggregates probability models using Wasserstein space and variational approach.
problem Model aggregation in the Wasserstein space of distributions.
method Data-driven calibration framework based on Γ-convergence. result Empirical minimizers converge to the minimizers of the actual problem.
Paper introduces WWAggr for ensemble CPD, improving accuracy and decision threshold selection.
problem Challenges in detecting abrupt distribution shifts in high-dimensional data streams.
method Introduces WWAggr, a novel task-specific ensemble aggregation method based on Wasserstein distance.
result Demonstrates WWAggr outperforms standard aggregation techniques and decision threshold selection.
Develops a method to efficiently compute Wasserstein barycenters with variational distributions.
problem High computational burden in computing Wasserstein barycenters for high-dimensional and continuous settings.
method Introduces a variational distribution to approximate the continuous Wasserstein barycenter, reformulating the problem as an optimization with c-cyclical monotonicity.
result The method provides a tractable dual formulation for efficient computation of Wasserstein barycenters, demonstrated on real applications.
We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any time spot follows a Gaussian mixture distribution, a fact exploited to softly matc…
We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any time position follows a Gaussian mixture distribution, a fact exploited to softly …
Method learns dynamics from aggregate data without full trajectories.
problem Learning nonlinear dynamics from aggregate data where individual trajectories are not available.
method Combines weak Fokker-Planck Equation description with Wasserstein GAN.
result Successfully learns nonlinear dynamics from aggregate data.
Extends DAMs to Gaussian distributions for efficient pattern storage and retrieval.
problem Limited storage capacity and retrieval methods for non-vector pattern representations.
method Introduces a log-sum-exp energy function over Gaussian distributions, using optimal transport maps for retrieval dynamics.
result Proves exponential storage capacity and provides quantitative retrieval guarantees.
Efficient federated algorithm for calculating transportation barycenter.
problem Efficiently calculating the free-support transportation barycenter in a federated setting.
method Single-loop dual decomposition algorithm that uses only aggregated information.
result Significantly scalable and low-complexity algorithm for federated computation.
New algorithm approximates continuous Wasserstein barycenters efficiently.
problem Computing Wasserstein barycenters for continuous distributions.
method Stochastic algorithm using dual potentials and stochastic gradient descent.
result Efficient online approximation of continuous Wasserstein barycenters.
A new algorithm computes Wasserstein barycenters without entropic regularization.
problem Computing Wasserstein barycenters efficiently and accurately.
method Free-support algorithm based on particle flow and Riemannian geometry.
result The algorithm avoids entropic regularization and is computationally tractable.
To address the challenges in learning deep generative models (e.g.,the blurriness of variational auto-encoder and the instability of training generative adversarial networks, we propose a novel deep generative model, named Wasserstein-Wasserstein auto-encoders (WWAE). We formulate WWAE as minimization of the penalized …
The paper bounds solutions to complex optimization problems with uncertain data.
problem Distributionally robust optimization problems with multivariate uncertainty sets.
method Conditions and bounds derived for multivariate and univariate Wasserstein distances, Bregman-Wasserstein divergences, and signed Choquet integrals.
result Computable lower and upper bounds for DRO problems, derived from scalar-valued aggregation functions and Wasserstein distances.
Paper proposes PRWB and RPRWB for Wasserstein barycenters.
problem Numerical challenges in computing Wasserstein barycenters.
method Projection robust Wasserstein barycenter (PRWB) and relaxed PRWB (RPRWB).
result RPRWB improves clustering performance on real text datasets.
New method estimates SW distance using CDFs for scalable data parallelism.
problem Estimating SW distance efficiently for large datasets.
method Estimators based on CDFs of projected measures, avoiding sorting.
result Efficient estimation for large datasets and federated learning.
PTOPOFL uses topological descriptors to protect privacy in federated learning.
problem Privacy and data reconstruction attacks in federated learning.
method PTOPOFL replaces gradient communication with persistent homology feature vectors for privacy and topology-guided aggregation.
result PTOPOFL achieves higher AUC and reduces reconstruction risk compared to gradient sharing.
Optimal transport offers an alternative to maximum likelihood for learning generative autoencoding models. We show that minimizing the p-Wasserstein distance between the generator and the true data distribution is equivalent to the unconstrained min-min optimization of the p-Wasserstein distance between the encoder agg…
MWGraD solves multi-objective distributional optimization using particle-based gradient descent.
problem Simultaneously minimize multiple objective functionals over probability distributions.
method Iterative particle-based algorithm MWGraD, estimating and aggregating Wasserstein gradients.
result Demonstrates effectiveness on synthetic and real-world datasets.
This paper improves MDS visualization by adjusting Wasserstein distances for heavy-tailed data.
problem Enhancing Multidimensional Scaling (MDS) for better pattern recognition with heavy-tailed distributions.
method Introduces Max-D-SW, a metric adjustment of Max-Sliced Wasserstein distance that aggregates over orthonormal bases.
result Max-D-SW provides a clear numerical advantage in MDS outcomes, especially for heavy-tailed distributions.
New method for scalable barycenter computation using Wasserstein gradient flows.
problem Scalability and integration of label information in barycenter computation.
method Gradient flows in Wasserstein space, time discretization, mini-batch optimal transport, modular regularization, task-aware functions, supervised information integration.
result Empirically validated new state-of-the-art barycenter solver with labeled barycenters outperforming unlabeled ones.
Proposes Gromov-Wasserstein methods for multi-view embedding.
problem Integrating multiple representations of the same samples in heterogeneous geometries.
method Gromov-Wasserstein optimal transport for multi-view embedding.
result Preserves intrinsic relational structure across views effectively.
Proposes using Wasserstein barycenters for robust optimization with multiple data sources.
problem Distributionally robust optimization with multiple heterogeneous data sources.
method Construct nominal distribution through Wasserstein barycenter of multiple data samples, reformulates as a finite convex program.
result Proposed scheme outperforms other estimators in sparse inverse covariance matrix estimation.
Most graph kernels are an instance of the class of R-Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of the final set of substructures, usually a sum or average, thereby potentially dis…
New autoencoder improves latent space learning by optimizing sliced Gromov-Wasserstein discrepancies.
problem Improving inner discrepancy between prior and posterior distributions in autoencoders.
method Proposed spherical sliced fused Gromov Wasserstein (SSFG) and variants (MSSFG, PSSFG) to find important directions.
result New autoencoders achieve favorable performance in latent manifold learning, image generation, and reconstruction.
New approach for prudent risk evaluation using model aggregation.
problem Risk evaluation and optimization under uncertainty.
method Model Aggregation (MA) approach based on stochastic dominance.
result Produces robust risk evaluation and distributional models.
A new method clusters complex networks using topological and geometric structure.
problem Clustering complex networks with intricate topology.
method Centroid-based clustering strategy using Wasserstein distance and barycenter for persistence barcodes.
result Demonstrated effectiveness on simulated and real-world networks.
WGNN learns graph representations from incomplete attribute data.
problem Missing node attributes in graphs.
method WGNN learns node representations from decomposed attribute matrices and uses Wasserstein space for message passing.
result WGNN outperforms existing methods in node classification tasks with missing attribute data.
Robust VB framework for large datasets with outliers.
problem Handling outliers and contamination in large datasets.
method Divide and conquer approach with geometric median aggregation.
result VM-Posterior distribution preserves contraction properties.
Optimal Transport Graph Neural Networks (OT-GNN) improves graph embeddings by using optimal transport.
problem Graph Neural Networks (GNN) often lose structural or semantic information when aggregating node embeddings.
method Combines optimal transport (OT) with parametric graph models to compute graph embeddings from Wasserstein distances between node embeddings and prototype point clouds.
result OT-GNN outperforms popular methods on molecular property prediction tasks and produces smoother graph representations.
In this paper we extend the setting of the online prediction with expert advice to function-valued forecasts. At each step of the online game several experts predict a function, and the learner has to efficiently aggregate these functional forecasts into a single forecast. We adapt basic mixable (and exponentially conc…
A new graph kernel uses LCS and Wasserstein distance for better graph comparisons.
problem Graph learning methods can be limited by information from distant vertices and path length constraints.
method Proposes a Graph Kernel based on LCS similarity and Wasserstein distance in a novel metric space.
result The new kernel emphasizes comparisons between similar paths and reduces information loss.
Learning nonlinear dynamics from diffusion data is a challenging problem since the individuals observed may be different at different time points, generally following an aggregate behaviour. Existing work cannot handle the tasks well since they model such dynamics either directly on observations or enforce the availabi…
WassFFed addresses fairness in Federated Learning by ensuring consistency between local and global models.
problem Achieving fairness in Federated Learning where data is distributed among diverse user groups.
method WassFFed employs a Wasserstein barycenter calculation to aggregate local models' outputs, ensuring consistency and fairness.
result WassFFed outperforms existing approaches in balancing accuracy and fairness.
Synthesizes robust estimators for domain adaptation.
problem Improving prediction accuracy in target domain with limited data.
method Synthesizes a family of robust least squares estimators using convex optimization.
result Robust strategies can outperform non-robust interpolations.
TQF models multivariate uncertainty by learning conditional quantiles.
problem Challenges in fully nonparametric estimation of multivariate conditional distributions.
method Tomographic Quantile Forests (TQF) learns conditional quantiles of directional projections.
result TQF reconstructs multivariate conditional distribution efficiently without convexity restrictions.
Study market efficiency under partial information using SDEs and optimization.
problem Market efficiency under partial information constraints.
method McKean-Vlasov-type SDEs, Wasserstein barycenters, KL divergence, convex optimization, optimal control, nonlinear filtering.
result Convergence of reduced-information market price processes to true price process under increasing information flow.
New bounds improve graph node classification using optimal transport.
problem Improving transductive generalization bounds for graph node classification.
method Representation-based generalization bounds via optimal transport, expressed in terms of Wasserstein distances.
result Strong correlation between derived bounds and empirical generalization in graph node classification.
Graphon autoencoder generates graphs with arbitrary sizes using Chebyshev filters.
problem Generating graphs with arbitrary sizes and arbitrary structures.
method Induces graphons from observed graphs, uses Chebyshev filters for latent representation, and learns encoder and decoder to minimize Wasserstein distance.
result Graphon autoencoder provides a new paradigm for graph generation with good generalizability and transferability.
We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a current best guess for the distribution, called reference measure, is available. We w…
Efficiently aggregating data from different sources is a challenging problem, particularly when samples from each source are distributed differently. These differences can be inherent to the inference task or present for other reasons: sensors in a sensor network may be placed far apart, affecting their individual meas…
Paper defends sensitive attributes in GNNs from inference attacks.
problem Protecting sensitive attributes in GNNs from inference attacks.
method Proposes adversarial training with TV and Wasserstein distance to locally filter sensitive attributes.
result Framework creates strong defense against inference attacks with minimal performance loss.
The Maximum Mean Discrepancy (MMD) has found numerous applications in statistics and machine learning, most recently as a penalty in the Wasserstein Auto-Encoder (WAE). In this paper we compute closed-form expressions for estimating the Gaussian kernel based MMD between a given distribution and the standard multivariat…
TimeLAVA: A Learning-Agnostic Framework for Valuing Time Series
problem Valuing time series data for critical domains like healthcare, finance, and industrial monitoring
method A novel Selective Wavelet-based Wasserstein discrepancy for segmenting and valuing temporal segments
result Significantly more informative value scores than existing methods
Wasserstein GANs fail to approximate Wasserstein distance, leading to their success.
problem Approximating Wasserstein distance in deep generative models.
method Analysis of differences between theoretical setup and training reality.
result Wasserstein GANs' success is due to their failure to approximate Wasserstein distance.
Study on conditions for achieving optimal robustness in statistical estimators.
problem Achieving the optimal robustness of estimators in statistical models.
method Developed a Wasserstein analogue of the Cramer-Rao inequality and investigated conditions for achieving the Wasserstein-Cramer-Rao lower bound.
result Conditions for the existence of asymptotically efficient estimators in one-parameter models and location-scale families.
A method for fast estimation of Wasserstein distances using sliced Wasserstein distances.
problem Efficiently computing Wasserstein distances for multiple pairs of distributions.
method Regression on sliced Wasserstein distances to predict true Wasserstein distances.
result The proposed method provides a better approximation of Wasserstein distance than state-of-the-art models, especially in low-data regimes.
The paper introduces a new Wasserstein distance for approximating posteriors in inverse problems.
problem Approximating posterior measures in inverse problems using conditional Wasserstein distances.
method Introduces a conditional Wasserstein distance with restricted couplings and derives its dual.
result Shows that conditional Wasserstein GANs can yield favorable properties for posterior sampling.
Stability of Wasserstein spaces under various convergence types.
problem Stability and finiteness of Wasserstein spaces over singular and non-singular spaces.
method Gromov--Hausdorff convergence and equivariant Gromov--Hausdorff convergence.
result Analogue of Perelman's stability theorem on Wasserstein spaces.
Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs) which are 2D multisets of points. Their variable size makes them, however, difficult to combine with typical machine learning workflows. In this paper we introduce persistence c…