Improved KLMC for sampling under various conditions.
problem Stable simulation of kinetic Langevin dynamics under different parameters.
method Revisited synchronous Wasserstein coupling analysis with stochastic exponential Euler discretization.
result Exponential integrator can simulate kinetic Langevin dynamics in the overdamped regime with proper time acceleration.
pHMC converges on infinite-dimensional spaces with bounds.
problem Convergence of pHMC on Hilbert spaces.
method Coupling of two pHMC copies, adapted from arXiv:1805.00452.
result Proven convergence bounds in 1-Wasserstein distance.
The sectoral synchronization observed for the Japanese business cycle in the Indices of Industrial Production data is an example of synchronization. The stability of this synchronization under a shock, e.g., fluctuation of supply or demand, is a matter of interest in physics and economics. We consider an economic syste…
Networks of coupled dynamical systems provide a powerful way to model systems with enormously complex dynamics, such as the human brain. Control of synchronization in such networked systems has far reaching applications in many domains, including engineering and medicine. In this paper, we formulate the synchronization…
New method linearizes nonlinear coupled oscillators on graphs.
problem Predicting global synchronization in nonlinear coupled oscillators on graphs.
method Latent dynamic filters learned through supervised matrix factorization.
result Latent dynamics filters enable effective prediction of global synchronization.
KuramotoGNN uses Kuramoto model to prevent over-smoothing in graph neural networks.
problem Over-smoothing in graph neural networks where node features become indistinguishable.
method Integrates Kuramoto model to prevent phase synchronization and instead achieve frequency synchronization.
result KuramotoGNN reduces over-smoothing on various graph deep learning tasks.
The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and…
Study on synchronization in financial markets with time delays.
problem Understanding market dynamics and synchronization in financial systems with time delays.
method Examined a system of coupled non-linear delay-differential equations, linearized for small delays, and analyzed collective dynamics using bifurcation diagrams and numerical solutions.
result Demonstrated that limit cycles can be maintained in coupled N-asset models with appropriate parameterization, leading to market synchronization.
Paper analyzes convergence of ODE samplers in Wasserstein distances.
problem Limited theoretical understanding of convergence properties of probability flow ODEs.
method Convergence analysis for general probability flow ODEs in 2-Wasserstein distance.
result First non-asymptotic convergence analysis for probability flow ODE samplers.
New Wasserstein divergence improves generative model robustness and structure preservation.
problem Improving generative model robustness and structure preservation.
method Introduces a novel Wasserstein-1 path-space divergence and a WUP theorem.
result Derives robustness and generalization bounds for flow-based models.
Study on nonsmooth contractive SA with constant stepsize and Q-learning.
problem Understanding convergence and bias in nonsmooth contractive SA with different noise types.
method Proposed prelimit coupling technique for steady-state convergence and derived asymptotic bias.
result Asymptotic bias of nonsmooth SA is proportional to the square root of the stepsize.
Research explores how interconnected systems synchronize and how to control their behavior.
problem Understanding and controlling the behavior of interconnected dynamical systems.
method Mean field games approach applied to controlled coupled oscillators.
result Developed methods to predict and influence emergent phenomena in interconnected systems.
New algorithm for low-rank optimal transport with improved interpretability and efficiency.
problem Quadratic scaling of optimal transport coupling matrix for massive datasets.
method Factor Relaxation with Latent Coupling (FRLC) algorithm.
result Superior performance on diverse applications including graph clustering and spatial transcriptomics.
Study financial markets using synchronization measures and clustering algorithms.
problem Analyze high-frequency trading dynamics and market states.
method Ordinal pattern series, information-theoretic synchronization measure, clustering algorithms, Markov model.
result Identify two coherent seasons of centralized and decentralized synchronicity.
Study predicts synchronization state of financial time series using cross-recurrence plots.
problem Predicting the state of synchronization of financial time series.
method Cross-correlation analysis and deep learning framework for predicting synchronization state based on cross-recurrence plots.
result Satisfactory performance in predicting synchronization state for certain pairs of stocks.
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.
In a complex system, the interactions between individual agents often lead to emergent collective behavior like spontaneous synchronization, swarming, and pattern formation. The topology of the network of interactions can have a dramatic influence over those dynamics. In many studies, researchers start with a specific …
A new method for conditional sampling using paired Wasserstein Autoencoders.
problem Conditional sampling from complex data distributions.
method Derive a novel loss function for Wasserstein Autoencoders to enable sampling from OT-type couplings.
result Learned cost-optimal transport maps and conditional sampling from an OT-type coupling.
Robust Q-learning for mean-field control under Wasserstein uncertainty
problem Mean-field control under Wasserstein uncertainty
method Quantization-and-projection scheme with Wasserstein dual reformulation
result Convergence and finite-time iteration bounds
New method synchronizes graphs with probability measures on rotations.
problem Synchronizing graphs with measure-valued edges over rotations.
method Formulated as maximization of cycle-consistency in probability measures over rotations, using Sinkhorn divergences.
result Proposes a nonparametric Riemannian particle optimization approach converging to global optimum under certain conditions.
The paper proposes methods to estimate MCMC quality with couplings, bounding Wasserstein distance.
problem Improving MCMC efficiency without sacrificing asymptotic consistency.
method Estimators based on couplings of Markov chains to assess quality of asymptotically biased sampling methods.
result Empirical upper bounds of Wasserstein distance for assessing MCMC quality.
We study the quantum synchronization between a pair of two-level systems inside two coupled cavities. By using a digital-analog decomposition of the master equation that rules the system dynamics, we show that this approach leads to quantum synchronization between both two-level systems. Moreover, we can identify in th…
SGLD proves geometric ergodicity via reflection coupling for nonconvex log-concave distributions.
problem Proving geometric ergodicity of SGLD in nonconvex, log-concave settings.
method Reflection coupling technique to handle SGLD's time discretization and minibatch issues.
result SGLD has an invariant distribution and geometric ergodicity in W1 distance. Algorithm samples from Wasserstein barycenter of measures.
problem Sampling from Wasserstein barycenter of measures.
method Gradient flow of multimarginal formulation with penalization.
result Algorithm samples close to Wasserstein barycenter.
New framework models graph signals as distribution-valued signals in Wasserstein space.
problem Limitations of classical vector-based GSP, including synchronous observations and uncertainty.
method Introduces graph distribution-valued signals (GDSs) in the Wasserstein space.
result GDSs naturally encode uncertainty and stochasticity, generalizing traditional graph signals.
Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations. In this paper, we propose a new variant of sliced Wasserstein distance, study the use …
Multi-simulator training has contributed to the recent success of Deep Reinforcement Learning by stabilizing learning and allowing for higher training throughputs. We propose Gossip-based Actor-Learner Architectures (GALA) where several actor-learners (such as A2C agents) are organized in a peer-to-peer communication t…
New method improves sampling efficiency in complex stochastic systems.
problem Sampling efficiency in nonconvex stochastic gradient cases.
method Reflection coupling for unadjusted generalized Hamiltonian Monte Carlo.
result Quantitative Gaussian concentration bounds and convergence rates established.
New couplings improve understanding of molecular dynamics convergence.
problem Understanding convergence of Andersen dynamics in high dimensions.
method Presented couplings to obtain sharp convergence bounds in the Wasserstein sense.
result Sharp convergence bounds in the Wasserstein sense without global convexity.
This work improves convergence guarantees for unadjusted HMC in KL and Rényi divergences.
problem Understanding convergence properties of unadjusted HMC in divergences like KL and Rényi.
method One-shot couplings to establish regularization and lift convergence bounds.
result Quantitative control of relative density mismatch and warm-start requirements.
Proposes an efficient lower bound for Gromov-Wasserstein discrepancy.
problem Comparing structured data from different metric-measure spaces.
method Orthogonal Gromov-Wasserstein (OGW) discrepancy with efficient closed-form lower bound.
result Efficient and tight lower bounds for Gromov-Wasserstein discrepancy.
The paper optimizes estimating transport maps between distributions.
problem Estimating optimal transport maps between distributions.
method Plugin approach using optimal couplings and extensions.
result Minimax optimality of the proposed estimators.
In this paper we will give a new proof of the monotonicity of Wasserstein distances of two diffusions under super Ricci flow. Our proof is based on the coupling method of B.Andrew and J.Clutterbuck. The same method can also be applied to the contractivity of normalized L-Wasserstein distance under backward Ricci flow.
ARK improves knockoffs robustness to feature distribution misspecification.
problem Robustness of knockoffs inference to misspecified feature distributions.
method Coupling approximate knockoffs with model-X knockoffs to achieve FDR and FWER control.
result The approximate knockoffs procedure can control FDR and FWER asymptotically.
Trade is a fundamental pillar of economy and a form of social organization. Its empirical characterization at the worldwide scale is represented by the World Trade Web (WTW), the network built upon the trade relationships between the different countries. Several scientific studies have focused on the structural charact…
Introduces new Wasserstein distances for more intrinsic metrics.
problem Improve metric for comparing distributions.
method Introduces RWp distances, designs algorithms for computation. result New distances are more intrinsic and computable.
Faster GW alignment for incomparable point clouds via low-rank couplings.
problem Aligning points across incomparable point clouds.
method Low-rank couplings and costs to solve Gromov-Wasserstein framework in linear time.
result Linear-time computation of Gromov-Wasserstein distances.
We introduce tools to capture the dynamics of three different pathways, in which the synchronization of human decision-making could lead to turbulent periods and contagion phenomena in financial markets. The first pathway is caused when stock market indices, seen as a set of coupled integrate-and-fire oscillators, sync…
The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of coupled maps as a synchronous update graph dynamical systems. Specifically, we study …
Develops a two-sample test using projected Wasserstein distance to handle high-dimensional data.
problem Testing whether two high-dimensional samples come from the same distribution.
method Optimal projection to find a low-dimensional linear mapping that maximizes the Wasserstein distance between projected probability distributions.
result Characterizes the convergence rate of the projected Wasserstein distance and presents practical algorithms.
CPFM integrates dimensionality reduction and reconstruction with flow networks.
problem Learning coupled continuous flows for data and embeddings.
method Coupled flow matching framework with Gromov-Wasserstein objective and dual-conditional flow network.
result CPFM preserves and recovers residual information in latent space.
New optimal transport divergences derived from scoring functions.
problem Developing new divergences for optimal transport.
method Using scoring functions as cost functions in optimal transport.
result Comonotonic coupling is optimal for many new divergences.
We introduce Primal-Dual Wasserstein GAN, a new learning algorithm for building latent variable models of the data distribution based on the primal and the dual formulations of the optimal transport (OT) problem. We utilize the primal formulation to learn a flexible inference mechanism and to create an optimal approxim…
A new metric HCP distance for comparing distributions.
problem Comparing high-dimensional probability distributions efficiently.
method Hilbert curve projection to low-dimensional coupling, followed by transport distance calculation.
result HCP distance is a proper metric for probability measures with bounded supports.
We have analyzed the Indices of Industrial Production (Seasonal Adjustment Index) for a long period of 240 months (January 1988 to December 2007) to develop a deeper understanding of the economic shocks. The angular frequencies estimated using the Hilbert transformation, are almost identical for the 16 industrial secto…
This work extends stochastic localization to joint probability measures for data analysis.
problem Data distributional analysis in high-dimensional probability.
method Unified stochastic localization under Eldan's α-scheme, coupled probability measures via shared Brownian motion.
result Eldan's α-distance as a scalable surrogate for Wasserstein distance.
A new method efficiently approximates Gromov-Wasserstein distance.
problem High computational complexity of Gromov-Wasserstein distance.
method Importance sparsification method to construct a sparse coupling matrix.
result Efficient approximation of GW distance with reduced complexity.
Unified framework for Brownian motion distances on specific geometric manifolds.
problem Understanding Brownian motion distances on radially isoparametric manifolds.
method Developed a geometric framework and derived drift-window inequalities.
result Unified framework for coadapted Brownian couplings on RIM.