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…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
Trend · papers per month
48 results for “Optimal Coupling”
Two probability distributions and in second stochastic order can be coupled by a supermartingale, and in fact by many. Is there a canonical choice? We construct and investigate two couplings which arise as optimizers for constrained Monge-Kantorovich optimal transport problems where only supermartingales are al…
A Flexible Optimization Framework for Regularized Matrix-Tensor Factorizations with Linear Couplingscs.LG
Flexible framework for CMTF with ADMM for various constraints and couplings.
problem Challenges in data fusion from multiple sources with varying characteristics.
method Flexible algorithmic framework using AO and ADMM for various constraints, loss functions, and couplings.
result Accurate and computationally efficient results for various loss functions, including KL divergence.
Entropic optimal transport beyond product reference couplings: the Gaussian case on Euclidean spacemath.ST
This work extends entropic optimal transport to non-product reference couplings, focusing on Gaussian cases.
problem Finding a diffuse coupling between two measures with non-product reference couplings.
method Reduction of the entropic optimal transport problem to a matrix optimization problem.
result Complete description of the solution for non-product reference couplings, including primal and dual variables.
Develops an algorithm for bilevel optimization with coupled constraints.
problem Challenges in bilevel optimization with coupled constraints.
method Primal-dual-assisted penalty approach and a fully first-order algorithm (BLOCC).
result Established rigorous convergence theory and demonstrated effectiveness on real-world applications.
New algorithm AG-OG optimizes separable convex-concave problems efficiently.
problem Efficiently solving separable convex-concave minimax optimization problems.
method Leverages Nesterov acceleration and optimistic gradient on component and coupling parts of the problem.
result Achieves optimal convergence rate for various settings including bilinearly coupled problems.
Researchers developed a new Riemannian manifold for SPD matrix-valued optimal transport problems.
problem Optimal transport between SPD matrix-valued measures.
method Formulated as a generalized optimal transport problem with block SPD matrices, endowed with a novel Riemannian manifold structure.
result The novel Riemannian manifold allows solving SPD matrix-valued optimal transport problems using Riemannian optimization.
Study on kinetic Langevin diffusions and their couplings, showing subtle TV bounds and new non-Markovian couplings.
problem Understanding and quantifying the TV distance between solutions of kinetic Langevin diffusions with different initial values.
method Established new non-Markovian couplings for kinetic Langevin diffusions, derived from optimal coalescence trajectories, and analyzed their TV bounds.
result No Markovian coupling can capture the asymptotic decay rate of the TV distance between solutions of kinetic Langevin diffusions with different initial values.
Study finds optimal martingale coupling between two distributions with minimal entropy.
problem Finding the optimal martingale coupling between two distributions with minimal relative entropy.
method Solving a dual problem to find the log-density of the optimal coupling, which represents the marginal and martingale constraints.
result The log-density of the optimal coupling is given by a triplet of real functions representing the marginal and martingale constraints.
Weak Convergence of Approximate reflection coupling and its Application to Non-convex Optimizationmath.PR
Paper proposes a weak approximation of reflection coupling for non-convex optimization.
problem Non-convex optimization problems with different drift terms.
method Proposes an approximate reflection coupling (ARC) for stochastic differential equations (SDEs).
result ARC converges weakly to the reflection coupling and can be applied to non-convex optimization.
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…
Paper proposes an algorithm for PARAFAC2-based CMTF models with various constraints.
problem Jointly analyze matrices and tensors with irregular/ragged data.
method Alternating Optimization (AO) and ADMM for fitting PARAFAC2-based CMTF models with various constraints.
result Accurately recovers underlying patterns using various constraints and linear couplings.
New MCMC method tackles label-switching problem for clustering.
problem Label-switching problem impedes MCMC efficiency in discrete clustering.
method Formulated optimal transport couplings for partition space.
result Our method efficiently overcomes label-switching problem.
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.
Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The tensor ring (TR) decomposition is invariant under the permutation of tensors with different mode properties, which ensures the uniformity of decomposed factors and mode attribut…
Sharp pseudospectral bounds prevent transient amplification in coupled gradient descent.
problem Transient amplification in coupled gradient descent systems.
method Developed a sharp pseudospectral theory for block-triangular Jacobians, proving Kreiss constant bounds and matching minimax lower bounds.
result Obtained a finite-horizon iteration-complexity bound of for stochastic coupled descent.
Paper proves CFlows can approximate any diffeomorphism and applies it in Bayesian optimization.
problem Proving the universality of CFlows in approximating diffeomorphisms.
method Deriving the universality of Para-CFlows through affine coupling layers and invertible linear transforms.
result Para-CFlows can approximate any diffeomorphism in C^k-norm.
Optimal coupling among random vectors with known statistics and correlation structure found using minimum spanning tree over measure-valued vertices.
problem Finding the optimal coupling among random vectors with known statistics and correlation structure.
method Formulating the problem as a minimum spanning tree over measure-valued vertices and solving it in two steps.
result Optimal coupling found using the minimum spanning tree approach.
We review recent quantitative results on the approximation of mean field diffusion equations by large systems of interacting particles, obtained by optimal coupling methods. These results concern a larger range of models, more precise senses of convergence and links with the long time behaviour of the systems to be con…
UNTIE learns representations of coupled categorical data.
problem Challenges in learning from unlabeled categorical data with complex couplings.
method UNTIE approach for unsupervised representation learning of heterogeneous couplings.
result UNTIE significantly improves categorical data representations on 25 diverse datasets.
Constructs supermartingale couplings with full marginals constraints.
problem Optimal transport for supermartingale couplings with multiple marginals.
method Markovian iteration of one-period optimal supermartingale couplings.
result Explicit construction of supermartingale processes solving optimal transport problem.
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.
New method designs joint initial noises for diffusion models to improve diversity and alignment.
problem Independent initial noises limit diversity in generated images.
method Coupling of initial noises, maintaining Gaussian distribution while allowing dependence.
result Repulsive Gaussian coupling improves diversity without increasing sampling cost.
We provide a verification and characterization result of optimal maximal sub-solutions of BSDEs in terms of fully coupled forward backward stochastic differential equations. We illustrate the application thereof in utility optimization with random endowment under probability and discounting uncertainty. We show with ex…
Paper proposes a coupling-based diagnostic for SGD stepsize optimization.
problem Optimizing stepsize for SGD convergence.
method Coupling-based convergence diagnostic for monitoring stationarity.
result Proposed stepsize scheme achieves superior performance across convex and non-convex problems.
Random features are improved by variance-reducing couplings, enhancing machine learning models.
problem Improving the efficiency and accuracy of random features in machine learning.
method Using optimal transport theory to find couplings that reduce variance in random features.
result Theoretical and practical gains in efficiency and accuracy for various machine learning models.
Extends martingale transport for robust finance problems.
problem Addressing specific robust finance problems not covered by standard martingale transport.
method Introduces an additional parameter to the weak martingale optimal transport problem and proves stability.
result Stability of the extended problem with respect to risk-neutral marginal distributions.
Develop a framework for barycentric projections of optimal transport plans on Riemannian manifolds.
problem Optimal transport couplings are probabilistic objects, while many learning pipelines require deterministic maps.
method Develop a framework for barycentric projections of transport couplings on Riemannian manifolds.
result The intrinsic projection maps each source point to the conditional Fréchet mean of its destination law and is shown to be the best deterministic representative under squared geodesic loss.
Theoretical models of the strong nuclear interaction contain unknown coupling constants (parameters) that must be determined using a pool of calibration data. In cases where the models are complex, leading to time consuming calculations, it is particularly challenging to systematically search the corresponding paramete…
This paper tackles multi-marginal optimal transport problems using DC programming.
problem Multi-marginal optimal transport problems in machine learning.
method Promoting structural information in MMOT leads to a DC programming problem.
result Solutions from DC optimization are as qualitative as current methods.
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.
NetOTC compares and aligns directed or undirected networks via random walk transitions.
problem Comparing and aligning networks of different types and sizes.
method NetOTC uses a transport-based approach to find optimal transition couplings of random walks.
result NetOTC quantifies network differences and provides vertex and edge alignments.
Study on convergence rates for optimal transport with regularization.
problem Convergence analysis of divergence-regularized optimal transport.
method Novel methodology using quantization and martingale couplings.
result Sharp rates for various divergences and transport costs.
REMAL: Residual Equilibrium Manifold Active Learning for Surrogate-Based Multidisciplinary Design Analysisphysics.comp-ph
REMAL: Residual Equilibrium Manifold Active Learning for Surrogate-Based Multidisciplinary Design Analysis
problem Multidisciplinary design analysis of coupled engineering systems requires solving equilibrium states where all disciplinary coupling variables are consistent.
method Residual manifold surrogate modeling framework for coupled systems.
result REMAL learns a surrogate model of the joint residual manifold via multitask Gaussian process models.
Using methods of statistical physics, we analyse the error of learning couplings in large Ising models from independent data (the inverse Ising problem). We concentrate on learning based on local cost functions, such as the pseudo-likelihood method for which the couplings are inferred independently for each spin. Assum…
Develops optimal decision-making framework for uncertain counterfactuals.
problem Ensuring reliability of predictions in high-stakes decisions.
method Policy-Coupled Risk-Averse Conformal Prediction (PC-RACP).
result Optimal prediction sets for counterfactual decisions with valid coverage.
C-VAE improves VAE by resolving prior issues and generating better samples.
problem Low-quality samples from VAE due to prior issues.
method Formulates VAE as OT, allows flexible priors, and uses OT formulations.
result C-VAE generates higher quality samples and latent representations.
Researchers analyze inverse optimal transport, deriving theoretical and empirical insights.
problem Understanding the inverse problem of inferring cost matrices from optimal couplings.
method Formalized and analyzed using entropy-regularized optimal transport, with theoretical and empirical contributions.
result Characterization of the manifold of cross-ratio equivalent costs and derivation of an MCMC sampler.
QDSB accelerates Schrödinger bridge learning with quantized approximations.
problem Learning generative models from unpaired samples.
method Quantized diffusion Schrödinger bridges (QDSB) using anchor-quantized distributions and cell-wise sampling.
result QDSB achieves sample quality similar to existing methods but with significantly less computational time.
We propose a set of convex low rank inducing norms for a coupled matrices and tensors (hereafter coupled tensors), which shares information between matrices and tensors through common modes. More specifically, we propose a mixture of the overlapped trace norm and the latent norms with the matrix trace norm, and then, w…
Paper proposes a new method to optimize robot body structure and control policy.
problem Optimizing robot body structure and control policy in a coupled manner.
method Revisits co-design problem as a Stackelberg game, incorporating control adaptation dynamics.
result Stackelberg PPO outperforms standard PPO in stability and performance.
A new framework optimizes fMRI and behavioral data for better understanding of Autism.
problem Linking complex fMRI data to behavioral measures is challenging.
method Coupled manifold optimization framework projecting fMRI onto a shared manifold and mapping to behavioral measures.
result Framework outperforms traditional methods in predicting clinical severity of Autism.
Variational perturbation and extended Plefka approaches to dynamics on random networks: the case of the kinetic Ising modelcond-mat.dis-nn
We describe and analyze some novel approaches for studying the dynamics of Ising spin glass models. We first briefly consider the variational approach based on minimizing the Kullback-Leibler divergence between independent trajectories and the real ones and note that this approach only coincides with the mean field equ…
New framework for efficient optimal transport distances between Markov chains.
problem Efficient computation of optimal transport distances between Markov chains.
method Developed a new perspective on optimal transport distances using discounted occupancy couplings and linear programming.
result Introduced Sinkhorn Value Iteration (SVI) for efficient calculation of optimal transport distances.
Cross-Layer Subspace Coupling for LLM Compression: A Unifying Framework and Its Empirical Limitscs.LG
Unified SVD compression fails in practical tasks, highlighting the importance of per layer activation reconstruction.
problem The failure of a unified SVD compression method in practical tasks like perplexity and accuracy.
method Unified optimization problem for SVD based compression methods, focusing on cross-layer coupling.
result Downstream metrics like perplexity and accuracy degrade severely compared to standard per layer SVD LLM.
Improved VAE models avoid posterior collapse in text modeling.
problem Posterior collapse in VAEs leads to poor data manifold parameterization.
method Coupled-VAE couples a VAE with a deterministic autoencoder to improve encoder and decoder parameterizations.
result Coupled-VAE consistently improves results in probability estimation and latent space richness.
We show that the left-monotone martingale coupling is optimal for any given performance function satisfying the martingale version of the Spence-Mirrlees condition, without assuming additional structural conditions on the marginals. We also give a new interpretation of the left monotone coupling in terms of Skorokhod e…
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.