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.
New algorithms solve weak optimal transport problems for nonlinear costs.
problem Computing weak optimal transport with nonlinear costs.
method Mirror descent algorithms for primal and dual versions of WOT.
result Solutions for WOT and WOTUK compared with classical OT.
A new variational inference method using sliced Wasserstein distance is proposed.
problem The inefficiency and unreasonable properties of Kullback-Leibler divergence.
method Minimizing sliced Wasserstein distance, a valid metric from optimal transport.
result The proposed method approximates the unnormalized distribution efficiently and without requiring a tractable density function.
New sampling method uses gradient-free IPS with RKHS velocity field.
problem Efficient sampling from unnormalized target densities.
method Gradient-free interacting particle systems (IPS) with RKHS velocity field.
result IPS produce high-quality samples from various target distributions.
A new method called TemperFlow tackles multimodality in sampling from unnormalized distributions.
problem Sampling from unnormalized distributions with isolated modes.
method TemperFlow learns a sequence of tempered distributions to progressively approach the target distribution.
result TemperFlow overcomes the limitations of existing methods and achieves superior performance.
PDDS samples from unnormalized densities using iterative particle scheme.
problem Sampling from unnormalized probability densities.
method Iterative particle scheme with novel score matching loss.
result Asymptotically consistent estimates for multimodal and high-dimensional tasks.
iEFM trains CNF models from unnormalized densities efficiently.
problem Training generators from energy functions or unnormalized densities.
method Iterated energy-based flow matching (iEFM) with simulation-free objective.
result iEFM outperforms existing methods in probabilistic modeling.
Extracts coarse-grained PDEs from microscopic simulations.
problem Discovering effective PDEs for macro-scale processes from microscopic data.
method Combining neural networks with equation-free numerics and data-driven approaches.
result Efficiently discovers macro-scale PDEs from microscopic simulations.
We develop underdamped diffusion bridges for sampling from unnormalized densities.
problem Sampling from unnormalized densities without direct access to samples.
method Underdamped diffusion bridges with rigorous score matching equivalence.
result State-of-the-art performance in sampling across various problems.
A new method combines energy-based models and entropy-regularized optimal transport.
problem Combining energy-based models and optimal transport for generative modeling.
method Energy-guided Entropic Neural Optimal Transport (E-ENT)
result Proves generalization bounds and validates scalability in image translation.
Combines SMC and diffusion-based samplers for improved sampling performance.
problem Sampling from unnormalized densities efficiently and robustly.
method Viewing SMC and diffusion-based samplers as continuous-time processes, SCLD combines their strengths.
result SCLD achieves improved performance on multiple benchmark problems with less training budget.
Improves QMC for complex distributions using transport maps.
problem Challenges in applying QMC to general target distributions.
method Train a transport map to approximate target distributions, ensuring RQMC achieves superior error rates.
result Transport QMC achieves faster convergence rates than standard Monte Carlo under mild conditions.
New method estimates model discrepancy without sampling for unnormalized models.
problem Evaluating and training unnormalized density models efficiently.
method Estimate Stein discrepancy using neural network parameterized vector function.
result Method outperforms existing goodness-of-fit tests and training methods.
LFIS uses a time-dependent velocity field to sample from complex distributions.
problem Sampling from unnormalized density functions.
method LFIS learns a time-dependent velocity field to transport samples from a simple initial distribution to a complex target distribution.
result LFIS achieves state-of-the-art performance on various benchmark problems.
CD algorithm achieves near-optimal convergence rate for unnormalized models.
problem Training unnormalized models with high efficiency.
method Non-asymptotic analysis of contrastive divergence algorithm.
result CD can achieve O(n−1/2) convergence rate under regularity assumptions. New method uses SoS densities and α-divergences for efficient sequential transport maps.
problem Efficiently generating samples from approximated densities.
method Sequential transport maps using Sum-of-Squares (SoS) densities and α-divergences.
result Convex optimization problems with efficient semidefinite programming solutions.
Paper optimizes change detection in unnormalized distributions.
problem Detecting changes in unnormalized pre- and post-change distributions.
method Log-Partition Approximation Cumulative Sum (LPA-CUSUM) algorithm based on thermodynamic integration.
result Asymptotically optimal performance achieved through unbiased estimation of CUSUM statistics.
ASBS improves sampling from Boltzmann distributions without importance weighting.
problem Sampling from Boltzmann distributions with known energies but unknown samples.
method Adjoint Schrödinger Bridge Sampler using kinetic-optimal transportation.
result ASBS achieves scalable and efficient sampling without importance weighting.
Several statistical models are given in the form of unnormalized densities, and calculation of the normalization constant is intractable. We propose estimation methods for such unnormalized models with missing data. The key concept is to combine imputation techniques with estimators for unnormalized models including no…
New CUSUM algorithm detects changes in unnormalized models.
problem Change detection in models with unknown normalization constants.
method Score-based CUSUM (SCUSUM) algorithm based on Fisher divergence and Hyvärinen score.
result Asymptotic optimality of the SCUSUM algorithm demonstrated.
New complexity analysis for estimating normalizing constants in high dimensions.
problem Estimating the normalizing constant of unnormalized probability densities in high dimensions.
method Analyze and derive the oracle complexity of annealed importance sampling.
result Oracle complexity of $\widetilde{O}\left(\frac{dβ^2{\mathcal{A}}^2}{\varepsilon^4}
ight)$ for estimating Z within ε relative error. CDS combines PT and diffusion for efficient sampling from multimodal distributions.
problem Sampling from unnormalized multimodal distributions efficiently.
method Conditional Diffusion Sampling (CDS) using Conditional Interpolants and Parallel Tempering.
result CDS achieves a superior trade-off between sample quality and density evaluation cost.
Unified view on learning unnormalized distributions using NCE.
problem Learning unnormalized distributions across different communities.
method Noise-Contrastive Estimation (NCE) for a unified perspective.
result Established finite-sample convergence rates for exponential families.
Paper presents a new method to learn unnormalized models efficiently.
problem Scalability issues in score matching for flexible unnormalized models.
method Connects learning objectives to Wasserstein gradient flows for scalability.
result Demonstrates improved learning of unnormalized models on manifolds.
REGS samples from unnormalized distributions using gradient flow and neural networks.
problem Sampling from unnormalized distributions with high accuracy and efficiency.
method REGS is a particle method that iteratively transforms samples from a reference distribution to match an unnormalized target distribution using Wasserstein gradient flow and neural networks.
result REGS outperforms state-of-the-art methods in sampling from challenging multimodal distributions and real datasets.
A new method optimizes a generalized Kullback-Leibler divergence for better simulation-based inference.
problem Optimizing likelihood functions when they are only known implicitly.
method Optimizes a generalized Kullback-Leibler divergence that accounts for normalization constants in unnormalized distributions.
result Unified approach that combines Neural Posterior Estimation and Neural Ratio Estimation.
We investigate adversarial learning in the case when only an unnormalized form of the density can be accessed, rather than samples. With insights so garnered, adversarial learning is extended to the case for which one has access to an unnormalized form u(x) of the target density function, but no samples. Further, new c…
The parameter estimation of unnormalized models is a challenging problem. The maximum likelihood estimation (MLE) is computationally infeasible for these models since normalizing constants are not explicitly calculated. Although some consistent estimators have been proposed earlier, the problem of statistical efficienc…
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.
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.
Unified empirical and variational Bayes for unnormalized densities.
problem Approximating unnormalized densities using latent variable models.
method Formulate a latent variable model for Y=X+N(0,σ2Id), use ELBO as parametrization of Y's energy function, and estimate X with empirical Bayes least-squares. result UVB has higher capacity to approximate energy functions than MLPs in DEEN.
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).
Unified framework for data-free sampling using Wasserstein gradient flows.
problem Efficient sampling from unnormalized distributions without data.
method Unified theoretical framework based on Wasserstein gradient flows.
result Unified form of velocity field for various f-divergences.
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.
We introduce a new family of estimators for unnormalized statistical models. Our family of estimators is parameterized by two nonlinear functions and uses a single sample from an auxiliary distribution, generalizing Maximum Likelihood Monte Carlo estimation of Geyer and Thompson (1992). The family is such that we can e…
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.
In this paper, we present a novel and principled approach to learn the optimal transport between two distributions, from samples. Guided by the optimal transport theory, we learn the optimal Kantorovich potential which induces the optimal transport map. This involves learning two convex functions, by solving a novel mi…
MT-SGD samples from multiple target distributions using gradient descent.
problem Sampling from multiple unnormalized target distributions.
method Proposes MT-SGD, a flow of intermediate distributions to sample from multiple target distributions.
result Asymptotic analysis shows MT-SGD reduces to multiple-gradient descent for multi-objective optimization.
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 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.
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 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.
Optimal transport as a loss for machine learning optimization problems has recently gained a lot of attention. Building upon recent advances in computational optimal transport, we develop an optimal transport non-negative matrix factorization (NMF) algorithm for supervised speech blind source separation (BSS). Optimal …
A scalable algorithm for sampling and fine-tuning models using Tilt Matching.
problem Efficient sampling and fine-tuning of generative models.
method Tilt Matching, arising from a dynamical equation, minimizes variance and inherits regularity from stochastic interpolants.
result Empirically verified to be efficient and highly scalable, providing state-of-the-art results.
Study optimal transport for robust optimization, showing how adversary's strategy relates to regularization.
problem Optimizing under uncertain parameters with a fictitious adversary reshaping a reference distribution.
method Introduces optimal transport and regularization to relate robustification to variation and Lipschitz norms.
result Conditions for existence and computability of Nash equilibrium between decision-maker and adversary.
Introduces a new divergence measure for optimal transport.
problem Optimal transport distances and information divergences.
method Infimal convolution formulation of proximal optimal transport divergence.
result Establishes connections to dynamic formulations and partial differential equations.
Optimal Transport enhances machine learning with new methods.
problem Comparing and manipulating probability distributions in machine learning.
method Probabilistic framework rooted in rich history and theory.
result New solutions in generative modeling and transfer learning.