Generative flows learn distributions on low-dimensional manifolds robustly via Wasserstein proximals.
problem Learning distributions supported on low-dimensional manifolds robustly.
method Combining Wasserstein-1 and Wasserstein-2 proximal operators to formulate well-posed continuous-time generative flows.
result The combination of Wasserstein-1 and Wasserstein-2 proximals ensures the well-posedness of generative flows, leading to unique and robust learning.
New sampling method using regularized Wasserstein proximal for Gibbs distributions.
problem Sampling from Gibbs distributions with numerical stability and efficiency.
method Preconditioned regularized Wasserstein proximal operator.
result Discrete-time convergence analysis and explicit bias characterization.
Sparse transformer architecture improves accuracy and speed in generative modeling and inverse problems.
problem Improving accuracy and speed in generative modeling and inverse problems.
method Proposes a sparse transformer architecture using regularized Wasserstein proximal operator with L1 prior. result Sparse transformer achieves higher accuracy and faster convergence than classical methods.
Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing. Major efforts have been under way to address its high computational complexity, some leading to approximate or regularized variations such as Sinkhorn distance. However, as we will demonstrate, regu…
Paper analyzes convergence of proximal algorithm in metric spaces without geodesic convexity.
problem Analyzing convergence of proximal algorithm in general metric spaces.
method Analysis of the Wasserstein proximal algorithm without geodesic convexity assumption.
result Establishes unbiased and linear convergence rate for proximal algorithm under natural Wasserstein inequality.
Mathematical analysis improves SGMs, resolving memorization issues.
problem Improving performance and avoiding memorization in SGMs.
method Formulated SGMs using Wasserstein proximal operators and mean-field games.
result Improved SGM performance in terms of training samples and time.
Improved sampling guarantees for weakly log-concave distributions.
problem Sampling from distributions that are not strongly log-concave.
method Proximal sampler with convergence guarantees under weaker assumptions.
result New state-of-the-art sampling guarantees for various target distributions.
GANs may not have Nash equilibria, but proximal training can find solutions.
problem Existence of Nash equilibria in GANs optimization.
method Proximal training approach to find solutions.
result Proximal training finds solutions to GAN problems.
Accelerates sampling from Gibbs distributions using ARWP method.
problem Sampling from Gibbs distributions efficiently.
method ARWP method, combining Nesterov acceleration and regularized Wasserstein proximal.
result ARWP exhibits higher contraction rate and faster tail exploration.
We propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPLA)---for sampling from a log concave distribution. Our method is a generalization of the Langevin algorithm to potentials expressed as the sum of one stochastic smooth term and multiple stochastic nonsmooth terms. In each iteration, our splitting t…
Noise-free sampling method using Wasserstein proximal for faster convergence.
problem Sampling from distributions governed by potential functions.
method Deterministic score-based MCMC with regularized Wasserstein proximal.
result Improved mixing time bounds for Gaussian distributions compared to ULA and MALA.
Proposes a Riemannian optimization for policy improvement in MDPs.
problem Optimizing policy functions in Markov decision processes (MDPs).
method Riemannian proximal optimization algorithm with Gaussian mixture model (GMM).
result Guaranteed convergence and efficacy demonstrated in preliminary experiments.
Riemannian Proximal Sampler improves sampling on manifold data.
problem Sampling from densities on Riemannian manifolds.
method Uses MBI and RHK oracles for high-accuracy sampling.
result Sampling with ε-accuracy requires O(log(1/ε)) iterations in KL divergence.
A new algorithm for minimizing functions on Wasserstein space.
problem Discretization of continuous Wasserstein gradient flows in machine learning.
method Forward-Backward discretization scheme for minimizing functions with smooth and nonsmooth components.
result The FB scheme converges similarly to proximal gradient algorithms in Euclidean spaces.
Assume that an agent models a financial asset through a measure Q with the goal to price / hedge some derivative or optimize some expected utility. Even if the model Q is chosen in the most skilful and sophisticated way, she is left with the possibility that Q does not provide an "exact" description of reality. This le…
Flow-based models generate data with improved theoretical guarantees.
problem Theoretical analysis of flow-based generative models.
method Proximal gradient descent in Wasserstein space for JKO flow model.
result KL guarantee of data generation by JKO flow model is O(ε2). Proposes variational Gaussian approximations for solving the Kushner equation.
problem Solving the Kushner equation for state estimation with observations.
method Tractable variational Gaussian approximations of proximal losses based on Wasserstein and Fisher metrics.
result The proposed method leads to a Gaussian flow consistent with Kalman-Bucy and Riccati flows.
WAPPO optimizes feature distributions for better visual transfer in RL.
problem Improving visual transfer in reinforcement learning.
method WAPPO uses Wasserstein Confusion to minimize feature distribution distance.
result WAPPO outperforms previous methods in visual transfer across different environments.
ITSPACE improves covariance alignment faster than other methods.
problem Optimizing covariance matrices for machine learning tasks.
method Proximal majorization-minimization method that directly optimizes the Bures-Wasserstein objective.
result ITSPACE achieves lower BW gap solutions faster than other methods.
This work optimizes bid strategies for online auctions using measure-valued optimization.
problem Optimizing bid strategies in first-price auctions to maximize expected surplus.
method Formulates the problem as convex optimization over the joint distribution of shading parameters, adapts the distribution after each auction using a Wasserstein-proximal update.
result The proposed algorithm encourages bids on values with high expected surplus.
WDAIL uses Wasserstein distance for more effective reward shaping in IL.
problem Fixed reward functions in GAIL limit performance on complex tasks.
method Introduces Wasserstein distance and PPO for improved reward shaping and stability.
result Significant performance improvement in complex MuJoCo tasks.
In machine learning research, the proximal gradient methods are popular for solving various optimization problems with non-smooth regularization. Inexact proximal gradient methods are extremely important when exactly solving the proximal operator is time-consuming, or the proximal operator does not have an analytic sol…
DE-PSGLD samples from constrained distributions in a decentralized manner.
problem Sampling from log-concave distributions with constraints.
method Decentralized Proximal Stochastic Gradient Langevin Dynamics with proximal regularization.
result DE-PSGLD converges to a regularized Gibbs distribution and maintains posterior concentration.
A new method reformulates Optimal Transport Conditional Flow Matching using proximal operators.
problem Optimal Transport Conditional Flow Matching (OT-CFM) for generating models.
method Reformulate OT-CFM using proximal operators and extended Brenier potential.
result OT-CFM dynamics are terminally normally hyperbolic for manifold-supported targets.
A new framework solves complex optimization problems with continuous worst-case distributions.
problem Optimizing under uncertain distributions with continuous worst-case scenarios.
method Flow-based distributionally robust optimization (DRO) with Wasserstein uncertainty sets and invertible transport maps.
result The framework finds continuous worst-case distributions and samples efficiently.
We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a collection of proximal operators that share the same quadratic form, or if the qu…
We analyze the local convergence of proximal splitting algorithms to solve optimization problems that are convex besides a rank constraint. For this, we show conditions under which the proximal operator of a function involving the rank constraint is locally identical to the proximal operator of its convex envelope, hen…
The paper develops methods for sampling from log-concave distributions with constraints.
problem Sampling from log-concave distributions with constraints.
method Randomized midpoint discretization of Langevin diffusions with various projections.
result New convergence guarantees for constrained Langevin algorithms.
The OSCAR (octagonal selection and clustering algorithm for regression) regularizer consists of a L_1 norm plus a pair-wise L_inf norm (responsible for its grouping behavior) and was proposed to encourage group sparsity in scenarios where the groups are a priori unknown. The OSCAR regularizer has a non-trivial proximit…
In this work, we highlight a connection between the incremental proximal method and stochastic filters. We begin by showing that the proximal operators coincide, and hence can be realized with, Bayes updates. We give the explicit form of the updates for the linear regression problem and show that there is a one-to-one …
We propose a new proximal, path-following framework for a class of constrained convex problems. We consider settings where the nonlinear---and possibly non-smooth---objective part is endowed with a proximity operator, and the constraint set is equipped with a self-concordant barrier. Our approach relies on the followin…
A novel Gromov-Wasserstein learning framework is proposed to jointly match (align) graphs and learn embedding vectors for the associated graph nodes. Using Gromov-Wasserstein discrepancy, we measure the dissimilarity between two graphs and find their correspondence, according to the learned optimal transport. The node …
node2coords learns interpretable graph node representations robust to graph perturbations.
problem Need representations that capture graph structure and are robust to perturbations.
method Proposes a graph representation learning algorithm using Wasserstein barycenters.
result Learned representations are interpretable and stable to graph perturbations.
New method speeds up optimization over probability measures.
problem High computational overhead in optimizing probability measures.
method Randomized coordinate descent on Wasserstein space.
result Significant speedups over full-gradient methods.
New algorithm proves convergence for MAP estimation with denoisers.
problem Proving convergence of MAP estimation methods using pretrained denoisers.
method A simple gradient descent algorithm on smoothed proximal objectives.
result Algorithm provably converges to the proximal operator under log-concavity.
New method for efficient proximal mapping of 1-path-norm in shallow networks.
problem Efficiently handling the 1-path-norm of shallow neural networks.
method Closed-form proximal operator for efficient computation and upper bound on Lipschitz constant.
result Proximal mapping allows robust training against adversarial perturbations.
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.
We propose a new optimization method for training feed-forward neural networks. By rewriting the activation function as an equivalent proximal operator, we approximate a feed-forward neural network by adding the proximal operators to the objective function as penalties, hence we call the lifted proximal operator machin…
We propose a scalable Gromov-Wasserstein learning (S-GWL) method and establish a novel and theoretically-supported paradigm for large-scale graph analysis. The proposed method is based on the fact that Gromov-Wasserstein discrepancy is a pseudometric on graphs. Given two graphs, the optimal transport associated with th…
This paper proposes a new method to solve functional minimization problems in probability distributions using sliced-Wasserstein gradient flows.
problem Solving functional minimization problems in high-dimensional probability distributions is computationally challenging.
method The paper introduces a new approach using sliced-Wasserstein gradient flows to approximate the Jordan-Kinderlehrer-Otto (JKO) scheme, parameterizing densities with generative models.
result The proposed method is more flexible and computationally tractable compared to existing methods like JKO-ICNN.
Sharp bounds for max-sliced Wasserstein distances derived for empirical distributions.
problem Estimating the expected max-sliced Wasserstein distance between a probability measure and its empirical distribution.
method Banach space version and operator norm approach for upper bounds.
result Upper bounds for max-sliced Wasserstein distances are essentially matching and sharp up to a log factor.
Improved bounds for proximal gradient algorithms with computational errors.
problem Analyzing convergence of proximal gradient algorithms with inaccuracies.
method Deriving new tighter deterministic and probabilistic bounds for convex composite problems.
result Probabilistic bounds are more robust and accurate for algorithm verification and performance guarantees.
This study approximates distances between Gaussian processes and covariance operators using RKHS.
problem Approximating distances between Gaussian processes and covariance operators from finite samples.
method Using reproducing kernel Hilbert space (RKHS) covariance and cross-covariance operators, the study shows how to consistently and efficiently estimate Sinkhorn divergence from finite samples.
result Convergence rates are dimension-independent and of the same order as Hilbert-Schmidt distance.
A new method for comparing image probability measures using convolution operators.
problem Efficiently comparing images using conventional sliced Wasserstein methods.
method Proposed convolution sliced Wasserstein (CSW) methods with stride, dilation, and non-linear activation.
result CSW demonstrates favorable performance over conventional sliced Wasserstein in image comparison and deep generative modeling.
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form solutions of proximal operators and envelope representations based on the Moreau, Fo…
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 …
We show that eigenvalues and eigenfunctions of the Laplace-Beltrami operator on a Riemannian manifold are approximated by eigenvalues and eigenvectors of a (suitably weighted) graph Laplace operator of a proximity graph on an epsilon-net.
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.