Related papers: A Wasserstein Minimum Velocity Approach to Learnin…
Score matching is a popular method for estimating unnormalized statistical models. However, it has been so far limited to simple, shallow models or low-dimensional data, due to the difficulty of computing the Hessian of log-density…
Wasserstein distributionally robust optimization offers a framework for model fitting in machine learning under potential shifts in the data distribution. We study a regularized variant of this problem in which entropic smoothing produces a…
Gradient boosting is a sequential ensemble method that fits a new weaker learner to pseudo residuals at each iteration. We propose Wasserstein gradient boosting, a novel extension of gradient boosting that fits a new weak learner to…
Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space. Existing discrete methods are not scalable as they assume access to the complete set of…
Flow matching has recently emerged as a promising alternative to diffusion-based generative models, offering faster sampling and simpler training by learning continuous flows governed by ordinary differential equations. Despite growing…
We propose a deterministic sampling framework using Score-Based Transport Modeling for sampling an unnormalized target density $\pi$ given only its score $\nabla \log \pi$. Our method approximates the Wasserstein gradient flow on…
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…
Score-based diffusion models have emerged as powerful tools in generative modeling, yet their theoretical foundations remain underexplored. In this work, we focus on the Wasserstein convergence analysis of score-based diffusion models.…
Diffusion models are commonly interpreted as learning the score function, i.e., the gradient of the log-density of noisy data. However, this assumption implies that the target of learning is a conservative vector field, which is not…
Among generative neural models, flow matching techniques stand out for their simple applicability and good scaling properties. Here, velocity fields of curves connecting a simple latent and a target distribution are learned. Then the…
Score matching is a recently developed parameter learning method that is particularly effective to complicated high dimensional density models with intractable partition functions. In this paper, we study two issues that have not been…
Many machine learning problems can be seen as approximating a \textit{target} distribution using a \textit{particle} distribution by minimizing their statistical discrepancy. Wasserstein Gradient Flow can move particles along a path that…
In this paper, we propose a novel numerical scheme to optimize the gradient flows for learning energy-based models (EBMs). From a perspective of physical simulation, we redefine the problem of approximating the gradient flow utilizing…
In this work, we propose a novel generalized Wasserstein-2 distance approach for efficiently training stochastic neural networks to reconstruct random field models, where the target random variable comprises both continuous and categorical…
Wasserstein Gradient Flows (WGF) with respect to specific functionals have been widely used in the machine learning literature. Recently, neural networks have been adopted to approximate certain intractable parts of the underlying…
This paper studies the optimization of the KL functional on the Wasserstein space of probability measures, and develops a sampling framework based on Wasserstein gradient descent (WGD). We identify two important subclasses of the…
Semantic segmentation is important for many real-world systems, e.g., autonomous vehicles, which predict the class of each pixel. Recently, deep networks achieved significant progress w.r.t. the mean Intersection-over Union (mIoU) with the…
Several machine learning applications involve the optimization of higher-order derivatives (e.g., gradients of gradients) during training, which can be expensive in respect to memory and computation even with automatic differentiation. As a…
We propose a novel scalable end-to-end pipeline that uses symbolic domain knowledge as constraints for learning a neural network for classifying unlabeled data in a weak-supervised manner. Our approach is particularly well-suited for…
Gradient matching is a promising tool for learning parameters and state dynamics of ordinary differential equations. It is a grid free inference approach, which, for fully observable systems is at times competitive with numerical…