Related papers: Neural Local Wasserstein Regression
Computing optimal transport maps between high-dimensional and continuous distributions is a challenging problem in optimal transport (OT). Generative adversarial networks (GANs) are powerful generative models which have been successfully…
Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…
In this work, we propose Wasserstein distributionally robust shallow convex neural networks (WaDiRo-SCNNs) to provide reliable nonlinear predictions when subject to adverse and corrupted datasets. Our approach is based on the reformulation…
We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of…
The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution $P$ to another distribution $Q$…
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…
Distributionally robust optimization has emerged as an attractive way to train robust machine learning models, capturing data uncertainty and distribution shifts. Recent statistical analyses have proved that generalization guarantees of…
Advancements in modern science have led to the increasing availability of non-Euclidean data in metric spaces. This paper addresses the challenge of modeling relationships between non-Euclidean responses and multivariate Euclidean…
We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises…
Robust estimation is an important problem in statistics which aims at providing a reasonable estimator when the data-generating distribution lies within an appropriately defined ball around an uncontaminated distribution. Although minimax…
In regression analysis under artificial neural networks, the prediction performance depends on determining the appropriate weights between layers. As randomly initialized weights are updated during back-propagation using the gradient…
Distributionally robust supervised learning (DRSL) is emerging as a key paradigm for building reliable machine learning systems for real-world applications -- reflecting the need for classifiers and predictive models that are robust to 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…
Disentangling polysemantic neurons is at the core of many current approaches to interpretability of large language models. Here we attempt to study how disentanglement can be used to understand performance, particularly under weight…
This study addresses the challenge of inaccurate gradients in computing the empirical Fisher Information Matrix during neural network pruning. We introduce SWAP, a formulation of Entropic Wasserstein regression (EWR) for pruning,…
In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recently, other distances…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
In this paper, we propose a local squared Wasserstein-2 (W_2) method to solve the inverse problem of reconstructing models with uncertain latent variables or parameters. A key advantage of our approach is that it does not require prior…
A generalization of the Wasserstein metric, the integrated transportation distance, establishes a novel distance between probability kernels of Markov systems. This metric serves as the foundation for an efficient approximation technique,…
A common feature of methods for analyzing samples of probability density functions is that they respect the geometry inherent to the space of densities. Once a metric is specified for this space, the Fr\'echet mean is typically used to…