Related papers: Latent Space Optimal Transport for Generative Mode…
Optimal transport (OT) is a powerful geometric tool for comparing two distributions and has been employed in various machine learning applications. In this work, we propose a novel OT formulation that takes feature correlations into account…
In the standard formulation of the denoising problem, one is given a probabilistic model relating a latent variable $\Theta \in \Omega \subset \mathbb{R}^m \; (m\ge 1)$ and an observation $Z \in \mathbb{R}^d$ according to: $Z \mid \Theta…
Generative Adversarial Networks (GAN) is currently widely used as an unsupervised image generation method. Current state-of-the-art GANs can generate photorealistic images with high resolution. However, a large amount of data is required,…
Generative Adversarial Networks (GANs) are susceptible to bias, learned from either the unbalanced data, or through mode collapse. The networks focus on the core of the data distribution, leaving the tails - or the edges of the distribution…
Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important…
Generative adversarial networks (GANs) nowadays are capable of producing images of incredible realism. One concern raised is whether the state-of-the-art GAN's learned distribution still suffers from mode collapse, and what to do if so.…
Dynamical formulations of optimal transport (OT) frame the task of comparing distributions as a variational problem which searches for a path between distributions minimizing a kinetic energy functional. In applications, it is frequently…
Optimal transport aligns samples across distributions by minimizing the transportation cost between them, e.g., the geometric distances. Yet, it ignores coherence structure in the data such as clusters, does not handle outliers well, and…
Generative Adversarial Networks (GANs) have become a popular method to learn a probability model from data. In this paper, we aim to provide an understanding of some of the basic issues surrounding GANs including their formulation,…
Variational autoencoders have been widely applied for natural language generation, however, there are two long-standing problems: information under-representation and posterior collapse. The former arises from the fact that only the last…
Modeling non-stationary data is a challenging problem in the field of continual learning, and data distribution shifts may result in negative consequences on the performance of a machine learning model. Classic learning tools are often…
Although deep neural networks are well-known for their outstanding performance in tackling complex tasks, their hunger for computational resources remains a significant hurdle, posing energy-consumption issues and restricting their…
An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…
This paper presents a novel deep learning based data-driven optimization method. A novel generative adversarial network (GAN) based data-driven distributionally robust chance constrained programming framework is proposed. GAN is applied to…
Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study…
We study the use of amortized optimization to predict optimal transport (OT) maps from the input measures, which we call Meta OT. This helps repeatedly solve similar OT problems between different measures by leveraging the knowledge and…
We propose a new approach to Generative Adversarial Networks (GANs) to achieve an improved performance with additional robustness to its so-called and well recognized mode collapse. We first proceed by mapping the desired data onto a…
Transportation of samples across different domains is a central task in several machine learning problems. A sensible requirement for domain transfer tasks in computer vision and language domains is the sparsity of the transportation map,…
We present a novel method and analysis to train generative adversarial networks (GAN) in a stable manner. As shown in recent analysis, training is often undermined by the probability distribution of the data being zero on neighborhoods of…
Many important problems in science and engineering, such as drug design, involve optimizing an expensive black-box objective function over a complex, high-dimensional, and structured input space. Although machine learning techniques have…