Related papers: Wasserstein Generative Learning of Conditional Dis…
This paper addresses a new active learning strategy for regression problems. The presented Wasserstein active regression model is based on the principles of distribution-matching to measure the representativeness of the labeled dataset. The…
We train a generator by maximum likelihood and we also train the same generator architecture by Wasserstein GAN. We then compare the generated samples, exact log-probability densities and approximate Wasserstein distances. We show that an…
Conformal prediction yields a prediction set with guaranteed $1-\alpha$ coverage of the true target under the i.i.d. assumption, which may not hold and lead to a gap between $1-\alpha$ and the actual coverage. Prior studies bound the gap…
Conditional generative models represent a significant advancement in the field of machine learning, allowing for the controlled synthesis of data by incorporating additional information into the generation process. In this work we introduce…
The purpose of unconditional text generation is to train a model with real sentences, then generate novel sentences of the same quality and diversity as the training data. However, when different metrics are used for comparing the methods…
In this paper we tackle the problem of comparing distributions of random variables and defining a mean pattern between a sample of random events. Using barycenters of measures in the Wasserstein space, we propose an iterative version as an…
The Boltzmann machine provides a useful framework to learn highly complex, multimodal and multiscale data distributions that occur in the real world. The default method to learn its parameters consists of minimizing the Kullback-Leibler…
Standard Distributional Synthetic Controls (DSC) estimate counterfactual distributions by minimizing the Euclidean $L_2$ distance between quantile functions. We demonstrate that this geometric reliance renders estimators fragile: they lack…
In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional…
In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional…
We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze…
Score-based generative models are shown to achieve remarkable empirical performances in various applications such as image generation and audio synthesis. However, a theoretical understanding of score-based diffusion models is still…
We develop a novel clustering method for distributional data, where each data point is regarded as a probability distribution on the real line. For distributional data, it has been challenging to develop a clustering method that utilizes…
In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a…
Generative autoencoders learn compact latent representations of data distributions through jointly optimized encoder--decoder pairs. In particular, Wasserstein autoencoders (WAEs) minimize a relaxed optimal transport (OT) objective, where…
We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to…
Generative modeling typically concerns transporting a single source distribution to a target distribution via simple probability flows. However, in fields like computer graphics and single-cell genomics, samples themselves can be viewed as…
Generative models and in particular Generative Adversarial Networks (GANs) have become very popular and powerful data generation tool. In recent years, major progress has been made in extending this concept into the quantum realm. However,…
A new generative adversarial network is developed for joint distribution matching. Distinct from most existing approaches, that only learn conditional distributions, the proposed model aims to learn a joint distribution of multiple random…
In many applications in statistics and machine learning, the availability of data samples from multiple possibly heterogeneous sources has become increasingly prevalent. On the other hand, in distributionally robust optimization, we seek…