Related papers: Wasserstein information matrix
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.…
We provide statistical theory for conditional and unconditional Wasserstein generative adversarial networks (WGANs) in the framework of dependent observations. We prove upper bounds for the excess Bayes risk of the WGAN estimators with…
We study the classical and quantum Fisher information for the Lieb-Liniger model. The Fisher information has been studied extensively when the parameter is inscribed on a quantum state by a unitary process, e.g., Mach-Zehnder or Ramsey…
We introduce a positive Hermitian operator, the Fisher operator, and use it to examine a measurement process incorporating unitary dynamics and complete measurements. We develop the idea of information complement, the minimization of which…
In this paper, we propose Wasserstein Isometric Mapping (Wassmap), a nonlinear dimensionality reduction technique that provides solutions to some drawbacks in existing global nonlinear dimensionality reduction algorithms in imaging…
This paper introduces a method for efficiently approximating the inverse of the Fisher information matrix, a crucial step in achieving effective variational Bayes inference. A notable aspect of our approach is the avoidance of analytically…
We introduce Primal-Dual Wasserstein GAN, a new learning algorithm for building latent variable models of the data distribution based on the primal and the dual formulations of the optimal transport (OT) problem. We utilize the primal…
The optimization of system parameters is a ubiquitous problem in science and engineering. The traditional approach involves setting to zero the partial derivatives of the objective function with respect to each parameter, in order to…
In this paper, we study statistical inference for the Wasserstein distance, which has attracted much attention and has been applied to various machine learning tasks. Several studies have been proposed in the literature, but almost all of…
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
Variational inference is a technique that approximates a target distribution by optimizing within the parameter space of variational families. On the other hand, Wasserstein gradient flows describe optimization within the space of…
This paper introduces a new stochastic optimization method based on the regularized Fisher information matrix (FIM), named SOFIM, which can efficiently utilize the FIM to approximate the Hessian matrix for finding Newton's gradient update…
Thermal states play a fundamental role in various areas of physics, and they are becoming increasingly important in quantum information science, with applications related to semi-definite programming, quantum Boltzmann machine learning,…
We theoretically investigate parameter quantum estimation in quantum chaotic systems. Our analysis is based on an effective description of non-integrable quantum systems in terms of a random matrix Hamiltonian. Based on this approach we…
This paper deals with a clustering algorithm for histogram data based on a Self-Organizing Map (SOM) learning. It combines a dimension reduction by SOM and the clustering of the data in a reduced space. Related to the kind of data, a…
We use Stein characterizations to obtain new moment-type estimators for the parameters of three classical spherical distributions (namely the Fisher-Bingham, the von Mises-Fisher, and the Watson distributions) in the i.i.d. case. This leads…
The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…
Current experimental design techniques for dynamical systems often only incorporate measurement noise, while dynamical systems also involve process noise. To construct experimental designs we need to quantify their information content. The…
Random probabilities are a key component to many nonparametric methods in Statistics and Machine Learning. To quantify comparisons between different laws of random probabilities several works are starting to use the elegant Wasserstein over…
Using i.i.d. data to estimate a high-dimensional distribution in Wasserstein distance is a fundamental instance of the curse of dimensionality. We explore how structural knowledge about the data-generating process which gives rise to the…