Related papers: discretize_distributions: Efficient Quantization o…
In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty. We measure the uncertainty using the Wasserstein distance, and for a given input…
In this paper we propose a new deterministic approximation method, called discretization approximation, for Bayesian computation. Discretization approximation is very simple to understand and to implement, It only requires calculating…
Recently, a Wasserstein-type distance for Gaussian mixture models has been proposed. However, that framework can only be generalized to identifiable mixtures of general elliptically contoured distributions whose components come from the…
This paper introduces a comprehensive framework to adjust a discrete test statistic for improving its hypothesis testing procedure. The adjustment minimizes the Wasserstein distance to a null-approximating continuous distribution, tackling…
Gaussian mixture models find their place as a powerful tool, mostly in the clustering problem, but with proper preparation also in feature extraction, pattern recognition, image segmentation and in general machine learning. When faced with…
The verification of differential privacy algorithms that employ Gaussian distributions is little understood. This paper tackles the challenge of verifying such programs by introducing a novel approach to approximating probability…
In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We…
This paper develops an in-depth treatment concerning the problem of approximating the Gaussian smoothing and Gaussian derivative computations in scale-space theory for application on discrete data. With close connections to previous…
The Wasserstein barycenter problem seeks a probability measure that minimizes the weighted average of the Wasserstein distances to a given collection of probability measures. We study the discrete setting, where each measure has finite…
This paper presents an analysis of properties of two hybrid discretization methods for Gaussian derivatives, based on convolutions with either the normalized sampled Gaussian kernel or the integrated Gaussian kernel followed by central…
The Wasserstein distance has emerged as a key metric to quantify distances between probability distributions, with applications in various fields, including machine learning, control theory, decision theory, and biological systems.…
Obtaining solutions to Optimal Transportation (OT) problems is typically intractable when the marginal spaces are continuous. Recent research has focused on approximating continuous solutions with discretization methods based on i.i.d.…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
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…
Resource-efficiently computing representations of probability distributions and the distances between them while only having access to the samples is a fundamental and useful problem across mathematical sciences. In this paper, we propose a…
In this paper, we study the problem of sampling from a distribution under the constraint of differential privacy (DP). Prior works measure the utility of DP sampling with density ratio-based measures such as KL divergence. However, such…
We study discretizations of Hamiltonian systems on the probability density manifold equipped with the $L^2$-Wasserstein metric. Based on discrete optimal transport theory, several Hamiltonian systems on graph (lattice) with different…
Diffusion or score-based models recently showed high performance in image generation. They rely on a forward and a backward stochastic differential equations (SDE). The sampling of a data distribution is achieved by numerically solving the…
Existing methods to summarize posterior inference for mixture models focus on identifying a point estimate of the implied random partition for clustering, with density estimation as a secondary goal (Wade and Ghahramani, 2018; Dahl et al.,…
Generative modeling aims to produce new random examples from an unknown target distribution, given access to a finite collection of examples. Among the leading approaches, denoising diffusion probabilistic models (DDPMs) construct such…