Related papers: Fast Variable Density Poisson-Disc Sample Generati…
This paper studies the fundamental limits of the minimum average length of lossless and lossy variable-length compression, allowing a nonzero error probability $\epsilon$, for lossless compression. We give non-asymptotic bounds on the…
In a preliminary attempt to address the problem of data scarcity in physics-based machine learning, we introduce a novel methodology for data generation in physics-based simulations. Our motivation is to overcome the limitations posed by…
We consider a fast, data-sparse directional method to realize matrix-vector products related to point evaluations of the Helmholtz kernel. The method is based on a hierarchical partitioning of the point sets and the matrix. The considered…
We propose a novel approach which employs random sampling to generate an accurate non-uniform mesh for numerically solving Partial Differential Equation Boundary Value Problems (PDE-BVP's). From a uniform probability distribution U over a…
Density-based clustering methodology has been widely considered in the statistical literature for classifying Euclidean observations. However, this approach has not been contemplated for directional data yet. In this work, directional…
We propose a novel perspective on varied-density clustering for high-dimensional data by framing it as a label propagation process in neighborhood graphs that adapt to local density variations. Our method formally connects density-based…
Diffusion models have become emerging generative models. Their sampling process involves multiple steps, and in each step the models predict the noise from a noisy sample. When the models make prediction, the output deviates from the ground…
Gaussian processes (GPs) are widely used in non-parametric Bayesian modeling, and play an important role in various statistical and machine learning applications. In a variety tasks of uncertainty quantification, generating random sample…
This paper presents the Poisson-randomized gamma dynamical system (PRGDS), a model for sequentially observed count tensors that encodes a strong inductive bias toward sparsity and burstiness. The PRGDS is based on a new motif in Bayesian…
A method is described to solve the Poisson problem for a three dimensional source distribution that is periodic into one direction. Perpendicular to the direction of periodicity a free space (or open) boundary is realized. In beam physics,…
In 2020, two novel distributions for the analysis of directional data were introduced: the spherical Cauchy distribution and the Poisson kernel-based distribution. This paper provides a detailed exploration of both distributions within…
We propose a simple algorithm to train stochastic neural networks to draw samples from given target distributions for probabilistic inference. Our method is based on iteratively adjusting the neural network parameters so that the output…
Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…
Imaging techniques based on single-pixel detection, such as ghost imaging, can reconstruct or recognize a target scene from multiple measurements using a sequence of random mask patterns. However, the processing speed is limited by the low…
Subsampling from a large data set is useful in many supervised learning contexts to provide a global view of the data based on only a fraction of the observations. Diverse (or space-filling) subsampling is an appealing subsampling approach…
Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In…
With the aim of generalizing histogram statistics to higher dimensional cases, density estimation via discrepancy based sequential partition (DSP) has been proposed to learn an adaptive piecewise constant approximation defined on a binary…
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…
We use a functional analogue of the quantile function for probability measures on $\mathbb{R}^d$ to characterize a novel limit Poisson point process for radially recentred and rescaled random vectors under a radial-directional…
Based on the Denoising Diffusion Probabilistic Model (DDPM), medical image segmentation can be described as a conditional image generation task, which allows to compute pixel-wise uncertainty maps of the segmentation and allows an implicit…