Related papers: Semi-Discrete Normalizing Flows through Differenti…
Poisson point processes provide a versatile framework for modeling the distributions of random points in space. When the space is partitioned into cells, each associated with a single generating point from the Poisson process, there appears…
In this paper we investigate relationships between the volumes of cells of three-dimensional Voronoi tessellations and the lengths and areas of sections obtained by intersecting the tessellation with a randomly oriented plane. Here, in…
Normalizing Flows are generative models that directly maximize the likelihood. Previously, the design of normalizing flows was largely constrained by the need for analytical invertibility. We overcome this constraint by a training procedure…
We present a new open source code for massive parallel computation of Voronoi tessellations(VT hereafter) in large data sets. The code is focused for astrophysical purposes where VT densities and neighbors are widely used. There are several…
This paper proposes a semi-conditional normalizing flow model for semi-supervised learning. The model uses both labelled and unlabeled data to learn an explicit model of joint distribution over objects and labels. Semi-conditional…
Recent work on distinct multicellular organisms has revealed a hitherto unknown type of biological noise; rather than a regular arrangement, cellular neighborhood volumes, obtained by Voronoi tessellations of the cell locations, are broadly…
We study the problem of learning a distribution from samples, when the underlying distribution is a mixture of product distributions over discrete domains. This problem is motivated by several practical applications such as crowd-sourcing,…
Normalizing flows, a category of probabilistic models famed for their capabilities in modeling complex data distributions, have exhibited remarkable efficacy in unsupervised anomaly detection. This paper explores the potential of…
Higher-order regularization problem formulations are popular frameworks used in machine learning, inverse problems and image/signal processing. In this paper, we consider the computational problem of finding the minimizer of the Sobolev…
Ray flow methods provide efficient tools for modelling wave energy transport in complex systems at high-frequencies. We compare two Petrov-Galerkin discretizations of a phase-space boundary integral model for stationary wave energy…
We study Flow Matching in a semi-discrete setting where a Gaussian source is transported toward a discrete target supported on finitely many points. This semi-discrete regime is the theoretical setting behind the use of Flow Matching for…
In this work, we approach the problem of resource allocation in a team of agents through the framework of Centroidal Voronoi Tessellations. CVTs provide a natural way to embed a desired global trend in the team through probability…
Discretizing multi-dimensional data distributions is a fundamental step of modern indexing methods. State-of-the-art techniques learn parameters of quantizers on training data for optimal performance, thus adapting quantizers to the data.…
Vessel segmentation is an essential task in many clinical applications. Although supervised methods have achieved state-of-art performance, acquiring expert annotation is laborious and mostly limited for two-dimensional datasets with a…
Learned denoisers play a fundamental role in various signal generation (e.g., diffusion models) and reconstruction (e.g., compressed sensing) architectures, whose success derives from their ability to leverage low-dimensional structure in…
In this paper we address the problem of discretization in the context of learning Bayesian networks (BNs) from data containing both continuous and discrete variables. We describe a new technique for <EM>multivariate</EM> discretization,…
In this work, we propose a method to learn multivariate probability distributions using sample path data from stochastic differential equations. Specifically, we consider temporally evolving probability distributions (e.g., those produced…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…
In this paper we study a gradient flow approach to the problem of quantization of measures in one dimension. By embedding our problem in $L^2$, we find a continuous version of it that corresponds to the limit as the number of particles…
Recently, there has been a surge of interest in incorporating neural networks into particle filters, e.g. differentiable particle filters, to perform joint sequential state estimation and model learning for non-linear non-Gaussian…