Related papers: A Two-Step Geometric Framework For Density Modelin…
This invited paper proposes and discusses several Bayesian attempts at nonparametric and semiparametric density estimation. The main categories of these ideas are as follows: 1) Build a nonparametric prior around a given parametric model.…
CDF2PDF is a method of PDF estimation by approximating CDF. The original idea of it was previously proposed in [1] called SIC. However, SIC requires additional hyper-parameter tunning, and no algorithms for computing higher order derivative…
We propose the tensorizing flow method for estimating high-dimensional probability density functions from the observed data. The method is based on tensor-train and flow-based generative modeling. Our method first efficiently constructs an…
Density ratio estimation (DRE) is a paramount task in machine learning, for its broad applications across multiple domains, such as covariate shift adaptation, causal inference, independence tests and beyond. Parametric methods for…
Diffusion models indirectly estimate the probability density over a data space, which can be used to study its structure. In this work, we show that geodesics can be computed in diffusion latent space, where the norm induced by the…
We address the following problem: given two smooth densities on a manifold, find an optimal diffeomorphism that transforms one density into the other. Our framework builds on connections between the Fisher-Rao information metric on the…
We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…
Modes and ridges of the probability density function behind observed data are useful geometric features. Mode-seeking clustering assigns cluster labels by associating data samples with the nearest modes, and estimation of density ridges…
In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…
Realistic human geometry generation is an important yet challenging task, requiring both the preservation of fine clothing details and the accurate modeling of clothing-body interactions. To tackle this challenge, we build upon Geometry…
This paper develops a novel approach to density estimation on a network. We formulate nonparametric density estimation on a network as a nonparametric regression problem by binning. Nonparametric regression using local polynomial…
We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…
In this study, a density-on-density regression model is introduced, where the association between densities is elucidated via a warping function. The proposed model has the advantage of a being straightforward demonstration of how one…
We derive a multifractal model for the velocity probability density distribution function (PDF), which is valid from the inertial range to the viscous range. The model gives a continuous evolution of velocity PDFs from large to small…
We present a new Bayesian methodology to learn the unknown material density of a given sample by inverting its two-dimensional images that are taken with a Scanning Electron Microscope. An image results from a sequence of projections of the…
We propose a linear algebraic framework for performing density estimation. It consists of three simple steps: convolving the empirical distribution with certain smoothing kernels to remove the exponentially large variance; compressing the…
The crucial step in designing a particle filter for a particular application is the choice of importance density. The optimal scheme is to use the conditional posterior density of the state, but this cannot be sampled or calculated…
Deep learning models are widely used across computer vision and other domains. When working on the model induction, selecting the right architecture for a given dataset often relies on repetitive trial-and-error procedures. This procedure…
We quantify the cosmological constraining power of the `lensing PDF' - the one-point probability density of weak lensing convergence maps - by modelling this statistic numerically with an emulator trained on $w$CDM cosmic shear simulations.…
We discuss an approach to probabilistic forecasting based on two chained machine-learning steps: a dimensional reduction step that learns a reduction map of predictor information to a low-dimensional space in a manner designed to preserve…