Related papers: Shape-Constrained Univariate Density Estimation
We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We…
To analyze high-dimensional and complex data in the real world, deep generative models, such as variational autoencoder (VAE) embed data in a low-dimensional space (latent space) and learn a probabilistic model in the latent space. However,…
It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…
We consider the problem of optimization of cost functionals on the infinite-dimensional manifold of diffeomorphisms. We present a new class of optimization methods, valid for any optimization problem setup on the space of diffeomorphisms by…
A probability density function (PDF) of a spatially dependent field provides a means of calculating moments of the field or, equivalently, the proportion of a spatial domain that is mapped to a given set of values. This paper describes a…
In this letter, we present a novel exponentially embedded families (EEF) based classification method, in which the probability density function (PDF) on raw data is estimated from the PDF on features. With the PDF construction, we show that…
This paper focuses on the problem of unbounded density ratio estimation -- an understudied yet critical challenge in statistical learning -- and its application to covariate shift adaptation. Much of the existing literature assumes that the…
This article addresses the different methods of estimation of the probability density function (PDF) and the cumulative distribution function (CDF) for the Lindley distribution. Following estimation methods are considered: uniformly minimum…
Shape-constrained optimization arises in a wide range of problems including distributionally robust optimization (DRO) that has surging popularity in recent years. In the DRO literature, these problems are usually solved via reduction into…
Research is taking place to find effective algorithms for content-based image representation and description. There is a substantial amount of algorithms available that use visual features (color, shape, texture). Shape feature has…
Anatomy is undergoing a renaissance driven by availability of large digital data sets generated by light microscopy. A central computational task is to map individual data volumes to standardized templates. This is accomplished by…
Two methods are proposed for high-dimensional shape-constrained regression and classification. These methods reshape pre-trained prediction rules to satisfy shape constraints like monotonicity and convexity. The first method can be applied…
The one-point probability distribution function (PDF) of the matter density field in the universe is a fundamental property that plays an essential role in cosmology for estimates such as gravitational weak lensing, non-linear clustering,…
This paper introduces a new framework for quantifying predictive uncertainty for both data and models that relies on projecting the data into a Gaussian reproducing kernel Hilbert space (RKHS) and transforming the data probability density…
In this work, we study non-parametric estimation of joint probabilities of a given set of discrete and continuous random variables from their (empirically estimated) 2D marginals, under the assumption that the joint probability could be…
The formula for probability density functions (PDFs) has been extended to include PDF for energy dissipation rates in addition to other PDFs such as for velocity fluctuations, velocity derivatives, fluid particle accelerations, energy…
We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…
One of the popular measures of central tendency that provides better representation and interesting insights of the data compared to the other measures like mean and median is the metric mode. If the analytical form of the density function…
We present a new approach to discretizing shape optimization problems that generalizes standard moving mesh methods to higher-order mesh deformations and that is naturally compatible with higher-order finite element discretizations of…
One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…