Related papers: Data-driven deep density estimation
In high dimensional settings, density estimation algorithms rely crucially on their inductive bias. Despite recent empirical success, the inductive bias of deep generative models is not well understood. In this paper we propose a framework…
Establishing dense correspondences between a pair of images is an important and general problem. However, dense flow estimation is often inaccurate in the case of large displacements or homogeneous regions. For most applications and…
Depth information is useful for many applications. Active depth sensors are appealing because they obtain dense and accurate depth maps. However, due to issues that range from power constraints to multi-sensor interference, these sensors…
Given i.i.d samples from some unknown continuous density on hyper-rectangle $[0, 1]^d$, we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a…
Important information concerning a multivariate data set, such as clusters and modal regions, is contained in the derivatives of the probability density function. Despite this importance, nonparametric estimation of higher order derivatives…
If two probability density functions (PDFs) have values for their first $n$ moments which are quite close to each other (upper bounds of their differences are known), can it be expected that the PDFs themselves are very similar? Shown below…
The Document Set Expansion (DSE) task involves identifying relevant documents from large collections based on a limited set of example documents. Previous research has highlighted Positive and Unlabeled (PU) learning as a promising approach…
The ratio between two probability density functions is an important component of various tasks, including selection bias correction, novelty detection and classification. Recently, several estimators of this ratio have been proposed. Most…
The probability density function (PDF) associated with a given set of samples is approximated by a piecewise-linear polynomial constructed with respect to a binning of the sample space. The kernel functions are a compactly supported basis…
Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…
We present a deep transformation model for probabilistic regression. Deep learning is known for outstandingly accurate predictions on complex data but in regression tasks, it is predominantly used to just predict a single number. This…
Bayesian estimation strategies represent the most fundamental formulation of the state estimation problem available, and apply readily to nonlinear systems with non-Gaussian uncertainties. The present paper introduces a novel method for…
Conditional density estimation (CDE) models can be useful for many statistical applications, especially because the full conditional density is estimated instead of traditional regression point estimates, revealing more information about…
Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…
We introduce a method for calculating the probability density function (PDF) of a turbulent density field in three dimensions using only information contained in the projected two-dimensional column density field. We test the method by…
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…
The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the…
This work studies distributed (probability) density estimation of large-scale systems. Such problems are motivated by many density-based distributed control tasks in which the real-time density of the swarm is used as feedback information,…
Deep neural networks lack interpretability and tend to be overconfident, which poses a serious problem in safety-critical applications like autonomous driving, medical imaging, or machine vision tasks with high demands on reliability.…
Dimension Estimation (DE) and Dimension Reduction (DR) are two closely related topics, but with quite different goals. In DE, one attempts to estimate the intrinsic dimensionality or number of latent variables in a set of measurements of a…