Related papers: Density Estimation on Manifolds with Boundary
We introduce the manifold density function, which is an intrinsic method to validate manifold learning techniques. Our approach adapts and extends Ripley's $K$-function, and categorizes in an unsupervised setting the extent to which an…
We investigate the problem of density estimation on the unit circle and the unit sphere from a computational perspective. Our primary goal is to develop new density estimators that are both rate-optimal and computationally efficient for…
Machine learning models suffer from overfitting, which is caused by a lack of labeled data. To tackle this problem, we proposed a framework of regularization methods, called density-fixing, that can be used commonly for supervised and…
This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…
Diffusion models often generate novel samples even when the learned score is only \emph{coarse} -- a phenomenon not accounted for by the standard view of diffusion training as density estimation. In this paper, we show that, under the…
Selectivity estimation - the problem of estimating the result size of queries - is a fundamental problem in databases. Accurate estimation of query selectivity involving multiple correlated attributes is especially challenging. Poor…
In this article we study the problem of quantifying the uncertainty in an experiment with a technical system. We propose new density estimates which combine observed data of the technical system and simulated data from an (imperfect)…
A nonparametric kernel density estimator for directional-linear data is introduced. The proposal is based on a product kernel accounting for the different nature of both (directional and linear) components of the random vector. Expressions…
Natural data observed in $\mathbb{R}^n$ is often constrained to an $m$-dimensional manifold $\mathcal{M}$, where $m < n$. This work focuses on the task of building theoretically principled generative models for such data. Current generative…
The manifold hypothesis (real world data concentrates near low-dimensional manifolds) is suggested as the principle behind the effectiveness of machine learning algorithms in very high dimensional problems that are common in domains such as…
Density ratio estimation (DRE) is a fundamental machine learning technique for comparing two probability distributions. However, existing methods struggle in high-dimensional settings, as it is difficult to accurately compare probability…
Mixed-precision Deep Neural Networks achieve the energy efficiency and throughput needed for hardware deployment, particularly when the resources are limited, without sacrificing accuracy. However, the optimal per-layer bit precision that…
Object counting and localization are key steps for quantitative analysis in large-scale microscopy applications. This procedure becomes challenging when target objects are overlapping, are densely clustered, and/or present fuzzy boundaries.…
Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely…
Uncertainty is prevalent in robotics. Due to measurement noise and complex dynamics, we cannot estimate the exact system and environment state. Since conservative motion planners are not guaranteed to find a safe control strategy in a…
We estimate the derivative of a probability density function defined on $[0,\infty)$. For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact…
We introduce the Binless Multidimensional Thermodynamic Integration (BMTI) method for nonparametric, robust, and data-efficient density estimation. BMTI estimates the logarithm of the density by initially computing log-density differences…
In this paper, we consider Bayesian point estimation and predictive density estimation in the binomial case. After presenting preliminary results on these problems, we compare the risk functions of the Bayes estimators based on the…
Deep learning methods have played a more and more important role in hyperspectral image classification. However, the general deep learning methods mainly take advantage of the information of sample itself or the pairwise information between…
It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth of kernel estimation,…