Related papers: Robust boundary detection and density estimation u…
This paper presents a novel method for fault detection in vibration/acoustic signals contaminated with non-Gaussian noise, specifically addressing the challenge of random impulsive and wideband disturbances in industrial measurements. While…
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…
Boundary detection is essential for a variety of computer vision tasks such as segmentation and recognition. In this paper we propose a unified formulation and a novel algorithm that are applicable to the detection of different types of…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
We present a new smooth, Gaussian-like kernel that allows the kernel density estimate for an angular distribution to be exactly represented by a finite number of its Fourier series coefficients. Distributions of angular quantities, such as…
Image acquisition and segmentation are likely to introduce noise. Further image processing such as image registration and parameterization can introduce additional noise. It is thus imperative to reduce noise measurements and boost signal.…
The performance and ease of use of deep learning-based binary classifiers have improved significantly in recent years. This has opened up the potential for automating critical inspection tasks, which have traditionally only been trusted to…
This paper studies the interpretability of neural network features from a Bayesian Gaussian view, where optimizing a cost is reaching a probabilistic bound; learning a model approximates a density that makes the bound tight and the cost…
We present an efficient algorithm to compute tight upper bounds of collision probability between two objects with positional uncertainties, whose error distributions are represented with non-Gaussian forms. Our approach can handle noisy…
The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…
Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…
Crowd counting is a fundamental problem in crowd analysis which is typically accomplished by estimating a crowd density map and summing over the density values. However, this approach suffers from background noise accumulation and loss of…
Detecting boundary of an image based on noisy observations is a fundamental problem of image processing and image segmentation. For a $d$-dimensional image ($d = 2, 3, \ldots$), the boundary can often be described by a closed smooth $(d -…
In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise…
In this paper we revisit the kernel density estimation problem: given a kernel $K(x, y)$ and a dataset of $n$ points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query $q$, a…
We prove finite-sample concentration and anti-concentration bounds for dimension estimation using Gaussian kernel sums. Our bounds provide explicit dependence on sample size, bandwidth, and local geometric and distributional parameters,…
We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and…
Traditional crowd counting approaches usually use Gaussian assumption to generate pseudo density ground truth, which suffers from problems like inaccurate estimation of the Gaussian kernel sizes. In this paper, we propose a new…
Accurate boundary detection in high-dimensional data remains a central challenge in unsupervised learning, particularly in the presence of non-linear structures and heterogeneous densities. In this work, we introduce Mean Curvature Boundary…
We consider the problem of clustering datasets in the presence of arbitrary outliers. Traditional clustering algorithms such as k-means and spectral clustering are known to perform poorly for datasets contaminated with even a small number…