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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…
An important feature of kernel mean embeddings (KME) is that the rate of convergence of the empirical KME to the true distribution KME can be bounded independently of the dimension of the space, properties of the distribution and smoothness…
In this study, a coarse-graining framework for discrete models is formulated on the basis of multiscale homogenization. The discrete model considered in this paper is the Lattice Discrete Particle Model (LDPM), which simulates concrete at…
Density estimation is a fundamental task in statistics and machine learning applications. Kernel density estimation is a powerful tool for non-parametric density estimation in low dimensions; however, its performance is poor in higher…
Probabilistic methods for point set registration have demonstrated competitive results in recent years. These techniques estimate a probability distribution model of the point clouds. While such a representation has shown promise, it is…
Wet particle separation is widely used in mineral processing and plastic recycling to separate mixtures of particulate materials into further usable fractions due to density differences. This work presents efforts aiming to numerically…
Estimating expected polynomials of density functions from samples is a basic problem with numerous applications in statistics and information theory. Although kernel density estimators are widely used in practice for such functional…
Electron density is a fundamental quantity, which can in principle determine all ground state electronic properties of a given system. Although machine learning (ML) models for electron density based on either an atom-centered basis or a…
Several emerging post-Bayesian methods target a probability distribution for which an entropy-regularised variational objective is minimised. This increased flexibility introduces a computational challenge, as one loses access to an…
Diffusion models show promise for image restoration, but existing methods often struggle with inconsistent fidelity and undesirable artifacts. To address this, we introduce Kernel Density Steering (KDS), a novel inference-time framework…
A custom apparatus designed to isolate and replicate the spreading process of metal powder in additive manufacturing demonstrates a sudden and unexplained increase in packing density beyond layers 5 to 10. We replicate the experiments that…
We show that rate-adaptive multivariate density estimation can be performed using Bayesian methods based on Dirichlet mixtures of normal kernels with a prior distribution on the kernel's covariance matrix parameter. We derive sufficient…
Stellar membership determination of an open cluster is an important process to do before further analysis. Basically, there are two classes of membership determination method: parametric and non-parametric. In this study, an alternative of…
We present some results and remarks based on a combinatorial approach of the evaluation of the nuclear level density. First, we show that it is possible to extract some reliable information from the output of the program whose rough data…
Smoothed particle hydrodynamics (SPH) has been extensively studied in computer graphics to animate fluids with versatile effects. However, SPH still suffers from two numerical difficulties: the particle deficiency problem, which will…
Consistency of the kernel density estimator requires that the kernel bandwidth tends to zero as the sample size grows. In this paper we investigate the question of whether consistency is possible when the bandwidth is fixed, if we consider…
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…
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…
We derive the properties and demonstrate the desirability of a model-based method for estimating the spatially-varying effects of covariates on the quantile function. By modeling the quantile function as a combination of I-spline basis…
Graph spectral techniques for measuring graph similarity, or for learning the cluster number, require kernel smoothing. The choice of kernel function and bandwidth are typically chosen in an ad-hoc manner and heavily affect the resulting…