Related papers: Spectral Methods for Nonparametric Models

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

The efficient computation of parametric solution sensitivities is a key challenge in the integration of learning-enhanced methods with nonlinear model predictive control (MPC), as their availability is crucial for many learning algorithms.…

Multi-physics models governed by coupled partial differential equation (PDE) systems, are naturally suited for partitioned, or modular numerical solution strategies. Although widely used in tackling deterministic coupled models, several…

De-interleaving of the mixtures of Hidden Markov Processes (HMPs) generally depends on its representation model. Existing representation models consider Markov chain mixtures rather than hidden Markov, resulting in the lack of robustness to…

We propose a Hermite spectral method for the inelastic Boltzmann equation, which makes two-dimensional periodic problem computation affordable by the hardware nowadays. The new algorithm is based on a Hermite expansion, where the expansion…

High-dimensional k-sample comparison is a common applied problem. We construct a class of easy-to-implement nonparametric distribution-free tests based on new tools and unexplored connections with spectral graph theory. The test is shown to…

Nonlocal diffusion model provides an appropriate description of the diffusion process of solute in the complex medium, which cannot be described properly by classical theory of PDE. However, the operators in the nonlocal diffusion models…

We propose computationally efficient methods for estimating stationary multivariate spatial and spatial-temporal spectra from incomplete gridded data. The methods are iterative and rely on successive imputation of data and updating of model…

The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on…

In binary-transaction data-mining, traditional frequent itemset mining often produces results which are not straightforward to interpret. To overcome this problem, probability models are often used to produce more compact and conclusive…

Elliptic partial differential equations arise in many fields of science and engineering such as steady state distribution of heat, fluid dynamics, structural/mechanical engineering, aerospace engineering and seismology etc. In three…

Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known…

A completely nonparametric method for the estimation of mixture cure models is proposed. A nonparametric estimator of the incidence is extensively studied and a nonparametric estimator of the latency is presented. These estimators, which…

Item response theory (IRT) models typically rely on a normality assumption for subject-specific latent traits, which is often unrealistic in practice. Semiparametric extensions based on Dirichlet process mixtures offer a more flexible…

In this study, a thorough investigation was conducted into the Homotopy Perturbation Method (HPM) and its application to solve the Burger and Blasius equations. The HPM is a mathematical technique that combines aspects of homotopy and…

This paper presents enhancement strategies for the Hermitian and skew-Hermitian splitting method based on gradient iterations. The spectral properties are exploited for the parameter estimation, often resulting in a better convergence. In…

Community detection has been an active research area for decades. Among all probabilistic models, Stochastic Block Model has been the most popular one. This paper introduces a novel probabilistic model: RW-HDP, based on random walks and…

In this paper, we introduce a new algorithm based on archetypal analysis for blind hyperspectral unmixing, assuming linear mixing of endmembers. Archetypal analysis is a natural formulation for this task. This method does not require the…

Although considerable effort has been dedicated to improving the solution to the hyperspectral unmixing problem, non-idealities such as complex radiation scattering and endmember variability negatively impact the performance of most…

There are several numerical models that describe real phenomena being used to solve complex problems. For example, an accurate numerical breast model can provide assistance to surgeons with visual information of the breast as a result of a…