Related papers: Metric/Nonmetric Elastic MDS
In this paper we consider the Modified Craig-Sneyd (MCS) scheme which forms a prominent time stepping method of the Alternating Direction Implicit type for multidimensional time-dependent convection-diffusion equations with mixed spatial…
The problem of noise covariance matrix identification of stochastic linear time-varying state-space models is addressed. The measurement difference method (MDM) is generalized to time-varying dimensions of the measurement and control. Three…
We explore learning pixelwise correspondences between images of deformable objects in different configurations. Traditional correspondence matching approaches such as SIFT, SURF, and ORB can fail to provide sufficient contextual information…
Effective elastic moduli for 3D solid-solid phononic crystals of arbitrary anisotropy and oblique lattice structure are formulated analytically using the plane-wave expansion (PWE) method and the recently proposed monodromy-matrix (MM)…
Many applications require recovering the geometry information of multiple elastic particles based on the scattering information. In this paper, we consider the inverse time-harmonic elastic scattering of multiple rigid particles in three…
An MCMC simulation method based on a two stage delayed rejection Metropolis-Hastings algorithm is proposed to estimate a factor multivariate stochastic volatility model. The first stage uses kstep iteration towards the mode, with k small,…
We propose efficient nonparametric statistics to compare medical imaging modalities in multi-reader multi-test data and to compare markers in longitudinal ROC data. The proposed methods are based on the weighted area under the ROC curve…
The E(xplicit)I(implicit)N(null) method was developed recently to remove numerical instability from PDEs, adding and subtracting an operator $\mathcal{D}$ of arbitrary structure, treating the operator implicitly in one case, and explicitly…
Numerical resolution of high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by…
Reversible jump Markov chain Monte Carlo (RJMCMC) proposals that achieve reasonable acceptance rates and mixing are notoriously difficult to design in most applications. Inspired by recent advances in deep neural network-based normalizing…
Multidimensional fitting (MDF) method is a multivariate data analysis method recently developed and based on the fitting of distances. Two matrices are available: one contains the coordinates of the points and the second contains the…
In this article, we propose a space-time Multi-Index Monte Carlo (MIMC) estimator for a one-dimensional parabolic stochastic partial differential equation (SPDE) of Zakai type. We compare the complexity with the Multilevel Monte Carlo…
Although multivariate stochastic volatility models usually produce more accurate forecasts compared to the MGARCH models, their estimation techniques such as Bayesian MCMC typically suffer from the curse of dimensionality. We propose a fast…
The aim of this work is to efficiently and robustly solve the statistical inverse problem related to the identification of the elastic properties at both macroscopic and mesoscopic scales of heterogeneous anisotropic materials with a…
We propose a data segmentation methodology for the high-dimensional linear regression problem where regression parameters are allowed to undergo multiple changes. The proposed methodology, MOSEG, proceeds in two stages: first, the data are…
A multilevel Monte Carlo (MLMC) method for quantifying model-form uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS) simulations is presented. Two, high-dimensional, stochastic extensions of the RANS equations are…
The Gini Multidimensional Scaling (Gini MDS) framework extends the Euclidean multidimensional scaling. We introduce a Gini pseudo-distance based on values and their ranks that depends on a fine-tunable hyperparameter. This pseudo-distance…
We present a multilevel Monte Carlo (MLMC) method for the uncertainty quantification of variably saturated porous media flow that are modeled using the Richards' equation. We propose a stochastic extension for the empirical models that are…
The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied Mathematics, such as non-parametric regression, multi-class…
Multiparticle collision dynamics (MPC), a particle-based mesoscale simulation technique for com- plex fluid, is widely employed in non-equilibrium simulations of soft matter systems. To maintain a defined thermodynamic state, thermalization…