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We study the problem of parameter estimation for discretely observed stochastic differential equations driven by small fractional noise. Under some conditions, we obtain strong consistency and rate of convergence of the least square…
The main contribution of this paper is the formulation of a diffuse approximation method(DAM), for two-dimensional channel flows. The proposed method is based on the vorticity-streamfunction formulation. The DAM which estimates derivates of…
We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the…
In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…
Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
In this technical report we analyse the performance of diffusion strategies applied to the Least-Mean-Square adaptive filter. We configure a network of cooperative agents running adaptive filters and discuss their behaviour when compared…
Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation…
We perform numerical analysis of a nonlinear gradient flow, which can be regarded as a parabolic minimal surface problem or a regularised total variation flow, using the gradient discretisation method (GDM). GDM is a unified convergence…
Longitudinal Dispersion(LD) is the dominant process of scalar transport in natural streams. An accurate prediction on LD coefficient(Dl) can produce a performance leap in related simulation. The emerging machine learning(ML) techniques…
A Bayesian approach termed BAyesian Least Squares Optimization with Nonnegative L1-norm constraint (BALSON) is proposed. The error distribution of data fitting is described by Gaussian likelihood. The parameter distribution is assumed to be…
This paper presents a numerical method to implement the parameter estimation method using response statistics that was recently formulated by the authors. The proposed approach formulates the parameter estimation problem of It\^o drift…
We consider structural equation modeling (SEM) with latent variables for diffusion processes based on high-frequency data. The quasi-likelihood estimators for parameters in the SEM are proposed. The goodness-of-fit test is derived from the…
We study the problem of distributed adaptive estimation over networks where nodes cooperate to estimate physical parameters that can vary over both space and time domains. We use a set of basis functions to characterize the space-varying…
In this paper we propose a semi-parametric Bayesian Generalized Least Squares estimator. In a generic setting where each error is a vector, the parametric Generalized Least Square estimator maintains the assumption that each error vector…
Linearization of power flow is an important topic in power system analysis. The computational burden can be greatly reduced under the linear power flow model while the model error is the main concern. Therefore, various linear power flow…
The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…
This paper proposes the use of a Spectral method to simulate diffusive moisture transfer through porous materials as a Reduced-Order Model (ROM). The Spectral approach is an a priori method assuming a separated representation of the…
This book is meant to provide an introduction to linear models and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to ordinary least squares. In machine learning, the output is…
In this paper we identify the source of a singularity in the training loss of key denoising models, that causes the denoiser's predictions to collapse towards the mean of the source or target distributions. This degeneracy creates false…