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In many industries, including aerospace and defense, waveform analysis is commonly conducted to compute the resonance of physical objects, with the Finite Element Method (FEM) being the standard approach. The Finite Difference Method (FDM)…
Gaussian graphical models (GGMs) are probabilistic tools of choice for analyzing conditional dependencies between variables in complex systems. Finding changepoints in the structural evolution of a GGM is therefore essential to detecting…
Longitudinal studies frequently incorporate covariates that evolve over time, creating complex dependence structures between outcomes and predictors. When covariates are time dependent, standard power analysis tools--largely developed for…
Gaussian mixture models (GMMs) are fundamental tools in statistical and data sciences. We study the moments of multivariate Gaussians and GMMs. The $d$-th moment of an $n$-dimensional random variable is a symmetric $d$-way tensor of size…
Instrumental variable analysis is a powerful tool for estimating causal effects when randomization or full control of confounders is not possible. The application of standard methods such as 2SLS, GMM, and more recent variants are…
A second order explicit one-step numerical method for the initial value problem of the general ordinary differential equation is proposed. It is obtained by natural modifications of the well-known leapfrog method, which is a second order,…
Moment restrictions and their conditional counterparts emerge in many areas of machine learning and statistics ranging from causal inference to reinforcement learning. Estimators for these tasks, generally called methods of moments, include…
Most papers on high-dimensional statistics are based on the assumption that none of the regressors are correlated with the regression error, namely, they are exogenous. Yet, endogeneity can arise incidentally from a large pool of regressors…
We introduce a new estimator, CRE-GMM, which exploits the correlated random effects (CRE) approach within the generalised method of moments (GMM), specifically applied to level equations, GMM-lev. It has the advantage of estimating the…
Modelling deformation of anatomical objects observed in medical images can help describe disease progression patterns and variations in anatomy across populations. We apply a stochastic generalisation of the Large Deformation Diffeomorphic…
In this study, we introduce a refined method for ascertaining error estimations in numerical simulations of dynamical systems via an innovative application of composition techniques. Our approach involves a dual application of a basic…
With recent advances in sequencing technologies, large amounts of epigenomic data have become available and computational methods are contributing significantly to the progress of epigenetic research. As an orthogonal approach to methods…
Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…
We propose a novel optimal transport-based version of the Generalized Method of Moment (GMM). Instead of handling overidentification by reweighting the data to satisfy the moment conditions (as in Generalized Empirical Likelihood methods),…
We propose two methods for computing the large deviations of the first-passage-time statistics in general open quantum systems. The first method determines the region of convergence of the joint Laplace transform and the $z$-transform of…
In the classic measurement error framework, covariates are contaminated by independent additive noise. This paper considers parameter estimation in such a linear errors-in-variables model where the unknown measurement error distribution is…
We propose a semi-partitioned Generalized Method of Moments (GMM) framework for analyzing longitudinal data with time-dependent covariates, within a marginal modeling paradigm. This approach addresses limitations of both aggregated and…
We present the evaluation of a closed form formula for the calculation of the original step between two randomly shifted fringe patterns. Our proposal extends the Gram--Schmidt orthonormalization algorithm for fringe pattern.…
This paper aims to clearly distinguish between Stochastic Gradient Descent with Momentum (SGDM) and Adam in terms of their convergence rates. We demonstrate that Adam achieves a faster convergence compared to SGDM under the condition of…
We introduce Midpoint Generative Models (MGM), a principled framework for training one-step generative models. MGM is based on a simple symmetry of Flow Matching with linear interpolation: when the two endpoint distributions coincide, the…