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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…
Application of Jarzynski nonequilibrium work relation to free energy calculation is limited by the very slow convergence of the estimate when dissipation is high. We present a novel perturbation protocol able to improve the convergence of…
Adaptive experiment designs can dramatically improve statistical efficiency in randomized trials, but they also complicate statistical inference. For example, it is now well known that the sample mean is biased in adaptive trials.…
The accurate estimation of free energy differences between two states is a long-standing challenge in molecular simulations. Traditional approaches generally rely on sampling multiple intermediate states to ensure sufficient overlap in…
Response-biased sampling, in which samples are drawn from a popula- tion according to the values of the response variable, is common in biomedical, epidemiological, economic and social studies. In particular, the complete obser- vations in…
We consider a wavelet thresholding approach to adaptive variance function estimation in heteroscedastic nonparametric regression. A data-driven estimator is constructed by applying wavelet thresholding to the squared first-order differences…
The dynamics of molecules are governed by rare event transitions between long-lived (metastable) states. To explore these transitions efficiently, many enhanced sampling protocols have been introduced that involve using simulations with…
We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules…
A modification of the Adaptive Biasing Force method is introduced, in which the free energy is approximated by a sum of tensor products of one-dimensional functions. This enables to handle a larger number of reaction coordinates than the…
The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard least squares problem and independent sampling of Fourier…
We present a detailed comparison of computational efficiency and precision for several free energy difference ($\Delta F$) methods. The analysis includes both equilibrium and non-equilibrium approaches, and distinguishes between…
This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with…
Ensuring a satisfactory statistical convergence of anharmonic thermodynamic properties requires sampling of many atomic configurations, however the methods to obtain those necessarily produce correlated samples, thereby reducing the…
A practical method for finding free energy barriers for transitions in high-dimensional classical and quantum systems is presented and used to calculate the dissociative sticking probability of H2 on a metal surface within transition state…
A new nonparametric estimator of a convex regression function in any dimension is proposed and its convergence properties are studied. We start by using any estimator of the regression function and we \emph{convexify} it by taking the…
The focus of this paper is on trend estimation for a general state-space model $Y_t=\mu_t+\varepsilon_t$, where the $d$th difference of the trend $\{\mu_t\}$ is assumed to be i.i.d., and the error sequence $\{\varepsilon_t\}$ is assumed to…
Many enhanced sampling techniques rely on the identification of a number of collective variables that describe all the slow modes of the system. By constructing a bias potential in this reduced space one is then able to sample efficiently…
In classical inverse linear optimization, one assumes a given solution is a candidate to be optimal. Real data is imperfect and noisy, so there is no guarantee this assumption is satisfied. Inspired by regression, this paper presents a…
Adaptive Finite Element Method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property…
The problem of estimating the mean of random functions based on discretely sampled data arises naturally in functional data analysis. In this paper, we study optimal estimation of the mean function under both common and independent designs.…