arXiv subjects

Mengyang Gu

Publications and source records attributed to Mengyang Gu.

At least 37 records · Page 2Linked to original sources

arXiv2024

RobustCalibration: Robust Calibration of Computer Models in R

Two fundamental research tasks in science and engineering are forward predictions and data inversion. This article introduces a recent R package RobustCalibration for Bayesian data inversion and model calibration by experiments and field observations. Mathematical models for forward predictions are often written in computer code, and they can be computationally expensive slow to run. To overcome the computational bottleneck from the simulator, we implemented a statistical emulator from the RobustGaSP package for emulating both scalar-valued or vector-valued computer model outputs. Both posterior sampling and maximum likelihood approach are implemented in the RobustCalibration package for parameter estimation. For imperfect computer models, we implement Gaussian stochastic process and the scaled Gaussian stochastic process for modeling the discrepancy function between the reality and mathematical model. This package is applicable to various types of field observations, such as repeated experiments and multiple sources of measurements. We discuss numerical examples of calibrating mathematical models that have closed-form expressions, and differential equations solved by numerical methods.

stat.CO↗

arXiv2024

Reliable emulation of complex functionals by active learning with error control

A statistical emulator can be used as a surrogate of complex physics-based calculations to drastically reduce the computational cost. Its successful implementation hinges on an accurate representation of the nonlinear response surface with a high-dimensional input space. Conventional "space-filling" designs, including random sampling and Latin hypercube sampling, become inefficient as the dimensionality of the input variables increases, and the predictive accuracy of the emulator can degrade substantially for a test input distant from the training input set. To address this fundamental challenge, we develop a reliable emulator for predicting complex functionals by active learning with error control (ALEC). The algorithm is applicable to infinite-dimensional mapping with high-fidelity predictions and a controlled predictive error. The computational efficiency has been demonstrated by emulating the classical density functional theory (cDFT) calculations, a statistical-mechanical method widely used in modeling the equilibrium properties of complex molecular systems. We show that ALEC is much more accurate than conventional emulators based on the Gaussian processes with "space-filling" designs and alternative active learning methods. Besides, it is computationally more efficient than direct cDFT calculations. ALEC can be a reliable building block for emulating expensive functionals owing to its minimal computational cost, controllable predictive error, and fully automatic features.

physics.chem-ph↗

arXiv2024

Sequential Kalman filter for fast online changepoint detection in longitudinal health records

This article introduces the sequential Kalman filter, a computationally scalable approach for online changepoint detection with temporally correlated data. The temporal correlation was not considered in the Bayesian online changepoint detection approach due to the large computational cost. Motivated by detecting COVID-19 infections for dialysis patients from massive longitudinal health records with a large number of covariates, we develop a scalable approach to detect multiple changepoints from correlated data by sequentially stitching Kalman filters of subsequences to compute the joint distribution of the observations, which has linear computational complexity with respect to the number of observations between the last detected changepoint and the current observation at each time point, without approximating the likelihood function. Compared to other online changepoint detection methods, simulated experiments show that our approach is more precise in detecting single or multiple changes in mean, variance, or correlation for temporally correlated data. Furthermore, we propose a new way to integrate classification and changepoint detection approaches that improve the detection delay and accuracy for detecting COVID-19 infection compared to other alternatives.

stat.AP↗

arXiv2023

Analyzing Disparity and Temporal Progression of Internet Quality through Crowdsourced Measurements with Bias-Correction

Crowdsourced speedtest measurements are an important tool for studying internet performance from the end user perspective. Nevertheless, despite the accuracy of individual measurements, simplistic aggregation of these data points is problematic due to their intrinsic sampling bias. In this work, we utilize a dataset of nearly 1 million individual Ookla Speedtest measurements, correlate each datapoint with 2019 Census demographic data, and develop new methods to present a novel analysis to quantify regional sampling bias and the relationship of internet performance to demographic profile. We find that the crowdsourced Ookla Speedtest data points contain significant sampling bias across different census block groups based on a statistical test of homogeneity. We introduce two methods to correct the regional bias by the population of each census block group. Whereas the sampling bias leads to a small discrepancy in the overall cumulative distribution function of internet speed in a city between estimation from original samples and bias-corrected estimation, the discrepancy is much smaller compared to the size of the sampling heterogeneity across regions. Further, we show that the sampling bias is strongly associated with a few demographic variables, such as income, education level, age, and ethnic distribution. Through regression analysis, we find that regions with higher income, younger populations, and lower representation of Hispanic residents tend to measure faster internet speeds along with substantial collinearity amongst socioeconomic attributes and ethnic composition. Finally, we find that average internet speed increases over time based on both linear and nonlinear analysis from state space models, though the regional sampling bias may result in a small overestimation of the temporal increase of internet speed.

stat.AP↗

arXiv2023

Perfecting Liquid-State Theories with Machine Intelligence

Recent years have seen a significant increase in the use of machine intelligence for predicting electronic structure, molecular force fields, and the physicochemical properties of various condensed systems. However, substantial challenges remain in developing a comprehensive framework capable of handling a wide range of atomic compositions and thermodynamic conditions. This perspective discusses potential future developments in liquid-state theories leveraging on recent advancements of functional machine learning. By harnessing the strengths of theoretical analysis and machine learning techniques including surrogate models, dimension reduction and uncertainty quantification, we envision that liquid-state theories will gain significant improvements in accuracy, scalability and computational efficiency, enabling their broader applications across diverse materials and chemical systems.

physics.chem-ph↗

arXiv2023

Probabilistic forecast of nonlinear dynamical systems with uncertainty quantification

Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict new scenarios unobserved before. In this work, we first extend parallel partial Gaussian processes for predicting the vector-valued transition function that links the observations between the current and next time points, and quantify the uncertainty of predictions by posterior sampling. Second, we show the equivalence between the dynamic mode decomposition and the maximum likelihood estimator of the linear mapping matrix in the linear state space model. The connection provides a {probabilistic generative} model of dynamic mode decomposition and thus, uncertainty of predictions can be obtained. Furthermore, we draw close connections between different data-driven models for approximating nonlinear dynamics, through a unified view of generative models. We study two numerical examples, where the inputs of the dynamics are assumed to be known in the first example and the inputs are unknown in the second example. The examples indicate that uncertainty of forecast can be properly quantified, whereas model or input misspecification can degrade the accuracy of uncertainty quantification.

stat.ME↗

arXiv2023

Data-driven model construction for anisotropic dynamics of active matter

The dynamics of cellular pattern formation is crucial for understanding embryonic development and tissue morphogenesis. Recent studies have shown that human dermal fibroblasts cultured on liquid crystal elastomers can exhibit an increase in orientational alignment over time, accompanied by cell proliferation, under the influence of the weak guidance of a molecularly aligned substrate. However, a comprehensive understanding of how this order arises remains largely unknown. This knowledge gap may be attributed, in part, to a scarcity of mechanistic models that can capture the temporal progression of the complex nonequilibrium dynamics during the cellular alignment process. The orientational alignment occurs primarily when cells reach a high density near confluence. Therefore, for accurate modeling, it is crucial to take into account both the cell-cell interaction term and the influence from the substrate, acting as a one-body external potential term. To fill in this gap, we develop a hybrid procedure that utilizes statistical learning approaches to extend the state-of-the-art physics models for quantifying both effects. We develop a more efficient way to perform feature selection that avoids testing all feature combinations through simulation. The maximum likelihood estimator of the model was derived and implemented in computationally scalable algorithms for model calibration and simulation. By including these features, such as the non-Gaussian, anisotropic fluctuations, and limiting alignment interaction only to neighboring cells with the same velocity direction, this model quantitatively reproduce the key system-level parameters--the temporal progression of the velocity orientational order parameters and the variability of velocity vectors, whereas models missing any of the features fail to capture these temporally dependent parameters.

physics.bio-ph↗

arXiv2023

Calibration of imperfect geophysical models by multiple satellite interferograms with measurement bias

Model calibration consists of using experimental or field data to estimate the unknown parameters of a mathematical model. The presence of model discrepancy and measurement bias in the data complicates this task. Satellite interferograms, for instance, are widely used for calibrating geophysical models in geological hazard quantification. In this work, we used satellite interferograms to relate ground deformation observations to the properties of the magma chamber at K\=ılauea Volcano in Hawai`i. We derived closed-form marginal likelihoods and implemented posterior sampling procedures that simultaneously estimate the model discrepancy of physical models, and the measurement bias from the atmospheric error in satellite interferograms. We found that model calibration by aggregating multiple interferograms and downsampling the pixels in the interferograms can reduce the computation complexity compared to calibration approaches based on multiple data sets. The conditions that lead to no loss of information from data aggregation and downsampling are studied. Simulation illustrates that both discrepancy and measurement bias can be estimated, and real applications demonstrate that modeling both effects helps obtain a reliable estimation of a physical model's unobserved parameters and enhance its predictive accuracy. We implement the computational tools in the RobustCalibration package available on CRAN.

stat.ME↗

arXiv2022

Molecular-scale substrate anisotropy and crowding drive long-range nematic order of cell monolayers

The ability of cells to reorganize in response to external stimuli is important in areas ranging from morphogenesis to tissue engineering. Elongated cells can co-align due to steric effects, forming states with local order. We show that molecular-scale substrate anisotropy can direct cell organization, resulting in the emergence of nematic order on tissue scales. To quantitatively examine the disorder-order transition, we developed a high-throughput imaging platform to analyze velocity and orientational correlations for several thousand cells over days. The establishment of global, seemingly long-ranged order is facilitated by enhanced cell division along the substrate's nematic axis, and associated extensile stresses that restructure the cells' actomyosin networks. Our work, which connects to a class of systems known as active dry nematics, provides a new understanding of the dynamics of cellular remodeling and organization in weakly interacting cell collectives. This enables data-driven discovery of cell-cell interactions and points to strategies for tissue engineering.

physics.bio-ph↗

arXiv2022

Efficient force field and energy emulation through partition of permutationally equivalent atoms

Gaussian process (GP) emulator has been used as a surrogate model for predicting force field and molecular potential, to overcome the computational bottleneck of molecular dynamics simulation. Integrating both atomic force and energy in predictions was found to be more accurate than using energy alone, yet it requires $O((NM)^3)$ computational operations for computing the likelihood function and making predictions, where $N$ is the number of atoms and $M$ is the number of simulated configurations in the training sample, due to the inversion of a large covariance matrix. The large computational need limits its applications to emulating simulation of small molecules. The computational challenge of using both gradient information and function values in GPs was recently noticed in statistics and machine learning communities, where conventional approximation methods, such as the low rank decomposition or sparse approximation, may not work well. Here we introduce a new approach, the atomized force field (AFF) model, that integrates both force and energy in the emulator with many fewer computational operations. The drastic reduction on computation is achieved by utilizing the naturally sparse structure of the covariance satisfying the constraints of the energy conservation and permutation symmetry of atoms. The efficient machine learning algorithm extends the limits of its applications on larger molecules under the same computational budget, with nearly no loss of predictive accuracy. Furthermore, our approach contains uncertainty assessment of predictions of atomic forces and potentials, useful for developing a sequential design over the chemical input space, with almost no increase in computational cost.

physics.chem-ph↗

arXiv2022

Uncertainty quantification and estimation in differential dynamic microscopy

Differential dynamic microscopy (DDM) is a form of video image analysis that combines the sensitivity of scattering and the direct visualization benefits of microscopy. DDM is broadly useful in determining dynamical properties including the intermediate scattering function for many spatiotemporally correlated systems. Despite its straightforward analysis, DDM has not been fully adopted as a routine characterization tool, largely due to computational cost and lack of algorithmic robustness. We present statistical analysis that quantifies the noise, reduces the computational order and enhances the robustness of DDM analysis. We propagate the image noise through the Fourier analysis, which allows us to comprehensively study the bias in different estimators of model parameters, and we derive a different way to detect whether the bias is negligible. Furthermore, through use of Gaussian process regression (GPR), we find that predictive samples of the image structure function require only around 0.5%-5% of the Fourier transforms of the observed quantities. This vastly reduces computational cost, while preserving information of the quantities of interest, such as quantiles of the image scattering function, for subsequent analysis. The approach, which we call DDM with uncertainty quantification (DDM-UQ), is validated using both simulations and experiments with respect to accuracy and computational efficiency, as compared with conventional DDM and multiple particle tracking. Overall, we propose that DDM-UQ lays the foundation for important new applications of DDM, as well as to high-throughput characterization. We implement the fast computation tool in a new, publicly available MATLAB software package.

cond-mat.soft↗

arXiv2021

Gaussian orthogonal latent factor processes for large incomplete matrices of correlated data

We introduce Gaussian orthogonal latent factor processes for modeling and predicting large correlated data. To handle the computational challenge, we first decompose the likelihood function of the Gaussian random field with a multi-dimensional input domain into a product of densities at the orthogonal components with lower-dimensional inputs. The continuous-time Kalman filter is implemented to compute the likelihood function efficiently without making approximations. We also show that the posterior distribution of the factor processes is independent, as a consequence of prior independence of factor processes and orthogonal factor loading matrix. For studies with large sample sizes, we propose a flexible way to model the mean, and we derive the marginal posterior distribution to solve identifiability issues in sampling these parameters. Both simulated and real data applications confirm the outstanding performance of this method.

stat.ME↗

arXiv2021

Characterizing Performance Inequity Across U.S. Ookla Speedtest Users

The Internet has become indispensable to daily activities, such as work, education and health care. Many of these activities require Internet access data rates that support real-time video conferencing. However, digital inequality persists across the United States, not only in who has access but in the quality of that access. Speedtest by Ookla allows users to run network diagnostic tests to better understand the current performance of their network. In this work, we leverage an Internet performance dataset from Ookla, together with an ESRI demographic dataset, to conduct a comprehensive analysis that characterizes performance differences between Speedtest users across the U.S. Our analysis shows that median download speeds for Speedtest users can differ by over 150Mbps between states. Further, there are important distinctions between user categories. For instance, all but one state showed statistically significant differences in performance between Speedtest users in urban and rural areas. The difference also exists in urban areas between high and low income users in 27 states. Our analysis reveals that states that demonstrate this disparity in Speedtest results are geographically bigger, more populous and have a wider dispersion of median household income. We conclude by highlighting several challenges to the complex problem space of digital inequality characterization and provide recommendations for furthering research on this topic.

cs.NI↗

arXiv2021

Robust estimation of SARS-CoV-2 epidemic in US counties

The COVID-19 outbreak is asynchronous in US counties. Mitigating the COVID-19 transmission requires not only the state and federal level order of protective measures such as social distancing and testing, but also public awareness of time-dependent risk and reactions at county and community levels. We propose a robust approach to estimate the heterogeneous progression of SARS-CoV-2 at all US counties having no less than 2 COVID-19 associated deaths, and we use the daily probability of contracting (PoC) SARS-CoV-2 for a susceptible individual to quantify the risk of SARS-CoV-2 transmission in a community. We found that shortening by $5\%$ of the infectious period of SARS-CoV-2 can reduce around $39\%$ (or $78$K, $95\%$ CI: $[66$K $, 89$K $]$) of the COVID-19 associated deaths in the US as of 20 September 2020. Our findings also indicate that reducing infection and deaths by a shortened infectious period is more pronounced for areas with the effective reproduction number close to 1, suggesting that testing should be used along with other mitigation measures, such as social distancing and facial mask-wearing, to reduce the transmission rate. Our deliverable includes a dynamic county-level map for local officials to determine optimal policy responses and for the public to better understand the risk of contracting SARS-CoV-2 on each day.

stat.AP↗

arXiv2020

Emulating the First Principles of Matter: A Probabilistic Roadmap

This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the electronic structure and diverse static properties of of many-particle systems useful for practical applications. Pedagogical examples are given to illustrate the basic concepts and simple applications of quantum Monte Carlo and density functional theory -- two representative methods commonly used in the literature of first principles modeling. In addition, this chapter highlights the practical needs for the integration of physics-based modeling and data-science approaches to reduce the computational cost and expand the scope of applicability. A special emphasis is placed on recent developments of statistical surrogate models to emulate first principles calculation from a probabilistic point of view. The probabilistic approach provides an internal assessment of the approximation accuracy of emulation that quantifies the uncertainty in predictions. Various recent advances toward this direction establish a new marriage between Gaussian processes and first principles calculation, with physical properties, such as translational, rotational, and permutation symmetry, naturally encoded in new kernel functions. Finally, it concludes with some prospects on future advances in the field toward faster yet more accurate computation leveraging a synergetic combination {of} novel theoretical concepts and efficient numerical algorithms.

cs.CE↗

arXiv2020

A theoretical framework of the scaled Gaussian stochastic process in prediction and calibration

Model calibration or data inversion is one of fundamental tasks in uncertainty quantification. In this work, we study the theoretical properties of the scaled Gaussian stochastic process (S-GaSP), to model the discrepancy between reality and imperfect mathematical models. We establish the explicit connection between Gaussian stochastic process (GaSP) and S-GaSP through the orthogonal series representation. The predictive mean estimator in the S-GaSP calibration model converges to the reality at the same rate as the GaSP with a suitable choice of the regularization and scaling parameters. We also show the calibrated mathematical model in the S-GaSP calibration converges to the one that minimizes the $L_2$ loss between the reality and mathematical model, whereas the GaSP model with other widely used covariance functions does not have this property. Numerical examples confirm the excellent finite sample performance of our approaches compared to a few recent approaches.

math.ST↗

arXiv2019

Generalized probabilistic principal component analysis of correlated data

Principal component analysis (PCA) is a well-established tool in machine learning and data processing. The principal axes in PCA were shown to be equivalent to the maximum marginal likelihood estimator of the factor loading matrix in a latent factor model for the observed data, assuming that the latent factors are independently distributed as standard normal distributions. However, the independence assumption may be unrealistic for many scenarios such as modeling multiple time series, spatial processes, and functional data, where the outcomes are correlated. In this paper, we introduce the generalized probabilistic principal component analysis (GPPCA) to study the latent factor model for multiple correlated outcomes, where each factor is modeled by a Gaussian process. Our method generalizes the previous probabilistic formulation of PCA (PPCA) by providing the closed-form maximum marginal likelihood estimator of the factor loadings and other parameters. Based on the explicit expression of the precision matrix in the marginal likelihood that we derived, the number of the computational operations is linear to the number of output variables. Furthermore, we also provide the closed-form expression of the marginal likelihood when other covariates are included in the mean structure. We highlight the advantage of GPPCA in terms of the practical relevance, estimation accuracy and computational convenience. Numerical studies of simulated and real data confirm the excellent finite-sample performance of the proposed approach.

stat.ME↗

arXiv2018

Jointly Robust Prior for Gaussian Stochastic Process in Emulation, Calibration and Variable Selection

Gaussian stochastic process (GaSP) has been widely used in two fundamental problems in uncertainty quantification, namely the emulation and calibration of mathematical models. Some objective priors, such as the reference prior, are studied in the context of emulating (approximating) computationally expensive mathematical models. In this work, we introduce a new class of priors, called the jointly robust prior, for both the emulation and calibration. This prior is designed to maintain various advantages from the reference prior. In emulation, the jointly robust prior has an appropriate tail decay rate as the reference prior, and is computationally simpler than the reference prior in parameter estimation. Moreover, the marginal posterior mode estimation with the jointly robust prior can separate the influential and inert inputs in mathematical models, while the reference prior does not have this property. We establish the posterior propriety for a large class of priors in calibration, including the reference prior and jointly robust prior in general scenarios, but the jointly robust prior is preferred because the calibrated mathematical model typically predicts the reality well. The jointly robust prior is used as the default prior in two new R packages, called "RobustGaSP" and "RobustCalibration", available on CRAN for emulation and calibration, respectively.

stat.ME↗