Information Theoretic Optimal Learning of Gaussian Graphical Models
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A network analysis of the long-term quality of life and mental distress of COVID-19 survivors 1 year after hospital discharge
Objectives COVID-19 survivors suffer from persistent mental distress and impaired quality of life (QOL) after recovery from the infection. However, the symptom-symptom interaction between these psychological variables remained unexplored. The present study aimed to determine the symptom network of mental distress (depression, anxiety, sleep disturbance, fatigue, and post-traumatic stress disorder) and their association with QOL among 535 COVID-19 survivors 1 year after hospital discharge. Methods 9-item Patient Health Questionnaire, 7-item Generalized Anxiety Disorder Scale, Chalder fatigue scale, Impact of Event Scale-Revised, Pittsburgh Sleep Quality Index, and 36-Item Short-Form Health Survey were applied to measure depression, anxiety, fatigue, PTSD, sleep disturbances, and QOL, respectively. Two networks were estimated using Gaussian graphical model. Network 1 consisted of mental symptoms to determine the central and bridge symptoms. Network 2 additionally included QOL to determine which mental symptoms were mostly related to QOL. Results 60% of the COVID-19 survivors experienced mental distress 1 year after hospital discharge. Uncontrollable and excessive worry, psychomotor symptoms, intrusion, and daytime dysfunction were the most central symptoms. Daytime dysfunction and fatigue (especially mental fatigue and loss of energy) served as the bridge symptoms across the mental distress network and exhibited the most substantial association with QOL. Conclusion Our study demonstrated several key symptoms that played a vital role in mental distress and QOL among COVID-19 survivors. Prompt screening and targeted interventions for these symptoms might hold great promise in preventing mental distress and improving QOL in COVID-19 survivors.
Peng, Pu↗
Graphical Gaussian Process Regression Model for Aqueous Solvation Free Energy Prediction of Organic Molecules in Redox Flow Battery
The solvation free energy of organic molecules is a critical parameter in determining emergent properties such as solubility, liquid-phase equilibrium constants, and pKa and redox potentials in an organic redox flow battery. In this work, we present a machine learning (ML) model that can learn and predict the aqueous solvation free energy of an organic molecule using Gaussian process regression method based on a new molecular graph kernel. To investigate the performance of the ML model on electrostatic interaction, the nonpolar interaction contribution of solvent and the conformational entropy of solute in solvation free energy, three data sets with implicit or explicit water solvent models, and contribution of conformational entropy of solute are tested. We demonstrate that our ML model can predict the solvation free energy of molecules at chemical accuracy with a mean absolute error of less than 1 kcal/mol for subsets of the QM9 dataset and the Freesolv database. To solve the general data scarcity problem for a graph-based ML model, we propose a dimension reduction algorithm based on the distance between molecular graphs, which can be used to examine the diversity of the molecular data set. It provides a promising way to build a minimum training set to improve prediction for certain test sets where the space of molecular structures is predetermined.
25 ENERGY STORAGE↗
TensorGraphicalModels: A Julia toolbox for multiway covariance models and ensemble Kalman filter
Not Available
97 MATHEMATICS AND COMPUTING↗
Computationally efficient Bayesian estimation of graphical networks for omics data
Graphical networks are useful, widely-used modeling approaches to represent complex biological processes with biological measurements generated by platforms such as mass spectrometry. Bayesian analyses of graphical networks for omics data have several advantages over their frequentist counterparts, such as the inclusion of prior knowledge in the estimation of models. However, Bayesian approaches to date have only been feasible for data with a couple hundred biomolecules due to prohibitive computational time, but omics data often contains tens of thousands of biomolecules. Here, we present and illustrate a more computationally efficient approach named BPlane (Bayesian PseudoLikelihood-based Algorithm for Network Estimation) to extend Bayesian modeling capabilities for larger-sized datasets, such as most untargeted proteomics data. Via simulation, we demonstrate that BPlane produces substantial computational savings over a current state-of-the-art Bayesian algorithm while maintaining competitive edge detection accuracy. On a SARS-CoV2 proteomics data with 7000 proteins, the competing algorithm takes three times as long to complete the first iteration as BPlane takes to converge after over 100 iterations.
EM algorithm↗
Particle Filtering for Model-Based Anomaly Detection in Sensor Networks
A novel technique has been developed for anomaly detection of rocket engine test stand (RETS) data. The objective was to develop a system that postprocesses a csv file containing the sensor readings and activities (time-series) from a rocket engine test, and detects any anomalies that might have occurred during the test. The output consists of the names of the sensors that show anomalous behavior, and the start and end time of each anomaly. In order to reduce the involvement of domain experts significantly, several data-driven approaches have been proposed where models are automatically acquired from the data, thus bypassing the cost and effort of building system models. Many supervised learning methods can efficiently learn operational and fault models, given large amounts of both nominal and fault data. However, for domains such as RETS data, the amount of anomalous data that is actually available is relatively small, making most supervised learning methods rather ineffective, and in general met with limited success in anomaly detection. The fundamental problem with existing approaches is that they assume that the data are iid, i.e., independent and identically distributed, which is violated in typical RETS data. None of these techniques naturally exploit the temporal information inherent in time series data from the sensor networks. There are correlations among the sensor readings, not only at the same time, but also across time. However, these approaches have not explicitly identified and exploited such correlations. Given these limitations of model-free methods, there has been renewed interest in model-based methods, specifically graphical methods that explicitly reason temporally. The Gaussian Mixture Model (GMM) in a Linear Dynamic System approach assumes that the multi-dimensional test data is a mixture of multi-variate Gaussians, and fits a given number of Gaussian clusters with the help of the wellknown Expectation Maximization (EM) algorithm. The parameters thus learned are used for calculating the joint distribution of the observations. However, this GMM assumption is essentially an approximation and signals the potential viability of non-parametric density estimators. This is the key idea underlying the new approach.
Solano, Wanda↗
On the Solution of ℓ 0 -Constrained Sparse Inverse Covariance Estimation Problems
The sparse inverse covariance matrix is used to model conditional dependencies between variables in a graphical model to fit a multivariate Gaussian distribution. Estimating the matrix from data are well known to be computationally expensive for large-scale problems. Sparsity is employed to handle noise in the data and to promote interpretability of a learning model. Although the use of a convex ℓ 1 regularizer to encourage sparsity is common practice, the combinatorial ℓ 0 penalty often has more favorable statistical properties. In this paper, we directly constrain sparsity by specifying a maximally allowable number of nonzeros, in other words, by imposing an ℓ 0 constraint. Here, we introduce an efficient approximate Newton algorithm using warm starts for solving the nonconvex ℓ 0 -constrained inverse covariance learning problem. Numerical experiments on standard data sets show that the performance of the proposed algorithm is competitive with state-of-the-art methods.
$\ell_0$-Constrained↗
Assessing correlated truncation errors in modern nucleon-nucleon potentials
We test the BUQEYE model of correlated effective field theory (EFT) truncation errors on Reinert, Krebs, and Epelbaum's semilocal momentum-space implementation of the chiral EFT (𝜒EFT ) expansion of the nucleon-nucleon (NN) potential. This Bayesian model hypothesizes that dimensionless coefficient functions extracted from the order-by-order corrections to NN observables can be treated as draws from a Gaussian process (GP). We combine a variety of graphical and statistical diagnostics to assess when predicted observables have a 𝜒EFT convergence pattern consistent with the hypothesized GP statistical model. Our conclusions are that, first, the BUQEYE model is generally applicable to the potential investigated here, which enables statistically principled estimates of the impact of higher EFT orders on observables. Second, parameters defining the extracted coefficients such as the expansion parameter 𝑄 must be well chosen for the coefficients to exhibit a regular convergence pattern—a property we exploit to obtain posterior distributions for such quantities. Third, the assumption of GP stationarity across lab energy and scattering angle is not generally met; this necessitates adjustments in future work. We provide a workflow and interpretive guide for our analysis framework, and show what can be inferred about probability distributions for 𝑄, the EFT breakdown scale Λ 𝑏 , the scale associated with soft physics in the 𝜒EFT potential 𝑚 eff , and the GP hyperparameters. All our results can be reproduced using a publicly available Jupyter notebook, which can be straightforwardly modified to analyze other 𝜒EFT NN potentials.
Bayesian methods↗
An improvement in the numerical integration procedure used in the NASA Marshall engineering thermosphere model
A proposed replacement scheme for the integration of the barometric and diffusion equations in the NASA Marshall Engineering Thermosphere (MET) model is presented. This proposed integration scheme is based on Gaussian Quadrature. Extensive numerical testing reveals it to be faster, more accurate and more reliable than the present integration scheme (a modified form of Simpson's Rule) used in the MET model. Numerous graphical examples are provided, along with a listing of a modified form of the MET model in which subroutine INTEGRATE (using Simpson's Rule) is replaced by subroutine GAUSS (which uses Gaussian Quadrature). It is recommended that the Gaussian Quadrature integration scheme, as used here, be used in the MET model.
Hickey, Michael Philip↗
TEMImageNet training library and AtomSegNet deep-learning models for high-precision atom segmentation, localization, denoising, and deblurring of atomic-resolution images
Abstract Atom segmentation and localization, noise reduction and deblurring of atomic-resolution scanning transmission electron microscopy (STEM) images with high precision and robustness is a challenging task. Although several conventional algorithms, such has thresholding, edge detection and clustering, can achieve reasonable performance in some predefined sceneries, they tend to fail when interferences from the background are strong and unpredictable. Particularly, for atomic-resolution STEM images, so far there is no well-established algorithm that is robust enough to segment or detect all atomic columns when there is large thickness variation in a recorded image. Herein, we report the development of a training library and a deep learning method that can perform robust and precise atom segmentation, localization, denoising, and super-resolution processing of experimental images. Despite using simulated images as training datasets, the deep-learning model can self-adapt to experimental STEM images and shows outstanding performance in atom detection and localization in challenging contrast conditions and the precision consistently outperforms the state-of-the-art two-dimensional Gaussian fit method. Taking a step further, we have deployed our deep-learning models to a desktop app with a graphical user interface and the app is free and open-source. We have also built a TEM ImageNet project website for easy browsing and downloading of the training data.
25 ENERGY STORAGE↗
Uncertainty quantification for Multiphase-CFD simulations of bubbly flows: a machine learning-based Bayesian approach supported by high-resolution experiments
In this paper, we developed a machine learning-based Bayesian approach to inversely quantify and reduce the uncertainties of multiphase computational fluid dynamics (MCFD) simulations for bubbly flows. The proposed approach is supported by high-resolution two-phase flow measurements, including those by double-sensor conductivity probes, high-speed imaging, and particle image velocimetry. Local distributions of key physical quantities of interest (QoIs), including the void fraction and phasic velocities, are obtained to support the Bayesian inference. In the process, the epistemic uncertainties of the closure relations are inversely quantified while the aleatory uncertainties from stochastic fluctuations of the system are evaluated based on experimental uncertainty analysis. The combined uncertainties are then propagated through the MCFD solver to obtain uncertainties of the QoIs, based on which probability-boxes are constructed for validation. The proposed approach relies on three machine learning methods: feedforward neural networks and principal component analysis for surrogate modeling, and Gaussian processes for model form uncertainty modeling. The whole process is implemented within the framework of an open-source deep learning library PyTorch with graphics processing unit (GPU) acceleration, thus ensuring the efficiency of the computation. The results demonstrate that with the support of high-resolution data, the uncertainties of MCFD simulations can be significantly reduced. The proposed approach has the potential for other applications that involve numerical models with empirical parameters.
42 ENGINEERING↗
Operations for Learning with Graphical Models
This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known examples of graphical models include Bayesian net- works, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, and the manipulation of probability models from the exponential family. These operations adapt existing techniques from statistics and automatic differentiation to graphs. Two standard algorithm schemes for learning are reviewed in a graphical framework: Gibbs sampling and the expectation maximization algorithm. Some algorithms are developed in this graphical framework including a generalized version of linear regression, techniques for feed-forward networks, and learning Gaussian and discrete Bayesian networks from data. The paper concludes by sketching some implications for data analysis and summarizing some popular algorithms that fall within the framework presented. The main original contributions here are the decomposition techniques and the demonstration that graphical models provide a framework for understanding and developing complex learning algorithms.
Buntine, Wray L.↗
A new efficient grain growth model using a random Gaussian-sampled mode filter
This paper presents the use of a Gaussian neighborhood mode filter for predicting grain growth in a manner similar to the solutions obtained by a Monte Carlo Potts model. This flexible grain growth model can quickly utilize modern, computationally optimized data science strategies on graphics processing units to simulate grain growth up to 100 times faster than the state-of-the-art, publicly available Monte Carlo Potts model. We show that, given the correct neighborhood, the mode filter can replicate normal grain growth in two or three dimensions. In addition, the paper briefly demonstrates the ability to model limited anisotropic in grain boundary energy and mobility. Anisotropic grain boundary energy is modeled by defining a weighted mode filter operation. Anisotropic grain boundary mobility is modeled by scaling and orienting the Gaussian neighborhood in a particular direction.
Anisotropy↗
The Effect of the Prior and the Experimental Design on the Inference of the Precision Matrix in Gaussian Chain Graph Models
Here, we investigate whether (and how) experimental design could aid in the estimation of the precision matrix in a Gaussian chain graph model, especially the interplay between the design, the effect of the experiment and prior knowledge about the effect. Estimation of the precision matrix is a fundamental task to infer biological graphical structures like microbial networks. We compare the marginal posterior precision of the precision matrix under four priors: flat, conjugate Normal-Wishart, Normal-MGIG and a general independent. Under the flat and conjugate priors, the Laplace-approximated posterior precision is not a function of the design matrix rendering useless any efforts to find an optimal experimental design to infer the precision matrix. In contrast, the Normal-MGIG and general independent priors do allow for the search of optimal experimental designs, yet there is a sharp upper bound on the information that can be extracted from a given experiment. We confirm our theoretical findings via a simulation study comparing (i) the KL divergence between prior and posterior and (ii) the Stein’s loss difference of MAPs between random and no experiment. Our findings provide practical advice for domain scientists conducting experiments to better infer the precision matrix as a representation of a biological network.
54 ENVIRONMENTAL SCIENCES↗
A Bayesian model for multivariate discrete data using spatial and expert information with application to inferring building attributes
When modeling sparsely observed multivariate data, strong prior information elicited from experts can be used to bolster predictive accuracy and counteract sampling bias. Similarly, modeling autocorrelation in space can help make use of co-occurrence patterns present in many types of spatial data. To make use of both expert prior information and spatial structure, we propose a novel graphical model for a spatial Bayesian network developed specifically to address challenges in inferring the attributes of buildings from geographically sparse observational data. This model is implemented as the sum of a spatial multivariate Gaussian random field and a tabular conditional probability function in real-valued space prior to projection onto the probability simplex. This modeling form is especially suitable for the usage of prior information in the form of sets of atomic rules obtained from experts. To perform inference with missing data, we implement a Markov chain Monte Carlo scheme composed of alternating steps of Gibbs sampling of missing entries and Hamiltonian Monte Carlo for model parameters. A case study in building attribution is presented to highlight the advantages and limitations of this approach.
97 MATHEMATICS AND COMPUTING↗
BatteryPro: A Python Toolkit for Battery Data Analysis and Machine Learning Predictions
Analyzing battery test data for research & development can be time-consuming since battery tests often run on the order of months to years, generating large volumes of data. BatteryPro is a comprehensive Python package and software designed to facilitate advanced analysis and performance predictions for battery test data. Developed for battery researchers, it supports data types from widely used battery testing instruments, including MACCOR and Biologic cycling systems. The software provides a variety of tools for extracting and plotting key battery parameters such as time, voltage, capacity, current, and pressure. In addition to its extensive data analysis capabilities, BatteryPro features a dedicated machine learning module that employs a Bayesian Gaussian Mixture Model (GMM) to predict battery performance and degradation. Users can generate synthetic capacity fade data, calculate fade metrics, and leverage predictive models to forecast long-term battery behavior. The software's graphical user interface (GUI) enhances usability, allowing researchers to upload, merge, and analyze multiple data files with full customizability. The GUI also supports machine learning predictions, enabling users to fit models and make predictions based on selected data and parameters. BatteryPro is built using QtDesigner, scikit-learn, matplotlib, and pandas, ensuring a high level of customization, flexibility, and accuracy in battery data analysis. This tool aims to empower researchers with the ability to perform detailed battery analysis and make informed predictions, ultimately advancing the field of battery research.
25 - ENERGY STORAGE↗
Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization
In this paper, we compare and contrast the use of second-order response surface models and kriging models for approximating non-random, deterministic computer analyses. After reviewing the response surface method for constructing polynomial approximations, kriging is presented as an alternative approximation method for the design and analysis of computer experiments. Both methods are applied to the multidisciplinary design of an aerospike nozzle which consists of a computational fluid dynamics model and a finite-element model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations, and four optimization problems m formulated and solved using both sets of approximation models. The second-order response surface models and kriging models-using a constant underlying global model and a Gaussian correlation function-yield comparable results.
Simpson, Timothy W.↗
Comparison of Response Surface and Kriging Models in the Multidisciplinary Design of an Aerospike Nozzle
The use of response surface models and kriging models are compared for approximating non-random, deterministic computer analyses. After discussing the traditional response surface approach for constructing polynomial models for approximation, kriging is presented as an alternative statistical-based approximation method for the design and analysis of computer experiments. Both approximation methods are applied to the multidisciplinary design and analysis of an aerospike nozzle which consists of a computational fluid dynamics model and a finite element analysis model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations. Four optimization problems are formulated and solved using both approximation models. While neither approximation technique consistently outperforms the other in this example, the kriging models using only a constant for the underlying global model and a Gaussian correlation function perform as well as the second order polynomial response surface models.
Simpson, Timothy W.↗