Multivariate Gaussian Research Articles

Thermodynamics-based data-driven combustion modelling for modern spark-ignition engines

Combustion modelling is complicated, computationally expensive, and crucial for the development of modern spark-ignition (SI) engines. This study introduces a novel data-driven approach to improve the predictability of phenomenological SI engine models. First, a physics-based model is used to generate Mass Fraction Burned (MFB) profiles for 1,258 precisely controlled knock-limited combustion experiments. To predict these MFB profiles based on the operating conditions, Artificial Neural Networks (ANN), Multiple Output Support Vector Regression (MOSVR), and Multivariate Gaussian Process (MGP) are then applied. Among these, MGP demonstrates superior performance due to the Gaussian-like distribution of the outputs. Further sensitivity analysis using MGP identifies critical inputs that are not engine specific to develop a thermodynamics-based data-driven model. The model demonstrates high accuracy, uses normalised inputs that are independent of engine geometry, and consistently performs well with small datasets. When applied to a different but similarly sized engine, the model accurately predicts the knock-limited spark timing and captures the MFB profile relatively well, showing strong generalisability. This study not only improves the predictability of engine combustion simulations but also establishes a valuable dataset for further development of data-driven models in different engines.

Single Station Seismic Event Location With a Neural‐Guided Mixture Model: Model‐Based Weighting for Improved Accuracy

AbstractIn many regions of the world with complex seismic activity, the availability of seismic stations is limited. This motivated us to develop a probabilistic method for single‐station earthquake location. Single station location methods may provide an efficient and cost‐effective way to monitor small‐magnitude seismic events over large areas of the world. This method relies on the outputs of two neural networks, which predict the initial spatial location of specific areas (convolutional) used in the prior probability and seismic phase recognition (combination of convolutional and Long Short Term Memory) used in the likelihood function. These estimates and a 3D travel time likelihood function are used in a Bayesian framework. In this model, the initial spatial location is expressed as a Multivariate Gaussian Mixture Model, and the likelihood function refines the localization using the arrival time difference between S and P waves in a 3D space. The likelihood function uses a Fast Marching Eikonal method with a 3D velocity structure. We tested this method on the Ridgecrest 2019 seismic sequence (Mw = 7.1) and on West Texas and found promising results for locating with a single station. Our approach demonstrates that using a Bayesian model with strong priors obtained through deep learning algorithms is effective. Our model can predict epicenter and depth with mean errors of 7.55 km in longitude, 13.54 km in latitude and 0.630 km in depth at the two different locations studied. This method demonstrates the effectiveness of combining deep learning for initial estimations with probabilistic 3D location refinement.

Reinforcement Learning for EV Fleet Smart Charging with On-Site Renewable Energy Sources

In 2020, the transportation sector was the second largest source of carbon emissions in the UK and in Newcastle upon Tyne, responsible for about 33% of total emissions. To support the UK’s target of reaching net zero emissions by 2050, electric vehicles (EVs) are pivotal in advancing carbon-neutral road transportation. Optimal EV charging requires a better understanding of the unpredictable output from on-site renewable energy sources (ORES). This paper proposes an integrated EV fleet charging schedule with a proximal policy optimization method based on a framework for deep reinforcement learning. For the design of the reinforcement learning environment, mathematical models of wind and solar power generation are created. In addition, the multivariate Gaussian distributions derived from historical weather and EV fleet charging data are utilized to simulate weather and charging demand uncertainty in order to create large datasets for training the model. The optimization problem is expressed as a Markov decision process (MDP) with operational constraints. For training artificial neural networks (ANNs) through successive transition simulations, a proximal policy optimization (PPO) approach is devised. The optimization approach is deployed and evaluated on a real-world scenario comprised of council EV fleet charging data from Leicester, UK. The results show that due to the design of the rewards function and system limitations, the charging action is biased towards the time of day when renewable energy output is maximum (midday). The charging decision by reinforcement learning improves the utilization of renewable energy by 2–4% compared to the random charging policy and the priority charging policy. This study contributes to the reduction in battery charging and discharging, electricity sold to the grid to create benefits and the reduction in carbon emissions.

Protein language models learn evolutionary statistics of interacting sequence motifs

Protein language models (pLMs) have emerged as potent tools for predicting and designing protein structure and function, and the degree to which these models fundamentally understand the inherent biophysics of protein structure stands as an open question. Motivated by a finding that pLM-based structure predictors erroneously predict nonphysical structures for protein isoforms, we investigated the nature of sequence context needed for contact predictions in the pLM Evolutionary Scale Modeling (ESM-2). We demonstrate by use of a "categorical Jacobian" calculation that ESM-2 stores statistics of coevolving residues, analogously to simpler modeling approaches like Markov Random Fields and Multivariate Gaussian models. We further investigated how ESM-2 "stores" information needed to predict contacts by comparing sequence masking strategies, and found that providing local windows of sequence information allowed ESM-2 to best recover predicted contacts. This suggests that pLMs predict contacts by storing motifs of pairwise contacts. Our investigation highlights the limitations of current pLMs and underscores the importance of understanding the underlying mechanisms of these models.

Uncertainty prediction of conventional gas production in Sichuan Basin under multi factor control

The establishment of a natural gas production model under multi factor control provides support for the formulation of planning schemes and exploration deployment decisions, and is of great significance for the rapid development of natural gas. Especially the growth rate and decline rate of production can be regulated in the planning process to increase natural gas production. The exploration and development of conventional gas in the Sichuan Basin has a long history. Firstly, based on the development of conventional gas production, the influencing factors of production are determined and a production model under multi factor control is established. Then, single factor analysis and sensitivity analysis are conducted, and multi factor analysis is conducted based on Bayesian networks. Finally, combining the multivariate Gaussian mixture model and production sensitivity analysis, a production planning model is established to predict production uncertainty under the influence of multiple factors. The results show that: 1) the production is positively correlated with the five influencing factors, and the degree of influence is in descending order: recovery rate, proven rate, growth rate, decline rate, and recovery degree. After being influenced by multiple factors, the fluctuation range of production increases and the probability of realization decreases. 2) The growth rate controls the amplitude of the growth stage, the exploration rate and recovery rate control the amplitude of the stable production stage, the recovery degree controls the amplitude of the transition from the stable production stage to the decreasing stage, and the decreasing rate controls the amplitude of the decreasing stage. 3)The article innovatively combines multiple research methods to further obtain the probability of achieving production under the influence of multiple factors, providing a reference for the formulation of production planning goals.

Upscaling transport in heterogeneous media featuring local-scale dispersion: Flow channeling, macro-retardation and parameter prediction

Many theoretical treatments of transport in heterogeneous Darcy flows consider advection only. When local-scale dispersion is neglected, flux weighting persists over time; mean Lagrangian and Eulerian flow velocity distributions relate simply to each other and to the variance of the underlying hydraulic conductivity field. Local-scale dispersion complicates this relationship, potentially causing initially flux-weighted solute to experience lower-velocity regions as well as Taylor-type macrodispersion due to transverse solute movement between adjacent streamlines. To investigate the interplay of local-scale dispersion with conductivity log-variance, correlation length, and anisotropy, we perform a Monte Carlo study of flow and advective-dispersive transport in spatially-periodic 2D Darcy flows in large-scale, high-resolution multivariate Gaussian random conductivity fields. We observe flow channeling at all heterogeneity levels and quantify its extent. We find evidence for substantial effective retardation in the upscaled system, associated with increased flow channeling, and observe limited Taylor-type macrodispersion, which we physically explain. A quasi-constant Lagrangian velocity is achieved within a short distance of release, allowing usage of a simplified continuous-time random walk (CTRW) model we previously proposed in which the transition time distribution is understood as a temporal mapping of unit time in an equivalent system with no flow heterogeneity. The numerical data set is modeled with such a CTRW; we show how dimensionless parameters defining the CTRW transition time distribution are predicted by dimensionless heterogeneity statistics and provide empirical equations for this purpose.

TCDM: Transformational Complexity Based Distortion Metric for Perceptual Point Cloud Quality Assessment.

The goal of objective point cloud quality assessment (PCQA) research is to develop quantitative metrics that measure point cloud quality in a perceptually consistent manner. Merging the research of cognitive science and intuition of the human visual system (HVS), in this article, we evaluate the point cloud quality by measuring the complexity of transforming the distorted point cloud back to its reference, which in practice can be approximated by the code length of one point cloud when the other is given. For this purpose, we first make space segmentation for the reference and distorted point clouds based on a 3D Voronoi diagram to obtain a series of local patch pairs. Next, inspired by the predictive coding theory, we utilize a space-aware vector autoregressive (SA-VAR) model to encode the geometry and color channels of each reference patch with and without the distorted patch, respectively. Assuming that the residual errors follow the multi-variate Gaussian distributions, the self-complexity of the reference and transformational complexity between the reference and distorted samples are computed using covariance matrices. Additionally, the prediction terms generated by SA-VAR are introduced as one auxiliary feature to promote the final quality prediction. The effectiveness of the proposed transformational complexity based distortion metric (TCDM) is evaluated through extensive experiments conducted on five public point cloud quality assessment databases. The results demonstrate that TCDM achieves state-of-the-art (SOTA) performance, and further analysis confirms its robustness in various scenarios.

Multivariate reparameterized inverse Gaussian processes with common effects for degradation-based reliability prediction

In industry, many highly reliable products possess multiple performance characteristics (PCs) and they typically degrade simultaneously. When such PCs are governed by a common failure mechanism or influenced by a shared operating environmental condition, interdependence between these PCs arises. To model such dependence, this article proposes a novel multivariate reparameterized inverse Gaussian (rIG) process model. It utilizes an additive structure; that is, the degradation of each marginal PC is considered as the result of the sum of two independent rIG processes, with one capturing the shared common effects across all PCs and the other describing the intrinsic randomness specific to that PC. The model has some nice statistical properties, and the system lifetime distribution can be conveniently approximated. An expectation-maximization algorithm is proposed for estimating the model parameters, and a parametric bootstrap method is designed to derive the confidence intervals. Comprehensive numerical simulations are conducted to validate the performance of the inference method. Two case studies are thoroughly investigated to demonstrate the applicability of the proposed methodology. Supplementary materials for this article are available online.

Accelerated distributed expectation-maximization algorithms for the parameter estimation in multivariate Gaussian mixture models

Rapid development for modeling big data requires effective and efficient methods for estimating the parameters involved. Although several accelerated Expectation-Maximization algorithms have been developed, there still exist two major concerns: reducing computational cost and improving model estimation accuracy. We propose three distributed-like algorithms for multivariate Gaussian mixture models, which can accelerate speed and improve estimation accuracy. The first algorithm is distributed algorithm, which is used to speed up the calculation of classic algorithms and improve its estimation accuracy by averaging the one-step estimators obtained from distributed operators. The second algorithm is distributed online algorithm, which is a distributed stochastic approximation procedure that performs online updates when reading online data. The final algorithm is called distributed monotonically over-relaxed algorithm, which uses an over-relaxation factor and a distributing strategy to improve the estimation accuracy of multivariate Gaussian mixture models. We investigate the stability, sensitivity, convergence, and robustness of these algorithms in a numerical study. We also apply these algorithms to three real data sets for validation.

A Robust High-Dimensional Test for Two-Sample Comparisons

The Hotelling T2 statistic is used to compare the mean vectors of two independent multivariate Gaussian distributions. Nevertheless, this statistic is highly sensitive to outliers and is not suitable for high-dimensional datasets where the number of variables exceeds the sample size. This study introduces a robust permutation test based on the minimum regularized covariance determinant (MRCD) estimator to address these limitations of the two-sample Hotelling T2 statistic. Simulation studies were performed to evaluate the proposed test’s empirical size, power, and robustness. Additionally, the test was applied to both uncontaminated and contaminated Alzheimer’s Disease datasets. The findings from the simulations and real data examples provide clues that the proposed test can be effectively used with high-dimensional data without being impacted by outliers. Finally, an R function within the “MVTests” package was developed to implement the proposed test statistic on real-world data.

Transcriptome data are insufficient to control false discoveries in regulatory network inference

Inference of causal transcriptional regulatory networks (TRNs) from transcriptomic data suffers notoriously from false positives. Approaches to control the false discovery rate (FDR), for example, via permutation, bootstrapping, or multivariate Gaussian distributions, suffer from several complications: difficulty in distinguishing direct from indirect regulation, nonlinear effects, and causal structure inference requiring "causal sufficiency," meaning experiments that are free of any unmeasured, confounding variables. Here, we use a recently developed statistical framework, model-X knockoffs, to control the FDR while accounting for indirect effects, nonlinear dose-response, and user-provided covariates. We adjust the procedure to estimate the FDR correctly even when measured against incomplete gold standards. However, benchmarking against chromatin immunoprecipitation (ChIP) and other gold standards reveals higher observed than reported FDR. This indicates that unmeasured confounding is a major driver of FDR in TRN inference. A record of this paper's transparent peer review process is included in the supplemental information.

Accounting for regression to the mean under the bivariate -distribution.

Regression to the mean occurs when an unusual observation is followed by a more typical outcome closer to the population mean. In pre- and post-intervention studies, treatment is administered to subjects with initial measurements located in the tail of a distribution, and a paired sample -test can be utilized to assess the effectiveness of the intervention. The observed change in the pre-post means is the sum of regression to the mean and treatment effects, and ignoring regression to the mean could lead to erroneous conclusions about the effectiveness of the treatment effect. In this study, formulae for regression to the mean are derived, and maximum likelihood estimation is employed to numerically estimate the regression to the mean effect when the test statistic follows the bivariate -distribution based on a baseline criterion or a cut-off point. The pre-post degrees of freedom could be equal but also unequal such as when there is missing data. Additionally, we illustrate how regression to the mean is influenced by cut-off points, mixing angles which are related to correlation, and degrees of freedom. A simulation study is conducted to assess the statistical properties of unbiasedness, consistency, and asymptotic normality of the regression to the mean estimator. Moreover, the proposed methods are compared with an existing one assuming bivariate normality. The -values are compared when regression to the mean is either ignored or accounted for to gauge the statistical significance of the paired -test. The proposed method is applied to real data concerning schizophrenia patients, and the observed conditional mean difference called the total effect is decomposed into the regression to the mean and treatment effects.

Retweeting behavior prediction based on dynamic Bayesian network classifier in microblogging networks

Nowadays, predicting user retweeting behavior in microblogging networks has gained considerable attention. Solving this problem allows for understanding the underlying mechanism of information diffusion and analyzing diffusion's evolution concerning a particular original microblog over time. Time-series data from microblogging networks are ubiquitous, and user retweeting behavior prediction is primarily considered a classification task. Consequently, there is a significant demand for accurate classification of time-series data. Several influential factors affect user retweeting behavior prediction in microblogging networks. However, much of the existing research focuses on studies that neglect the impact of users' indirect social influence strength. This neglect leads to inaccurate forecasts of indirect retweeting behavior for a particular original microblog. To address this, this paper presents a new time-sensitive measure of social influence strength based on a combination of users' temporal behavior patterns and the shortest cascade path length. Second, it proposes a prediction model based on Dynamic Bayesian Network derivative classifiers called V-DBNC to accurately predict user retweeting behavior over time. The proposed time-sensitive social influence strength factor and other factors, such as individual behavior and similarity-based driving factors, are applied to the V-DBNC model to achieve accurate user retweeting behavior prediction in the microblogging network. The joint density of factors in this classifier is estimated using a multivariate Gaussian kernel function with smoothing parameters. The V-DBNC model is empirically optimized by splitting the smoothing parameters into different-scale intervals and using the model averaging method to select the optimal classifier. Additionally, the proposed model's relatively simple structure helps overcome the overfitting problem and allows it to accumulate classification information through iterative evolution, promoting generalization. The real Twitter microblogging dataset is used to evaluate the performance of V-DBNC. The experimental results demonstrated that the proposed model outperforms other compared approaches when dealing with the classification of time-series data.

A cognition-driven framework for few-shot class-incremental learning

Few-Shot Class-Incremental Learning (FSCIL) aims at integrating new concepts from a minimal set of instances while preserving previously acquired knowledge. This study explores the potential of Vision Transformers (ViTs) in addressing the challenges inherent in the FSCIL paradigm, such as catastrophic forgetting and overfitting problems. Drawing insights from cognitive neuroscience, we propose a Cognition-Driven Framework (CoDF) for FSCIL, leveraging Vision Transformers to emulate human cognitive processes from the aspects of Intuitive Acquisition and Structured Cognition. On the one hand, we employ self-supervised learning techniques to imbue the representations with richer information, thereby facilitating a more intuitive acquisition of essential information to solve FSCIL tasks. On the other hand, we propose to structure the learned representations by introducing biases into the prior distribution of the latent factors, which involves a multivariate Gaussian Mixture Model (GMM) and an intra-class distribution assumption. Furthermore, we apply an innovative extended warm-up strategy to effectively harness the acquired representations for downstream tasks. Comprehensive experiments on three public datasets substantiate the efficacy of our proposed framework.

A Partial Information Decomposition for Multivariate Gaussian Systems Based on Information Geometry.

There is much interest in the topic of partial information decomposition, both in developing new algorithms and in developing applications. An algorithm, based on standard results from information geometry, was recently proposed by Niu and Quinn (2019). They considered the case of three scalar random variables from an exponential family, including both discrete distributions and a trivariate Gaussian distribution. The purpose of this article is to extend their work to the general case of multivariate Gaussian systems having vector inputs and a vector output. By making use of standard results from information geometry, explicit expressions are derived for the components of the partial information decomposition for this system. These expressions depend on a real-valued parameter which is determined by performing a simple constrained convex optimisation. Furthermore, it is proved that the theoretical properties of non-negativity, self-redundancy, symmetry and monotonicity, which were proposed by Williams and Beer (2010), are valid for the decomposition Iig derived herein. Application of these results to real and simulated data show that the Iig algorithm does produce the results expected when clear expectations are available, although in some scenarios, it can overestimate the level of the synergy and shared information components of the decomposition, and correspondingly underestimate the levels of unique information. Comparisons of the Iig and Idep (Kay and Ince, 2018) methods show that they can both produce very similar results, but interesting differences are provided. The same may be said about comparisons between the Iig and Immi (Barrett, 2015) methods.

Lower Prevalence of Asymptomatic Alzheimer's Disease Among Healthy African Americans.

Alzheimer's disease (AD) is believed to be more common in African Americans (AA), but biomarker studies in AA populations are limited. This report represents the largest study to date examining cerebrospinal fluid AD biomarkers in AA individuals. We analyzed 3,006 cerebrospinal fluid samples from controls, AD cases, and non-AD cases, including 495 (16.5%) self-identified black/AA and 2,456 (81.7%) white/European individuals using cutoffs derived from the Alzheimer's Disease Neuroimaging Initiative, and using a data-driven multivariate Gaussian mixture of regressions. Distinct effects of race were found in different groups. Total Tauand phospho181-Tau were lower among AA individuals in all groups (p < 0.0001), and Aβ42 was markedly lower in AA controls compared with white controls (p < 0.0001). Gaussian mixture of regressions modeling of cerebrospinal fluid distributions incorporating adjustments for covariates revealed coefficient estimates for AA race comparable with 2-decade change in age. Using Alzheimer's Disease Neuroimaging Initiative cutoffs, fewer AA controls were classified as biomarker-positive asymptomatic AD (8.0% vs 13.4%). After adjusting for covariates, our Gaussian mixture of regressions model reduced this difference, but continued to predict lower prevalence of asymptomatic AD among AA controls (9.3% vs 13.5%). Although the risk of dementia is higher, data-driven modeling indicates lower frequency of asymptomatic AD in AA controls, suggesting that dementia among AA populations may not be driven by higher rates of AD. ANN NEUROL 2024;96:463-475.

Certification of MPC-based zonal controller security properties using accuracy-aware machine learning proxies

The fast growth of renewable energies increases the power congestion risk. To address this issue, the French Transmission System Operator (RTE) has developed closed-loop controllers to handle congestion. RTE wishes to estimate the probability that the controllers ensure the equipment’s safety to guarantee their proper functioning. The naive approach to estimating this probability relies on simulating many randomly drawn scenarios and then using all the outcomes to build a confidence interval around the probability. Although theory ensures convergence, the computational cost of power system simulations makes such a process intractable.The present paper aims to propose a faster process using machine-learning-based proxies. The amount of required simulations is significantly reduced thanks to an accuracy-aware proxy built with Multivariate Gaussian Processes. However, using a proxy instead of the simulator adds uncertainty to the outcomes. An adaptation of the Central Limit Theorem is thus proposed to include the uncertainty of the outcomes predicted with the proxy into the confidence interval. As a case study, we designed a simple simulator that was tested on a small network. Results show that the proxy learns to approximate the simulator’s answer accurately, allowing a significant time gain for the machine-learning-based process.

An improved crater-based navigation approach using projective invariants

This research presents an innovative approach designed to enhance the performance of crater-based navigation systems. The core of this approach revolves around proposing a novel method for calculating and incorporating the degree of perturbation observed in matched craters. The foundation of our algorithm lies in the concept of comparing the similarity of projective invariants between image and database craters during the crater matching process. The degree of perturbation in each extracted crater is quantified and normalized using a multivariate Gaussian model. These values are subsequently employed as observation weights within the navigation system. Simulation results confirm the effectiveness of our approach in accurately computing weights that reflect the varying levels of error between craters. Moreover, when integrated into the navigation system, proposed method substantially elevates navigation performance.

Multivariate anomaly detection models enhance identification of errors in routine clinical chemistry testing.

Conventional autoverification rules evaluate analytes independently, potentially missing unusual patterns of results indicative of errors such as serum contamination by collection tube additives. This study assessed whether multivariate anomaly detection algorithms could enhance the detection of such errors. Multivariate Gaussian, k-nearest neighbours (KNN) distance, and one-class support vector machine (SVM) anomaly detection models, along with conventional limit checks, were developed using a training dataset of 127,451 electrolyte, urea, and creatinine (EUC) results, with a 5 % flagging rate targeted for all approaches. The models were compared with limit checks for their ability to detect atypical EUC results from samples spiked with additives from collection tubes: EDTA, fluoride, sodium citrate, or acid citrate dextrose (n=200 per contaminant). The study additionally assessed the ability of the models to identify 127,449 single-analyte errors, a potential weakness of multivariate models. The KNN distance and SVM models outperformed limit checks for detecting all contaminants (p-values <0.05). The multivariate Gaussian model did not surpass limit checks for detecting EDTA contamination but was superior for detecting the other additives. All models surpassed limit checks for identifying single-analyte errors, with the KNN distance model demonstrating the highest overall sensitivity. Multivariate anomaly detection models, particularly the KNN distance model, were superior to the conventional approach for detecting serum contamination and single-analyte errors. Developing multivariate approaches to autoverification is warranted to optimise error detection and improve patient safety.

A generalizable method for estimating meteor shower false positives

Context. The determination of meteor shower or parent body associations is inherently a statistical problem. Traditional methods, primarily the similarity discriminants, have limitations, particularly in handling the increasing volume and complexity of meteoroid orbit data. Aims. We introduce a new more statistically robust and generalizable method for estimating false positive detections in meteor shower identification, leveraging kernel density estimation (KDE). The method is applied to fireball data from the European Fireball Network, a comprehensive photographic fireball observation network established in 1963 for the detailed monitoring and analysis of fireballs across central Europe Methods. Utilizing a dataset of 824 fireballs observed by the European Fireball Network, we applied a multivariate Gaussian kernel within KDE and Z-score data normalization. Our method analyzes the parameter space of meteoroid orbits and geocentric impact characteristics, focusing on four different similarity discriminants: DSH, D′, DH, and DN. Results. The KDE methodology consistently converges toward a true established shower-associated fireball rate within the EFN dataset of 18–25% for all criteria. This indicates that the approach provides a more statistically robust estimate of the shower-associated component. Conclusions. Our findings highlight the potential of KDE combined with appropriate data normalization in enhancing the accuracy and reliability of meteor shower analysis. This method addresses the existing challenges posed by traditional similarity discriminants and offers a versatile solution adaptable to varying datasets and parameters.