Conditional Probability Distribution Research Articles

On the extreme wall shear stress events in a turbulent pipe flow

This study investigates the extreme wall shear stress events in a turbulent pipe flow by direct numerical simulation at a frictional Reynolds number Reτ≈500. A two-step conditional averaging scheme is implemented to identify the locations of extreme events and construct their spatial structures. Combined with the joint probability density functions of shear stresses, further evidence is provided for the argument that extreme positive events occur below an intense sweep event (Q4), and the formation of the backflow events is predominantly aided by an identifiable oblique vortex. Moreover, the conditional probability distribution of shear stress for varying thresholds used to define extreme events reveals that, when the threshold is above or below the mean, the probability distributions of the extreme positive events or the backflow events generally follow an exponential relationship, suggesting the extreme wall shear stress events are a threshold-independent process. Finally, the conditional space–time proper orthogonal decomposition is performed to extract the dominant modes and characterize the evolution of the extreme events from inception to dissipation, which exhibits morphological features of real flow structures. It is found that the observation of uθ modes can provide a basic representation of the entire variation process and the extreme values return to normal levels in a very short time.

Maximum Likelihood Deconvolution of Beamforming Images with Signal-Dependent Speckle Fluctuations

Ocean Acoustic Waveguide Remote Sensing (OAWRS) typically utilizes large-aperture linear arrays combined with coherent beamforming to estimate the spatial distribution of acoustic scattering echoes. The conventional maximum likelihood deconvolution (DCV) method uses a likelihood model that is inaccurate in the presence of multiple adjacent targets with significant intensity differences. In this study, we propose a deconvolution algorithm based on a modified likelihood model of beamformed intensities (M-DCV) for estimation of the spatial intensity distribution. The simulated annealing iterative scheme is used to obtain the maximum likelihood estimation. An approximate expression based on the generalized negative binomial (GNB) distribution is introduced to calculate the conditional probability distribution of the beamformed intensity. The deconvolution algorithm is further simplified with an approximate likelihood model (AM-DCV) that can reduce the computational complexity for each iteration. We employ a direct deconvolution method based on the Fourier transform to enhance the initial solution, thereby reducing the number of iterations required for convergence. The M-DCV and AM-DCV algorithms are validated using synthetic and experimental data, demonstrating a maximum improvement of 73% in angular resolution and a sidelobe suppression of 15 dB. Experimental examples demonstrate that the imaging performance of the deconvolution algorithm based on a linear small-aperture array consisting of 16 array elements is comparable to that obtained through conventional beamforming using a linear large-aperture array consisting of 96 array elements. The proposed algorithm is applicable for Ocean Acoustic Waveguide Remote Sensing (OAWRS) and other sensing applications using linear arrays.

Predicting conditional probability distributions of redshifts of Active Galactic Nuclei using Hierarchical Correlation Reconstruction

Abstract The Large Area Telescope (LAT) on board the Fermi Gamma-ray observatory continuously scans the sky in an energy range from 50 MeV to 1 TeV. The telescope has identified over 6000 gamma-ray emitting sources, approximately half of which are classified as active galactic nuclei (AGN). However, not all of these gamma-ray sources have known redshift values for the reason that red-shift estimation following traditional methods can be an expensive, challenging task. Alternatively, as an effort to robustly predict the AGN redshift values, many researchers have recently turned to machine learning methods. However, while the focus has primarily been on predicting specific values, real-world data often allows us only to predict conditional probability distributions, constrained by conditional entropy (H(Y|X)). In our study, we employ the Hierarchical Correlation Reconstruction (HCR) approach to inexpensively predict complex conditional probability distributions, including multimodal ones. This is achieved through independent Mean Squared Error (MSE) estimation of multiple moment-like parameters, combined into reconstruction of the conditional distribution. By employing linear regression for this purpose, we can develop interpretable models where coefficients describe the contributions of features to conditional moments. This article extends the original approach by incorporating Canonical Correlation Analysis (CCA) for feature optimization and l1 ‘lasso’ regularization. Our primary focus is on the practical problem of predicting the redshift of Active Galactic Nuclei (AGN) using data from the Fourth Fermi-LAT Data Release 3 (4LAC-DR3) dataset.

Distilling dynamical knowledge from stochastic reaction networks

Stochastic reaction networks are widely used in the modeling of stochastic systems across diverse domains such as biology, chemistry, physics, and ecology. However, the comprehension of the dynamic behaviors inherent in stochastic reaction networks is a formidable undertaking, primarily due to the exponential growth in the number of possible states or trajectories as the state space dimension increases. In this study, we introduce a knowledge distillation method based on reinforcement learning principles, aimed at compressing the dynamical knowledge encoded in stochastic reaction networks into a singular neural network construct. The trained neural network possesses the capability to accurately predict the state conditional joint probability distribution that corresponds to the given query contexts, when prompted with rate parameters, initial conditions, and time values. This obviates the need to track the dynamical process, enabling the direct estimation of normalized state and trajectory probabilities, without necessitating the integration over the complete state space. By applying our method to representative examples, we have observed a high degree of accuracy in both multimodal and high-dimensional systems. Additionally, the trained neural network can serve as a foundational model for developing efficient algorithms for parameter inference and trajectory ensemble generation. These results collectively underscore the efficacy of our approach as a universal means of distilling knowledge from stochastic reaction networks. Importantly, our methodology also spotlights the potential utility in harnessing a singular, pretrained, large-scale model to encapsulate the solution space underpinning a wide spectrum of stochastic dynamical systems.

Prediction for underground seismic intensity measures using conditional generative adversarial networks

With the escalating development and utilization of subterranean spaces, the seismic hazards faced by underground structures are progressively increasing. However, owing to the challenges associated with acquiring underground seismic data and historical seismic design norms, pertinent regulations and research in this domain are scarce. This study focused on three crucial intensity measures in the seismic design process of underground structures peak ground acceleration (PGA), peak ground velocity (PGV), and peak ground displacement (PGD). The research leverages seismic data obtained from the California Strong Motion Instrumentation Program (CSMIP) to train and evaluate a conditional generative adversarial network (CGAN) model. This model was employed to establish a multivariate joint conditional probability distribution among the intensity measures at varying depths, facilitating the stochastic prediction of shallow intensity measures. In contrast to empirical formulas, the CGAN model eliminates the need for a predefined equation structure and enables the simultaneous prediction of multiple intensity measures. The performance of the model was evaluated by comparing the predictive accuracy of the CGAN model and empirical fitting formulas across diverse site conditions and depth intervals using metrics such as relative error coefficients. It can be concluded that the proposed CGAN model can accurately predict shallow seismic intensity measures, and the predictions conform to a specific conditional distribution while retaining the stochastic nature of seismic motion. Compared with empirical formula models, the CGAN model exhibited an enhanced predictive capability.

Modeling of Soil Water Distribution in a Small Mid-Latitude Watershed on the British Isle for Short Term Landslide and Flood Risk Assessment

The R-TopModel hydrological model coupled with two landslide and flood probability distribution models was applied to simulate the daily hydrological conditions of a small catchment in the Midlands of the British Isles, throughout 2017. Originally, the methodology was applied to a risk area in the tropical region. In this work, the application was extended to mid-latitude watersheds. The hydrographic basin around the Carsington Water dam (located in the Midlands of the Great Britain) is chosen because it presents risks. The model Nash-Sutcliffe Efficiency for the upstream discharge from the Carsington Water dam reached 50% with a correlation coefficient of the order of 70%, an acceptable value considering the seasonal effects of the dam on evapotranspiration and higher soil permeability. Modeling the distribution of soil moisture and excess surface water allowed obtaining the spatial distribution of the maximum conditional probability of landslides and floods in the Carsington Water catchment. These probability maps obtained are consistent with long-term susceptibility maps for Great Britain.

Multi-Source and Multi-modal Deep Network Embedding for Cross-Network Node Classification

In recent years, to address the issue of networked data sparsity in node classification tasks, cross-network node classification (CNNC) leverages the richer information from a source network to enhance the performance of node classification in the target network, which typically has sparser information. However, in real-world applications, labeled nodes may be collected from multiple sources with multiple modalities (e.g., text, vision, and video). Naive application of single-source and single-modal CNNC methods may result in sub-optimal solutions. To this end, in this paper, we propose a model called M 2 CDNE (Multi-source and Multi-modal Cross-network Deep Network Embedding) for cross-network node classification. In M 2 CDNE, we propose a deep multi-modal network embedding approach that combines the extracted deep multi-modal features to make the node vector representations network-invariant. In addition, we apply dynamic adversarial adaptation to assess the significance of marginal and conditional probability distributions between each source and target network to make node vector representations label-discriminative. Furthermore, we devise to classify nodes in the target network through the related source classifier and aggregate different predictions utilizing respective network weights, corresponding to the discrepancy between each source and target network. Extensive experiments performed on real-world datasets demonstrate that the proposed M 2 CDNE significantly outperforms the state-of-the-art approaches.

Statistical modelling of determinants of child stunting using secondary data and Bayesian networks: a UKRI Global Challenges Research Fund (GCRF) Action Against Stunting Hub protocol paper

IntroductionSeveral factors have been implicated in child stunting, but the precise determinants, mechanisms of action and causal pathways remain poorly understood. The objective of this study is to explore causal...

A Method for Enhancing the Simulation Continuity of the Snesim Algorithm in 2D Using Multiple Search Trees

Multiple-point geostatistics (MPS) has more advantages than two-point geostatistics in reproducing the continuity of geobodies in subsurface reservoir modeling. For fluvial reservoir modeling, the more continuous a channel, the more consistent it is with geological knowledge in general, and fluvial continuity is also of paramount importance when simulating fluid flow. Based on the pixel-based MPS algorithm Snesim, this study proposes a method that utilizes multiple search trees (MSTs) to enhance simulation continuity in 2D fluvial reservoir modeling. The objective of the MST method is to capture complete data events from a training image (TI), which aims to achieve enhanced continuity in fluvial reservoir sublayer modeling. By resorting to search neighborhoods based on their proximity to the central node of the data template, multiple data templates that correspond to the MSTs will be generated. Here, four data templates were generated by arranging the relative search neighborhood coordinates in ascending and descending order with respect to the central node. Parallel computing was tried for the construction of the search trees. This work calculated the conditional probability distribution function (CPDF) of the simulating nodes by averaging the CPDFs derived from the MSTs, and double retrieval was employed to filter out the search trees that possessed an inaccurate local CPDF for the simulating nodes. In addition, the connected component labeling (CCL) method was introduced to evaluate the simulation continuity in MPS. The results indicated that the MST method can enhance the simulation continuity of the Snesim algorithm by reproducing the fine connectivity of channel facies in 2D fluvial reservoir modeling.

Análisis de Vulnerabilidades de Ciberseguridad Mediante Técnicas de Ciencia de Datos

Cybersecurity analysis using data science and machine learning plays a crucial role in today's digital era, where information security has become imperative for organizations. This study focuses on the intersection between cybersecurity and data science, using machine learning methods and text analytics to understand and strengthen defenses against threats. The importance of TF-IDF (Term-Inverse Document Frequency) is highlighted as a tool to evaluate the relevance of terms in documents and its application in vulnerability classification.The Multinomial Naive Bayes classifier is presented as an efficient tool in text classification, calculating probabilities of belonging to specific classes based on the frequency of terms. The essential formulas used in this algorithm, such as conditional probability and multinomial distribution, are detailed.The KDD (Knowledge Discovery in Databases) methodology guides the process, from datacollection on platforms like Kaggle to data selection, cleaning and transformation. The use of `TfidfVectorizer` facilitates the discretization of text data, and the `GridSearchCV` method optimizes the model's hyperparameters, achieving an accuracy of 97.36%. Finally, the confusion matrix reveals good overall performance, although areas for improvement are identified, especially in the 'High' class.

Predicting the evolution of clinical skin aging in a multi-ethnic population: Developing causal Bayesian networks using dermatological expertise.

Software to predict the impact of aging on physical appearance is increasingly popular. But it does not consider the complex interplay of factors that contribute to skin aging. To predict the +15-year progression of clinical signs of skin aging by developing Causal Bayesian Belief Networks (CBBNs) using expert knowledge from dermatologists. Structures and conditional probability distributions were elicited worldwide from dermatologists with experience of at least 15 years in aesthetics. CBBN models were built for all phototypes and for ages ranging from 18 to 65 years, focusing on wrinkles, pigmentary heterogeneity and facial ptosis. Models were also evaluated by a group of independent dermatologists ensuring the quality of prediction of the cumulative effects of extrinsic and intrinsic skin aging factors, especially the distribution of scores for clinical signs 15 years after the initial assessment. For easiness, only models on African skins are presented in this paper. The forehead wrinkle evolution model has been detailed. Specific atlas and extrinsic factors of facial aging were used for this skin type. But the prediction method has been validated for all phototypes, and for all clinical signs of facial aging. This method proposes a skin aging model that predicts the aging process for each clinical sign, considering endogenous and exogenous factors. It simulates aging curves according to lifestyle. It can be used as a preventive tool and could be coupled with a generative AI algorithm to visualize aging and, potentially, other skin conditions, using appropriate images.

Fin-GAN: forecasting and classifying financial time series via generative adversarial networks

We investigate the use of Generative Adversarial Networks (GANs) for probabilistic forecasting of financial time series. To this end, we introduce a novel economics-driven loss function for the generator. This newly designed loss function renders GANs more suitable for a classification task, and places them into a supervised learning setting, whilst producing full conditional probability distributions of price returns given previous historical values. Our approach moves beyond the point estimates traditionally employed in the forecasting literature, and allows for uncertainty estimates. Numerical experiments on equity data showcase the effectiveness of our proposed methodology, which achieves higher Sharpe Ratios compared to classical supervised learning models, such as LSTMs and ARIMA.

Modeling forecast errors for microgrid operation using Gaussian process regression

Microgrids, denoting small-scale and self-sustaining grids, constitute a pivotal component in future power systems with a high penetration of renewable generators. The inherent uncertainty tied to renewable power generation, typified by photovoltaic and wind turbine systems, necessitates counterbalancing mechanisms. These mechanisms encompass Energy storage systems or conventional thermal fossil-fuel generators imbued with heightened flexibility. Addressing the uncertainty stemming from renewable generators mandates a cost-effective assessment and operational strategy for said compensatory devices. To this end, myriad uncertainty factors warrant scrutiny, conceivably concretized into a unified probability distribution function (PDF) that takes into account their temporal inter-dependencies. Diverse uncertainty factors, characterized by varying marginal distributions and scales, can be assimilated into a multivariate probability distribution through a conversion to normal distributions via rank correlation. However, with the escalation in the number of uncertainty factors embraced within a microgrid context, the endeavour becomes notably intricate when aiming to define conditional probability distributions originating from joint PDFs. This paper presents a method proposing the modelling of net-load forecast error distribution, considering the interplay among uncertainty factors. The approach introduces a data-driven Gaussian process regression technique for training and validating conditional PDFs among these uncertainty factors. Notably, this approach facilitates the transformation of said factors into normal distributions while preserving their inherent marginal characteristics. The resultant conditional density function, as per the proposed methodology, exhibits enhanced suitability for estimating net-load error distribution. Consequently, the conditional density function stemming from this proposed approach demonstrates superior aptitude in approximating the distribution of net load error.

Adaptable and Interpretable Framework for Anomaly Detection in SCADA-based industrial systems

In this paper, we introduce an Adaptable and Interpretable Framework for Anomaly Detection (AID) designed for industrial systems utilizing IoT data streams on top of well-established SCADA systems. AID leverages dynamic conditional probability distribution modeling to capture the normal operation of dynamic systems and isolate the root causes of anomalies at the level of individual inputs. The self-supervised framework dynamically updates parameters of underlying model, allowing it to adapt to non-stationarity. AID interprets anomalies as significant deviations from conditional probability, encompassing interactions as well as both spatial and temporal irregularities by exposing them as features. Crucially, AID provides dynamic operating limits to integrate with existing alarm handling mechanisms in SCADA-based IoT systems. Two industrial-scale case studies demonstrate AID’s capabilities. The first study showcases AID’s effectiveness on energy storage system, adapting to changes, setting context-aware limits for SCADA, and ability to leverage a physics-based model. The second study monitors battery module temperatures, where AID identifies hardware faults, emphasizing its relevance to energy storage safety. A benchmark evaluation on real data shows that AID delivers comparable performance to other self-learning adaptable anomaly detection methods, with the significant advancement in diagnostic capabilities for improved system reliability and performance.

DECISION THEORETIC BOOTSTRAPPING

The design and testing of supervised machine learning models combine two fundamental distributions: (1) the training data distribution and (2) the testing data distribution. Although these two distributions are identical and identifiable when the data set is infinite, they are imperfectly known when the data are finite (and possibly corrupted), and this uncertainty must be taken into account for robust uncertainty quantification (UQ). An important case is when the test distribution is coming from a modal or localized area of the finite sample distribution. We present a general decision theoretic bootstrapping solution to this problem: (1) partition the available data into a training subset and a UQ subset; (2) take m subsampled subsets of the training set and train m models; (3) partition the UQ set into n sorted subsets and take a random fraction of them to define <i>n</i> corresponding empirical distributions μ<sub>j</sub>; (4) consider the adversarial game where Player I selects a model i ∈ {1,.....,m}, Player II selects the UQ distribution μ<sub>j</sub>, and Player I receives a loss defined by evaluating the model <i>i</i> against data points sampled from μ<sub>j</sub>; (5) identify optimal mixed strategies (probability distributions over models and UQ distributions) for both players. These randomized optimal mixed strategies provide optimal model mixtures, and UQ estimates given the adversarial uncertainty of the training and testing distributions represented by the game. The proposed approach provides (1) some degree of robustness to in-sample distribution localization/concentration and (2) conditional probability distributions on the output space forming aleatory representations of the uncertainty on the output as a function of the input variable.

Probability distributions for dynamic and extreme responses of linear elastic structures under quasi-stationary harmonizable loads

The non-stationary load models based on the evolutionary power spectral density (EPSD) may lead to ambiguous structural responses. Quasi-stationary harmonizable processes with non-negative Wigner-Ville spectra are suitable for modeling non-stationary loads and analyzing their induced structural responses. In this study, random environmental loads are modeled as quasi-stationary harmonizable processes. The Loève spectrum of a harmonizable load process contains several random physical parameters. An explicit approach to calculate the probability distributions for the dynamic and extreme responses of a linear elastic structure subjected to a quasi-stationary harmonizable load is proposed. Conditioned on the specific values of the load spectral parameters, the harmonizable load process is assumed to be Gaussian. The conditional joint probability density function (PDF) of structural dynamic responses at any finite time instants and the conditional cumulative distribution function (CDF) of the structural extreme response are provided. By multiplying these two conditional probability distributions with the joint PDF of the load spectral parameters, and then integrating these two products over the parameter sample space, the joint PDF of structural dynamic responses at any finite time instants and the CDF of the structural extreme response can be calculated. The efficacy of the proposed approach is numerically validated using two linear elastic systems, which are subjected to non-stationary and non-Gaussian wind and seismic loads, respectively. The merit of the harmonizable load process model is highlighted through a comparative analysis with the EPSD load model.

Unsupervised Joint Domain Adaptation for Decoding Brain Cognitive States From tfMRI Images.

Recent advances in large model and neuroscience have enabled exploration of the mechanism of brain activity by using neuroimaging data. Brain decoding is one of the most promising researches to further understand the human cognitive function. However, current methods excessively depends on high-quality labeled data, which brings enormous expense of collection and annotation of neural images by experts. Besides, the performance of cross-individual decoding suffers from inconsistency in data distribution caused by individual variation and different collection equipments. To address mentioned above issues, a Join Domain Adapative Decoding (JDAD) framework is proposed for unsupervised decoding specific brain cognitive state related to behavioral task. Based on the volumetric feature extraction from task-based functional Magnetic Resonance Imaging (tfMRI) data, a novel objective loss function is designed by the combination of joint distribution regularizer, which aims to restrict the distance of both the conditional and marginal probability distribution of labeled and unlabeled samples. Experimental results on the public Human Connectome Project (HCP) S1200 dataset show that JDAD achieves superior performance than other prevalent methods, especially for fine-grained task with 11.5%-21.6% improvements of decoding accuracy. The learned 3D features are visualized by Grad-CAM to build a combination with brain functional regions, which provides a novel path to learn the function of brain cortex regions related to specific cognitive task in group level.

System reliability calculation based on the run-time analysis of ladder program

Programmable logic controller (PLC) system, a typical member in the embedded family, is now widely applied in industry. For safety critical PLC systems, reliability is of top significance. However, due to subcomponents’ temporal correlations caused by the run-time execution of embedded ladder programs, the complexity of reliability analysis is greatly increased. In this paper, we propose a novel probabilistic model to analyze reliability of PLC systems, called run-time reliability model (RRM). RRM is automatically constructed based on the structure and run-time execution of the embedded ladder program. Moreover, it is also a dynamic bayesian network (DBN) capturing full dependencies in a PLC system. Then, according to execution semantics of RRM nodes, we present customized conditional probability distribution (CPD) tables to calculate final reliability of the system, with failure probability of every referenced component as refinement. The strength of this model is that not only does it explicitly specify the correlations between run-time execution of embedded software and system components, but also it serves as a computational mechanism for probabilistic inference. Besides, the proposed approach is superior to previous works in both accuracy and efficiency. Compared to monte carlo based simulation, the average error rate of reliability values inferred from RRM model is small.

Deep Drug Synergy Prediction Network Using Modified Triangular Mutation-Based Differential Evolution.

Drug combination therapy is crucial in cancer treatment, but accurately predicting drug synergy remains a challenge due to the complexity of drug combinations. Machine learning and deep learning models have shown promise in drug combination prediction, but they suffer from issues such as gradient vanishing, overfitting, and parameter tuning. To address these problems, the deep drug synergy prediction network, named as EDNet is proposed that leverages a modified triangular mutation-based differential evolution algorithm. This algorithm evolves the initial connection weights and architecture-related attributes of the deep bidirectional mixture density network, improving its performance and addressing the aforementioned issues. EDNet automatically extracts relevant features and provides conditional probability distributions of output attributes. The performance of EDNet is evaluated over two well-known drug synergy datasets, NCI-ALMANAC and deep-synergy. The results demonstrate that EDNet outperforms the competing models. EDNet facilitates efficient drug interactions, enhancing the overall effectiveness of drug combinations for improved cancer treatment outcomes.

Ultra-high-dimensional feature screening of binary categorical response data based on Jensen-Shannon divergence

<abstract><p>Currently, most of the ultra-high-dimensional feature screening methods for categorical data are based on the correlation between covariates and response variables, using some statistics as the screening index to screen important covariates. Thus, with the increasing number of data types and model availability limitations, there may be a potential problem with the existence of a class of unimportant covariates that are also highly correlated with the response variable due to their high correlation with the other covariates. To address this issue, in this paper, we establish a model-free feature screening procedure for binary categorical response variables from the perspective of the contribution of features to classification. The idea is to introduce the Jensen-Shannon divergence to measure the difference between the conditional probability distributions of the covariates when the response variables take on different values. The larger the value of the Jensen-Shannon divergence, the stronger the covariate's contribution to the classification of the response variable, and the more important the covariate is. We propose two kinds of model-free ultra-high-dimensional feature screening methods for binary response data. Meanwhile, the methods are suitable for continuous or categorical covariates. When the numbers of covariate categories are the same, the feature screening is based on traditional Jensen-Shannon divergence. When the numbers of covariate categories are different, the Jensen-Shannon divergence is adjusted using the logarithmic factor of the number of categories. We theoretically prove that the proposed methods have sure screening and ranking consistency properties, and through simulations and real data analysis, we demonstrate that, in feature screening, the approaches proposed in this paper have the advantages of effectiveness, stability, and less computing time compared with an existing method.</p></abstract>