Sensitivity to evidence in Gaussian Bayesian networks using mutual information

Gaussian Bayesian network model of healthcare, food and energy sectors in the pandemic: Türkiye case

Extreme inaccuracies in Gaussian Bayesian networks

Atmospheric pollution in the Metropolitan Zone of the Valley of Mexico (ZMVM)has represented a daily problem due to the increase in industrial activities and the continuous increase in the vehicle fleet with internal combustion engines. The use of Fossil fuels have been the main cause of the emission of particulate matter, such as microscopic particles PM10 and, which can cause severe damage to the respiratory system human. This thesis presents a study of some of the statistical and dynamic properties, of the concentration of particulate matter PM10 that are emitted by combustion internal engines in the ZMVM. The study consisted of the analysis of temporal variability of PM10 concentrations recorded between 2019 and 2021. The acquisition of the data it was carried out at atmospheric monitoring stations in five zones (NW, NE, CE, SW and SE) of the Metropolitan Zone of the Valley of Mexico in charge of the Atmospheric Monitoring Network Automatic (RAMA). With the statistical analysis, the distribution functions were obtained,and the Dynamic study is based on the estimation of the Hurst exponent H, in this case, said exponent was obtained from the spectral exponent β through a linear relationship. With this information characterizes the dispersion of particulate matter as a movement Fractional Brownian. On the other hand, the processes involved in the dispersion of particulate matter are not linear and to determine the temporal correlation I applied the mutual information function, which is defined from Shannon entropy and information theory. The function of Mutual information takes into account all contributions, linear and non-linear, so gives a global measure of the correlation. The statistical results show that the emission of PM10 particulate matter is characterized by ripples through a log-normal distribution. The spectral analysis was carried out using the spectral power P(f), which is obtained from the perhyodogram. The spectral power displays a power law of the form P(f) / f− β. In the time series studied, a crossover is obtained from which two spectral exponents β 1 y β2. Said crossing is commonly interpreted as the coexistence of two diferent dynamic mechanisms, observing a behavior of a fractional (correlated) Brownian motion within the first 24 hrs, then of this time, a Brownian movement behavior is shown (without correlation). Finally, the correlations obtained through the mutual information function do not decay steel.

Learning parameters of Bayesian networks from datasets with systematically missing data: A meta–analytic approach

Previously published literature has identified a few predictors of health-related quality of life (HRQoL) after bariatric surgery. However, performance of the predictive models was not evaluated rigorously using real world data. To find better methods for predicting prognosis in patients after bariatric surgery, we examined performance of the Bayesian networks (BN) method in predicting long-term postoperative HRQoL and compared it with the convolution neural network (CNN) and multivariable logistic regression (MLR). The patients registered in the Scandinavian Obesity Surgery Registry (SOReg) were used for the current study. In total, 6542 patients registered in the SOReg between 2008 and 2012 with complete demographic and preoperative comorbidity information, and preoperative and postoperative 5-year HROoL scores and comorbidities were included in the study. HRQoL was measured using the RAND-SF-36 and the obesity-related problems scale. Thirty-five variables were used for analyses, including 19 predictors and 16 outcome variables. The Gaussian BN (GBN), CNN, and a traditional linear regression model were used for predicting 5-year HRQoL scores, and multinomial discrete BN (DBN) and MLR were used for 5-year comorbidities. Eighty percent of the patients were randomly selected as a training dataset and 20% as a validation dataset. The GBN presented a better performance than the CNN and the linear regression model; it had smaller mean squared errors (MSEs) than those from the CNN and the linear regression model. The MSE of the summary physical scale was only 0.0196 for GBN compared to the 0.0333 seen in the CNN. The DBN showed excellent predictive ability for 5-year type 2 diabetes and dyslipidemia (area under curve (AUC) = 0.942 and 0.917, respectively), good ability for 5-year hypertension and sleep apnea syndrome (AUC = 0.891 and 0.834, respectively), and fair ability for 5-year depression (AUC = 0.750). Bayesian networks provide useful tools for predicting long-term HRQoL and comorbidities in patients after bariatric surgery. The hybrid network that may involve variables from different probability distribution families deserves investigation in the future.

A job title usually implies the responsibility and the rank of a job position. While traditional job title analysis has been focused on studying the responsibilities of job titles, this paper attempts to reveal the rank of job titles. Specifically, we propose to extract job title hierarchy from employees' career trajectories. Along this line, we first quantify the Difficulty of Promotion (DOP) from one job title to another by a monotonic transformation of the length of tenure based on the assumption that a longer tenure usually implies a greater difficulty to be promoted. Then, the difference of two job title ranks is defined as a mapping of the DOP observed from job transitions. A Gaussian Bayesian Network (GBN) is adopted to model the joint distribution of the job title ranks and the DOPs in a career trajectory. Furthermore, a stochastic algorithm is developed for inferring the posterior job title rank by a given collection of DOPs in the GBN. Finally, experiments on more than 20 million job trajectories show that the job title hierarchy can be extracted precisely by the proposed method.

: Calculating the amount of information about a random function contained in another random function has important uses in communication theory. An expression for the mutual information for continuous time random processes has been given by Gelfand and Yaglom, Chiang, and Perez by generalizing Shannon's result in a natural way. Under a condition of absolute continuity of measures the continuous time expression has the same form as Shannon's result. For two Gaussian processes Gelfand and Yaglom express the mutual information in terms of a mean square estimation error. We generalize this result to diffusion processes and express the solution in a different form which is more naturally related to a corresponding filtering problem. We also use these results to calculate some information rates.

Causal analysis of continuous-valued variables typically uses either autoregressive models or linear Gaussian Bayesian networks with instantaneous effects. Estimation of Gaussian Bayesian networks poses serious identifiability problems, which is why it was recently proposed to use non-Gaussian models. Here, we show how to combine the non-Gaussian instantaneous model with autoregressive models. We show that such a non-Gaussian model is identifiable without prior knowledge of network structure, and we propose an estimation method shown to be consistent. This approach also points out how neglecting instantaneous effects can lead to completely wrong estimates of the autoregressive coefficients.

Multi-rate Gaussian Bayesian network soft sensor development with noisy input and missing data

An analysis of Brazilian agricultural commodities using permutation – information theory quantifiers: The influence of food crisis

We investigate the fundamental problem of generating bipartite classical distributions or quantum states. By designing efficient communication protocols and proving their optimality, we establish a number of intriguing connections to fundamental measures in optimization, convex geometry, and information theory. 1. To generate a classical distribution P(x, y), we tightly characterize the minimum amount of quantum communication needed by the psd-rank of P (as a matrix), a measure recently proposed by Fiorini, Massar, Pokutta, Tiwary and de Wolf (Proceedings of the 44th A CM Symposium on Theory of Computing, pages 95–106, 2012) in studies of the minimum size of extended formulations of optimization problems such as TSP. This echos the previous characterization for the optimal classical communication cost by the nonnegative rank of P. The result is obtained via investigating the more general case of bipartite quantum state generation and designing an optimal protocol for it. 2. When an approximation of ε is allowed to generate a distribution (X, Y) ∼ P, we present a classical protocol of the communication cost O((C(X, Y) + 1)/ε), where C(X, Y) is common information, a well-studied measure in information theory introduced by Wyner (IEEE Transactions on Information Theory, 21(2):163–179, 1975). This also links nonnegative rank and common information, two seemingly unrelated quantities in different fields. 3. For approximately generating a quantum pure state |ψ〉, we completely characterize the minimum cost by a corresponding approximate rank, closing a possibly exponential gap left in Ambainis, Schulman, Ta-Shma, Vazirani and Wigderson (SIAM Journal on Computing, 32(6):1570–1585, 2003).

During the last decades, "Transport Demand" and "Mobility" has been a continuously developing branch in the transport literature.This is reflected in the great amount of research papers published in scientific magazines dealing with trip matrix estimation (see (Doblas & Benítez, 2005)) and traffic assignment problems (see (Praskher & Bekhor, 2004)).Current traffic models reproduce the mobility using several data inputs, in particular prior trip matrix, link counts, etc. (see (Yang & Zhou, 1998)) which are data only from a subset of the problem variables, and its size will depend on the available budget for the study being carried on.Among the problems faced for solving these models we can emphasize the high number of possible solutions which is usually solved by choosing the solution where the model results best fits real data.Nevertheless a model does not have to reproduce only the real data, but also must reproduce accurately all the variables.To this end, the aim of this paper consists of presenting two Bayesian network models for traffic estimation, trying to bring a new tool to the transportation field.The first one deals with the problem of link flows, trip matrix estimation and traffic counting location and in the second one we propose a Bayesian network for route flow estimation (and hence link flows and OD flows) using data from plate scanning technique together with a model for optimal plate scanning device location.Since a Gaussian Bayesian network is used, these models allow us to update the predictions from a small subset of real data and probability intervals or regions are obtained to get an idea of the associated uncertainties.In addition dealing with data from the plate scanning approach we improve the under-specification level of the traffic flow estimation problem. Some background on Bayesian network modelsA Bayesian network (see, (Castillo et al., 1999)) is a pair (G, P ), where G is a directed acyclic graph (DAG) defined on a set of nodes X (the random variables), and P = {p(x 1 |π 1 ), . . ., p(x n |π n )} is a set of n conditional probability densities (CPD), one for each variable, and Π i is the set of parents of node X i in G.The set P defines the associated joint 19 www.intechopen.comBayesian Network 318 probability density of all nodes as p(1)The graph G contains all the qualitative information about the relationships among the variables, no matter which probability values are assigned to them 1 .Complementary, the probabilities in P contain the quantitative information, i.e., they complement the qualitative properties revealed by the graphical structure.

The diversity of bibliometric indices today poses the challenge of exploiting the relationships among them. Our research uncovers the best core set of relevant indices for predicting other bibliometric indices. An added difficulty is to select the role of each variable, that is, which bibliometric indices are predictive variables and which are response variables. This results in a novel multioutput regression problem where the role of each variable (predictor or response) is unknown beforehand. We use Gaussian Bayesian networks to solve the this problem and discover multivariate relationships among bibliometric indices. These networks are learnt by a genetic algorithm that looks for the optimal models that best predict bibliometric data. Results show that the optimal induced Gaussian Bayesian networks corroborate previous relationships between several indices, but also suggest new, previously unreported interactions. An extended analysis of the best model illustrates that a set of 12 bibliometric indices can be accurately predicted using only a smaller predictive core subset composed of citations, g‐index, q2‐index, and hr‐index. This research is performed using bibliometric data on Spanish full professors associated with the computer science area.

For the past decades, Virtual Metrology (VM) has been widely studied and covered in the literature for semiconductor industries where cycle time is a critical aspect and the elimination of non-productive metrology measurements is expected to significantly contribute to its reduction. A wide variety of approaches has been proposed but not effectively implemented. An ideal VM model should be able to provide accurate predictions and to reveal the hidden relationship among production/process factors. For this aim, we employ the Gaussian Bayesian Network (GBN) to investigate the implicit relationship not only between the metrology and the control factors but also among the production/process parameters. Instead of working purely as a black-box data-driven methodology, GBN enables the flexibility to integrate domain knowledge through the corresponding connected graph. The effectiveness of proposed approach is validated using real industrial data from a Chemical-Mechanical Polishing (CMP) process.

Identifying the causalities for air pollutants and answering questions, such as, where do Beijing's air pollutants come from, are crucial to inform government decision-making. In this paper, we identify the spatio-temporal (ST) causalities among air pollutants at different locations by mining the urban big data. This is challenging for two reasons: 1) since air pollutants can be generated locally or dispersed from the neighborhood, we need to discover the causes in the ST space from many candidate locations with time efficiency; 2) the cause-and-effect relations between air pollutants are further affected by confounding variables like meteorology. To tackle these problems, we propose a coupled Gaussian Bayesian model with two components: 1) a Gaussian Bayesian Network (GBN) to represent the cause-and-effect relations among air pollutants, with an entropy-based algorithm to efficiently locate the causes in the ST space; 2) a coupled model that combines cause-and-effect relations with meteorology to better learn the parameters while eliminating the impact of confounding. The proposed model is verified using air quality and meteorological data from 52 cities over the period Jun 1st 2013 to May 1st 2015. Results show superiority of our model beyond baseline causality learning methods, in both time efficiency and prediction accuracy.