Search results for: Bayesian hierarchical models

Authors: Paula Simões, Isabel Natário

Abstract:

This paper reviews a number of theoretical aspects for implementing an explicit spatial perspective in econometrics for modelling non-continuous data, in general, and count data, in particular. It provides an overview of the several spatial econometric approaches that are available to model data that are collected with reference to location in space, from the classical spatial econometrics approaches to the recent developments on spatial econometrics to model count data, in a Bayesian hierarchical setting. Considerable attention is paid to the inferential framework, necessary for structural consistent spatial econometric count models, incorporating spatial lag autocorrelation, to the corresponding estimation and testing procedures for different assumptions, to the constrains and implications embedded in the various specifications in the literature. This review combines insights from the classical spatial econometrics literature as well as from hierarchical modeling and analysis of spatial data, in order to look for new possible directions on the processing of count data, in a spatial hierarchical Bayesian econometric context.

Keywords: Spatial data analysis, spatial econometrics, Bayesian hierarchical models, count data.

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Authors: Leslie J.C.Bluck, Sarah J.Jackson, Georgios Vlasakakis, Adrian Mander

Abstract:

The use of a Bayesian Hierarchical Model (BHM) to interpret breath measurements obtained during a 13C Octanoic Breath Test (13COBT) is demonstrated. The statistical analysis was implemented using WinBUGS, a commercially available computer package for Bayesian inference. A hierarchical setting was adopted where poorly defined parameters associated with a delayed Gastric Emptying (GE) were able to "borrow" strength from global distributions. This is proved to be a sufficient tool to correct model's failures and data inconsistencies apparent in conventional analyses employing a Non-linear least squares technique (NLS). Direct comparison of two parameters describing gastric emptying ng ( tlag -lag phase, t1/ 2 -half emptying time) revealed a strong correlation between the two methods. Despite our large dataset ( n = 164 ), Bayesian modeling was fast and provided a successful fitting for all subjects. On the contrary, NLS failed to return acceptable estimates in cases where GE was delayed.

Keywords: Bayesian hierarchical analysis, 13COBT, Gastricemptying, WinBUGS.

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Authors: Susan J. Simmons, Fang Fang, Qijun Fang, Karl Ricanek

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Quantitative trait loci (QTL) experiments have yielded important biological and biochemical information necessary for understanding the relationship between genetic markers and quantitative traits. For many years, most QTL algorithms only allowed one observation per genotype. Recently, there has been an increasing demand for QTL algorithms that can accommodate more than one observation per genotypic distribution. The Bayesian hierarchical model is very flexible and can easily incorporate this information into the model. Herein a methodology is presented that uses a Bayesian hierarchical model to capture the complexity of the data. Furthermore, the Markov chain Monte Carlo model composition (MC3) algorithm is used to search and identify important markers. An extensive simulation study illustrates that the method captures the true QTL, even under nonnormal noise and up to 6 QTL.

Keywords: Bayesian hierarchical model, Markov chain MonteCarlo model composition, quantitative trait loci.

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Authors: Watcharin Sangma, Onsiri Chanmuang, Pitsanu Tongkhow

Abstract:

 A forecasting model for steel demand uncertainty in Thailand is proposed. It consists of trend, autocorrelation, and outliers in a hierarchical Bayesian frame work. The proposed model uses a cumulative Weibull distribution function, latent first-order autocorrelation, and binary selection, to account for trend, time-varying autocorrelation, and outliers, respectively. The Gibbs sampling Markov Chain Monte Carlo (MCMC) is used for parameter estimation. The proposed model is applied to steel demand index data in Thailand. The root mean square error (RMSE), mean absolute percentage error (MAPE), and mean absolute error (MAE) criteria are used for model comparison. The study reveals that the proposed model is more appropriate than the exponential smoothing method.

Keywords: Forecasting model, Steel demand uncertainty, Hierarchical Bayesian framework, Exponential smoothing method.

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Authors: Elizabeth Stojanovski

Abstract:

Associations between life events and various forms of cancers have been identified. The purpose of a recent random-effects meta-analysis was to identify studies that examined the association between adverse events associated with changes to financial status including decreased income and breast cancer risk. The same association was studied in four separate studies which displayed traits that were not consistent between studies such as the study design, location, and time frame. It was of interest to pool information from various studies to help identify characteristics that differentiated study results. Two random-effects Bayesian meta-analysis models are proposed to combine the reported estimates of the described studies. The proposed models allow major sources of variation to be taken into account, including study level characteristics, between study variance and within study variance, and illustrate the ease with which uncertainty can be incorporated using a hierarchical Bayesian modelling approach.

Keywords: Random-effects, meta-analysis, Bayesian, variation.

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Authors: Helyane B. Borges, Julio Cesar Nievola

Abstract:

Hierarchical classification is a problem with applications in many areas as protein function prediction where the dates are hierarchically structured. Therefore, it is necessary the development of algorithms able to induce hierarchical classification models. This paper presents experimenters using the algorithm for hierarchical classification called Multi-label Hierarchical Classification using a Competitive Neural Network (MHC-CNN). It was tested in ten datasets the Gene Ontology (GO) Cellular Component Domain. The results are compared with the Clus-HMC and Clus-HSC using the hF-Measure.

Keywords: Hierarchical Classification, Competitive Neural Network, Global Classifier.

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Authors: Fabio Fabris, Alex A. Freitas

Abstract:

Hierarchical classification is a special type of classification task where the class labels are organised into a hierarchy, with more generic class labels being ancestors of more specific ones. Meta-learning for classification-algorithm recommendation consists of recommending to the user a classification algorithm, from a pool of candidate algorithms, for a dataset, based on the past performance of the candidate algorithms in other datasets. Meta-learning is normally used in conventional, non-hierarchical classification. By contrast, this paper proposes a meta-learning approach for more challenging task of hierarchical classification, and evaluates it in a large number of bioinformatics datasets. Hierarchical classification is especially relevant for bioinformatics problems, as protein and gene functions tend to be organised into a hierarchy of class labels. This work proposes meta-learning approach for recommending the best hierarchical classification algorithm to a hierarchical classification dataset. This work’s contributions are: 1) proposing an algorithm for splitting hierarchical datasets into new datasets to increase the number of meta-instances, 2) proposing meta-features for hierarchical classification, and 3) interpreting decision-tree meta-models for hierarchical classification algorithm recommendation.

Keywords: Algorithm recommendation, meta-learning, bioinformatics, hierarchical classification.

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Authors: Amal Kr Sarma, H Zeen Devi, N Nimai Singh

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The Constraints imposed by non-thermal leptogenesis on the survival of the neutrino mass models describing the presently available neutrino mass patterns, are studied numerically. We consider the Majorana CP violating phases coming from right-handed Majorana mass matrices to estimate the baryon asymmetry of the universe, for different neutrino mass models namely quasi-degenerate, inverted hierarchical and normal hierarchical models, with tribimaximal mixings. Considering two possible diagonal forms of Dirac neutrino mass matrix as either charged lepton or up-quark mass matrix, the heavy right-handed mass matrices are constructed from the light neutrino mass matrix. Only the normal hierarchical model leads to the best predictions of baryon asymmetry of the universe, consistent with observations in non-thermal leptogenesis scenario.

Keywords: Thermal leptogenesis, Non-thermal leptogenesis.

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Authors: András Barta, István Vajk

Abstract:

In pattern recognition applications the low level segmentation and the high level object recognition are generally considered as two separate steps. The paper presents a method that bridges the gap between the low and the high level object recognition. It is based on a Bayesian network representation and network propagation algorithm. At the low level it uses hierarchical structure of quadratic spline wavelet image bases. The method is demonstrated for a simple circuit diagram component identification problem.

Keywords: Object recognition, Bayesian network, Wavelets, Document processing.

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Authors: Panudet Saengseedam, Nanthachai Kantanantha

Abstract:

This paper proposes a linear mixed model (LMM) with spatial effects to forecast rice and cassava yields in Thailand at the same time. A multivariate conditional autoregressive (MCAR) model is assumed to present the spatial effects. A Bayesian method is used for parameter estimation via Gibbs sampling Markov Chain Monte Carlo (MCMC). The model is applied to the rice and cassava yields monthly data which have been extracted from the Office of Agricultural Economics, Ministry of Agriculture and Cooperatives of Thailand. The results show that the proposed model has better performance in most provinces in both fitting part and validation part compared to the simple exponential smoothing and conditional auto regressive models (CAR) from our previous study.

Keywords: Bayesian method, Linear mixed model, Multivariate conditional autoregressive model, Spatial time series.

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Authors: András Barta, István Vajk

Abstract:

In pattern recognition applications the low level segmentation and the high level object recognition are generally considered as two separate steps. The paper presents a method that bridges the gap between the low and the high level object recognition. It is based on a Bayesian network representation and network propagation algorithm. At the low level it uses hierarchical structure of quadratic spline wavelet image bases. The method is demonstrated for a simple circuit diagram component identification problem.

Keywords: Object recognition, Bayesian network, Wavelets, Document processing.

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Authors: Jan Sindelar

Abstract:

The paper presents an applied study of a multivariate AR(p) process fitted to daily data from U.S. commodity futures markets with the use of Bayesian statistics. In the first part a detailed description of the methods used is given. In the second part two BVAR models are chosen one with assumption of lognormal, the second with normal distribution of prices conditioned on the parameters. For a comparison two simple benchmark models are chosen that are commonly used in todays Financial Mathematics. The article compares the quality of predictions of all the models, tries to find an adequate rate of forgetting of information and questions the validity of Efficient Market Hypothesis in the semi-strong form.

Keywords: Vector auto-regression, forecasting, financial, Bayesian, efficient markets.

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Authors: Amir Azizi, Amir Yazid B. Ali, Loh Wei Ping

Abstract:

Throughput is an important measure of performance of production system. Analyzing and modeling of production throughput is complex in today-s dynamic production systems due to uncertainties of production system. The main reasons are that uncertainties are materialized when the production line faces changes in setup time, machinery break down, lead time of manufacturing, and scraps. Besides, demand changes are fluctuating from time to time for each product type. These uncertainties affect the production performance. This paper proposes Bayesian inference for throughput modeling under five production uncertainties. Bayesian model utilized prior distributions related to previous information about the uncertainties where likelihood distributions are associated to the observed data. Gibbs sampling algorithm as the robust procedure of Monte Carlo Markov chain was employed for sampling unknown parameters and estimating the posterior mean of uncertainties. The Bayesian model was validated with respect to convergence and efficiency of its outputs. The results presented that the proposed Bayesian models were capable to predict the production throughput with accuracy of 98.3%.

Keywords: Bayesian inference, Uncertainty modeling, Monte Carlo Markov chain, Gibbs sampling, Production throughput

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Authors: Darren Zou

Abstract:

Forecasting the stock market is a very challenging task. Various economic indicators such as GDP, exchange rates, interest rates, and unemployment have a substantial impact on the stock market. Time series models are the traditional methods used to predict stock market changes. In this paper, a machine learning method, Bayesian Additive Regression Tree (BART) is used in predicting stock market indexes based on multiple economic indicators. BART can be used to model heterogeneous treatment effects, and thereby works well when models are misspecified. It also has the capability to handle non-linear main effects and multi-way interactions without much input from financial analysts. In this research, BART is proposed to provide a reliable prediction on day-to-day stock market activities. By comparing the analysis results from BART and with time series method, BART can perform well and has better prediction capability than the traditional methods.

Keywords: Bayesian, Forecast, Stock, BART.

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Authors: Rawaa H. El-Bidweihy, Hisham M. Abdelsalam, Ihab A. El-Khodary

Abstract:

In an era where machines run and shape our world, the need for a stable, non-ending source of energy emerges. In this study, the focus was on the solar energy in Egypt as a renewable source, the most important factors that could affect the solar energy’s market share throughout its life cycle production were analyzed and filtered, the relationships between them were derived before structuring a Bayesian network. Also, forecasted models were built for multiple factors to predict the states in Egypt by 2035, based on historical data and patterns, to be used as the nodes’ states in the network. 37 factors were found to might have an impact on the use of solar energy and then were deducted to 12 factors that were chosen to be the most effective to the solar energy’s life cycle in Egypt, based on surveying experts and data analysis, some of the factors were found to be recurring in multiple stages. The presented Bayesian network could be used later for scenario and decision analysis of using solar energy in Egypt, as a stable renewable source for generating any type of energy needed.

Keywords: ARIMA, auto correlation, Bayesian network, forecasting models, life cycle, partial correlation, renewable energy, SARIMA, solar energy.

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Authors: Hao Wu, Jonathan L. Shapiro

Abstract:

The Bayesian Optimization Algorithm (BOA) is an algorithm based on the estimation of distributions. It uses techniques from modeling data by Bayesian networks to estimating the joint distribution of promising solutions. To obtain the structure of Bayesian network, different search algorithms can be used. The key point that BOA addresses is whether the constructed Bayesian network could generate new and useful solutions (strings), which could lead the algorithm in the right direction to solve the problem. Undoubtedly, this ability is a crucial factor of the efficiency of BOA. Varied search algorithms can be used in BOA, but their performances are different. For choosing better ones, certain suitable method to present their ability difference is needed. In this paper, a greedy search algorithm and a stochastic search algorithm are used in BOA to solve certain optimization problem. A method using Kullback-Leibler (KL) Divergence to reflect their difference is described.

Keywords: Bayesian optimization algorithm, greedy search, KL divergence, stochastic search.

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Authors: Zhidong Zhang, Zhi-Chao Zhang

Abstract:

This study examined the mental health and behavioral problems in early adolescence with the instrument of Achenbach System of Empirically Based Assessment (ASEBA). The purpose of the study was stratified sampling method was used to collect data from 1975 participants. Multiple regression models and hierarchical regression models were applied to examine the relations between the background variables and internalizing problems, and the ones between students’ performance and internalizing problems. The results indicated that several background variables as predictors could significantly predict the anxious/depressed problem; reading and social study scores could significantly predict the anxious/depressed problem. However the class as a hierarchical macro factor did not indicate the significant effect. In brief, the majority of these models represented that the background variables, behaviors and academic performance were significantly related to the anxious/depressed problem.

Keywords: Behavioral problems, anxious/depression problems, empirical-based assessment, hierarchical modeling.

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Authors: Viliam Makis, Farnoosh Naderkhani, Leila Jafari

Abstract:

In this paper, we present a model and an algorithm for the calculation of the optimal control limit, average cost, sample size, and the sampling interval for an optimal Bayesian chart to control the proportion of defective items produced using a semi-Markov decision process approach. Traditional p-chart has been widely used for controlling the proportion of defectives in various kinds of production processes for many years. It is well known that traditional non-Bayesian charts are not optimal, but very few optimal Bayesian control charts have been developed in the literature, mostly considering finite horizon. The objective of this paper is to develop a fast computational algorithm to obtain the optimal parameters of a Bayesian p-chart. The decision problem is formulated in the partially observable framework and the developed algorithm is illustrated by a numerical example.

Keywords: Bayesian control chart, semi-Markov decision process, quality control, partially observable process.

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Authors: Dewan Md. Farid, Nguyen Huu Hoa, Jerome Darmont, Nouria Harbi, Mohammad Zahidur Rahman

Abstract:

In this paper, we present a new learning algorithm for anomaly based network intrusion detection using improved self adaptive naïve Bayesian tree (NBTree), which induces a hybrid of decision tree and naïve Bayesian classifier. The proposed approach scales up the balance detections for different attack types and keeps the false positives at acceptable level in intrusion detection. In complex and dynamic large intrusion detection dataset, the detection accuracy of naïve Bayesian classifier does not scale up as well as decision tree. It has been successfully tested in other problem domains that naïve Bayesian tree improves the classification rates in large dataset. In naïve Bayesian tree nodes contain and split as regular decision-trees, but the leaves contain naïve Bayesian classifiers. The experimental results on KDD99 benchmark network intrusion detection dataset demonstrate that this new approach scales up the detection rates for different attack types and reduces false positives in network intrusion detection.

Keywords: Detection rates, false positives, network intrusiondetection, naïve Bayesian tree.

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Authors: Ifeyinwa E. Achumba, Djamel Azzi, Rinat Khusainov

Abstract:

There are three approaches to complete Bayesian Network (BN) model construction: total expert-centred, total datacentred, and semi data-centred. These three approaches constitute the basis of the empirical investigation undertaken and reported in this paper. The objective is to determine, amongst these three approaches, which is the optimal approach for the construction of a BN-based model for the performance assessment of students- laboratory work in a virtual electronic laboratory environment. BN models were constructed using all three approaches, with respect to the focus domain, and compared using a set of optimality criteria. In addition, the impact of the size and source of the training, on the performance of total data-centred and semi data-centred models was investigated. The results of the investigation provide additional insight for BN model constructors and contribute to literature providing supportive evidence for the conceptual feasibility and efficiency of structure and parameter learning from data. In addition, the results highlight other interesting themes.

Keywords: Bayesian networks, model construction, parameterlearning, structure learning, performance index, model comparison.

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Authors: Min Min Swe Zin

Abstract:

This paper introduces the foundations of Bayesian probability theory and Bayesian decision method. The main goal of Bayesian decision theory is to minimize the expected loss of a decision or minimize the expected risk. The purposes of this study are to review the decision process on the issue of flood occurrences and to suggest possible process for decision improvement. This study examines the problem structure of flood occurrences and theoretically explicates the decision-analytic approach based on Bayesian decision theory and application to flood occurrences in Environmental Engineering. In this study, we will discuss about the flood occurrences upon an annual maximum water level in cm, 43-year record available from 1965 to 2007 at the gauging station of Sagaing on the Ayeyarwady River with the drainage area - 120193 sq km by using Bayesian decision method. As a result, we will discuss the loss and risk of vast areas of agricultural land whether which will be inundated or not in the coming year based on the two standard maximum water levels during 43 years. And also we forecast about that lands will be safe from flood water during the next 10 years.

Keywords: Bayesian decision method, conditional binomial distribution, minimax rules, prior beta distribution.

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Authors: Z. Abdullah, A. R. Hamdan

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Clustering is a process of grouping objects and data into groups of clusters to ensure that data objects from the same cluster are identical to each other. Clustering algorithms in one of the area in data mining and it can be classified into partition, hierarchical, density based and grid based. Therefore, in this paper we do survey and review four major hierarchical clustering algorithms called CURE, ROCK, CHAMELEON and BIRCH. The obtained state of the art of these algorithms will help in eliminating the current problems as well as deriving more robust and scalable algorithms for clustering.

Keywords: Clustering, method, algorithm, hierarchical, survey.

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Authors: M. Sangeetha, A. Sabari, T. Shanthi Priya

Abstract:

Recent advances in wireless networking technologies introduce several energy aware routing protocols in sensor networks. Such protocols aim to extend the lifetime of network by reducing the energy consumption of nodes. Many researchers are looking for certain challenges that are predominant in the grounds of energy consumption. One such protocol that addresses this energy consumption issue is ‘Cluster based hierarchical routing protocol’. In this paper, we intend to discuss some of the major hierarchical routing protocols adhering towards sensor networks. Furthermore, we examine and compare several aspects and characteristics of few widely explored hierarchical clustering protocols, and its operations in wireless sensor networks (WSN). This paper also presents a discussion on the future research topics and the challenges of hierarchical clustering in WSNs.

Keywords: Clustering, Energy Efficiency, Hierarchical routing, Wireless sensor networks.

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Authors: Siavash Asadi Ghajarloo

Abstract:

Nowadays predicting political risk level of country has become a critical issue for investors who intend to achieve accurate information concerning stability of the business environments. Since, most of the times investors are layman and nonprofessional IT personnel; this paper aims to propose a framework named GECR in order to help nonexpert persons to discover political risk stability across time based on the political news and events. To achieve this goal, the Bayesian Networks approach was utilized for 186 political news of Pakistan as sample dataset. Bayesian Networks as an artificial intelligence approach has been employed in presented framework, since this is a powerful technique that can be applied to model uncertain domains. The results showed that our framework along with Bayesian Networks as decision support tool, predicted the political risk level with a high degree of accuracy.

Keywords: Bayesian Networks, Data mining, GECRframework, Predicting political risk.

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Authors: Hany Alashwal, Safaai Deris, Razib M. Othman

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Understanding proteins functions is a major goal in the post-genomic era. Proteins usually work in context of other proteins and rarely function alone. Therefore, it is highly relevant to study the interaction partners of a protein in order to understand its function. Machine learning techniques have been widely applied to predict protein-protein interactions. Kernel functions play an important role for a successful machine learning technique. Choosing the appropriate kernel function can lead to a better accuracy in a binary classifier such as the support vector machines. In this paper, we describe a Bayesian kernel for the support vector machine to predict protein-protein interactions. The use of Bayesian kernel can improve the classifier performance by incorporating the probability characteristic of the available experimental protein-protein interactions data that were compiled from different sources. In addition, the probabilistic output from the Bayesian kernel can assist biologists to conduct more research on the highly predicted interactions. The results show that the accuracy of the classifier has been improved using the Bayesian kernel compared to the standard SVM kernels. These results imply that protein-protein interaction can be predicted using Bayesian kernel with better accuracy compared to the standard SVM kernels.

Keywords: Bioinformatics, Protein-protein interactions, Bayesian Kernel, Support Vector Machines.

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Authors: Hatem. Elmeddeb, Noureddine, Hamdi, Ammar. Bouallègue

Abstract:

In this paper, a joint source-channel coding (JSCC) scheme for time-varying channels is presented. The proposed scheme uses hierarchical framework for both source encoder and transmission via QAM modulation. Hierarchical joint source channel codes with hierarchical QAM constellations are designed to track the channel variations which yields to a higher throughput by adapting certain parameters of the receiver to the channel variation. We consider the problem of still image transmission over time-varying channels with channel state information (CSI) available at 1) receiver only and 2) both transmitter and receiver being informed about the state of the channel. We describe an algorithm that optimizes hierarchical source codebooks by minimizing the distortion due to source quantizer and channel impairments. Simulation results, based on image representation, show that, the proposed hierarchical system outperforms the conventional schemes based on a single-modulator and channel optimized source coding.

Keywords: Channel-optimized VQ (COVQ), joint optimization, QAM, hierarchical systems.

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Authors: Pavol Tanuska, Pavel Vazan, Michal Kebisek, Dominika Jurovata

Abstract:

The paper gives the results of the project that was oriented on the usage of knowledge discoveries from production systems for needs of the hierarchical process control. One of the main project goals was the proposal of knowledge discovery model for process control. Specifics data mining methods and techniques was used for defined problems of the process control. The gained knowledge was used on the real production system thus the proposed solution has been verified. The paper documents how is possible to apply the new discovery knowledge to use in the real hierarchical process control. There are specified the opportunities for application of the proposed knowledge discovery model for hierarchical process control.

Keywords: Hierarchical process control, knowledge discovery from databases, neural network.

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Authors: Moulay A. Akhloufi, Abdelhakim Bendada

Abstract:

Face recognition in the infrared spectrum has attracted a lot of interest in recent years. Many of the techniques used in infrared are based on their visible counterpart, especially linear techniques like PCA and LDA. In this work, we introduce a probabilistic Bayesian framework for face recognition in the infrared spectrum. In the infrared spectrum, variations can occur between face images of the same individual due to pose, metabolic, time changes, etc. Bayesian approaches permit to reduce intrapersonal variation, thus making them very interesting for infrared face recognition. This framework is compared with classical linear techniques. Non linear techniques we developed recently for infrared face recognition are also presented and compared to the Bayesian face recognition framework. A new approach for infrared face extraction based on SVM is introduced. Experimental results show that the Bayesian technique is promising and lead to interesting results in the infrared spectrum when a sufficient number of face images is used in an intrapersonal learning process.

Keywords: Face recognition, biometrics, probabilistic imageprocessing, infrared imaging.

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Authors: I. Oloyede

Abstract:

The study investigates the accuracy and loss of deep learning algorithms with the set of coronavirus (COVID-19) images dataset by comparing Bayesian convolutional neural network and traditional convolutional neural network in low dimensional dataset. 50 sets of X-ray images out of which 25 were COVID-19 and the remaining 20 were normal, twenty images were set as training while five were set as validation that were used to ascertained the accuracy of the model. The study found out that Bayesian convolution neural network outperformed conventional neural network at low dimensional dataset that could have exhibited under fitting. The study therefore recommended Bayesian Convolutional neural network (BCNN) for android apps in computer vision for image detection.

Keywords: BCNN, CNN, Images, COVID-19, Deep Learning.

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Authors: Farhad Asadi, S. Hossein Sadati

Abstract:

Bayesian approach can be used for parameter identification and extraction in state space models and its ability for analyzing sequence of data in dynamical system is proved in different literatures. In this paper, adaptive Kalman filter with Bayesian approach for identification of variances in measurement parameter noise is developed. Next, it is applied for estimation of the dynamical state and measurement data in discrete linear dynamical system. This algorithm at each step time estimates noise variance in measurement noise and state of system with Kalman filter. Next, approximation is designed at each step separately and consequently sufficient statistics of the state and noise variances are computed with a fixed-point iteration of an adaptive Kalman filter. Different simulations are applied for showing the influence of noise variance in measurement data on algorithm. Firstly, the effect of noise variance and its distribution on detection and identification performance is simulated in Kalman filter without Bayesian formulation. Then, simulation is applied to adaptive Kalman filter with the ability of noise variance tracking in measurement data. In these simulations, the influence of noise distribution of measurement data in each step is estimated, and true variance of data is obtained by algorithm and is compared in different scenarios. Afterwards, one typical modeling of nonlinear state space model with inducing noise measurement is simulated by this approach. Finally, the performance and the important limitations of this algorithm in these simulations are explained. 

Keywords: adaptive filtering, Bayesian approach Kalman filtering approach, variance tracking

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