for the linear regression case, parallel to Equation 2.3. The general properties of BMA have been studied extensively. A few of the most important papers, among many others, include the following. Madigan and Raftery (1994) verified that BMA beats out model choice under a logarithmic scoring rule in that BMA provides better predictive ability than using any one model, perhaps because of its optimal treatment of what we call here the within model list uncertainty; see also the examples by Hoeting et al. (1999, Section 7). Clyde (1999) addresses some of the prior selection questions and model search strategies. She directly confronts the problem of the model space being too large to permit an exhaustive search. To deal with model uncertainty, she implements the orthodox Bayes program by a stochastic, rather than an algorithmic, search. George and Foster (2000) address the model uncertainty problem in Bayesmodel selection by an empirical Bayes technique which they related to conventional model selection principles. For further references, see Clyde (1999).
This chart includes the two models using the same data; the x-axis of the chart represents the percentage of the test dataset that is used to compare the predictions while the y- axis of the chart represents the percentage of predicted values. To determine if there was sufficient information to learn patterns related to the predictable attribute, columns in the trained model were mapped to columns in the test dataset. The top red line shows the ideal model; it captured 100% of the target population for patients with Alzheimer's disease using 60% of the test dataset, the bottom blue line shows the random line which is always a 45 degree line across the chart. It shows that if we randomly guess the result for each case, 50% of the target population would be captured using 46% of the test dataset. Two models line (green represents Decision Trees Model and purple represents Naïve BayesModel) fall between the random- guess and ideal model lines, showing that both two have sufficient information to learn patterns in response to the predictable state.
single network and conceptually provide insights to the system behaviour. In causal models, derived numerical probabilities can be considered as representations of the probabilities of occurrence of a particular event. However, a disadvantage of causal models is that where a system is not well understood mechanistically and there are many dependent and independent nodes variables, the number of plausible models multiplies rapidly making parsimony a concern. Semi-naïve Bayes models, on the other hand, allow the strong assumption of node independency given the target variable to be relaxed. These models are an intermediate step between the naïve Bayesmodel and a causal model and empirical experience in other ﬁ elds has shown they can be very reliable (Korb and Nicholson, 2011). This approach also allowed dispassionate model construc- tion using various performance metrics in a stepwise fashion based on rules developed for BBNs generally. WEKA allowed us to assess whether there were suf ﬁ cient data records to generate stable model structures and what were credible discretization thresholds. The performance metrics informed us which nodes were most likely to in ﬂ uence LRVs. The metrics also allowed comparison of i) different model options, ii) their respective predictive power, and iii) assessment of whether the best models were credible or pro- vided no improvement over the ZeroR model.
Growing Internet connectivity and traffic volume, recent intrusion incidents have reemphasized the importance of network intrusion detection systems for struggling progressively sophisticated network attacks. Techniques such as pattern recognition and the data mining of network events are often used by intrusion detection systems to classify the network events as either normal events or attack events. That the Hidden Naive Bayes (HNB) model can be applied to intrusion detection problems that suffer from dimensionality highly correlated features, and high network Data stream volumes. HNB is a data mining model that relaxes the naive Bayes methods Conditional impartiality assumption. This paper mostly intensive to Hidden Naive Bayesmodel, The tentative results show that the HNB model exhibits a superior overall performance in terms of accuracy, error rate, and misclassification cost compared with the traditional naive Bayesmodel, leading extended naive Bayes models and the Knowledge Discovery and Data Mining (KDD) Cup 1999. HNB model performed better than other leading state-of-the art models, such as Support Vector Machine, in predictive accuracy. The results also indicate that HNB Model significantly improves the accuracy of detecting denial-of-services (DoS) attacks.
In order to support comparison between our new method and existing theory, we begin by considering a full Bayesian model. We express the predictive and posterior distributions in terms of well-known functions, and derive desirable properties about the posterior estimates. Our new method is then introduced by adjusting the prior estimates using a mixture of full Bayesian and Bayes linear kinematic updating to support faster and easier calculations than in the full Bayesmodel. So far, the prior is assumed to be specified subjectively, but we now provide a method for empirically obtaining priors and examine their statistical consistency. As well as examining the theoretical properties of our inference methods, we discuss the comparative performance of our proposed Bayes linear Bayes approach relative to full Bayesian inference based on a simulation study to examine the relative accuracy of estimates. An illustrative example, motivated by a real industrial problem across a supply chain but suitably de-sensitised, provides further insight into the use of the proposed inference and allows us to examine not only the results under the alternative inference methods but also the impact of failing to account for the correlation between events.
Some attributes in the data set might have continues values, this will cause a problem in the likeli- hood probabilities because it is rather impossible to cover all the values in an interval of continuous values. In order to describe this variables there are some procedures that can be made in order to summarize this variables. One option is to discretize the variable. In this case the continuous variable will be converted to discrete values (e.g. convert continuous intervals to discrete vari- ables) thus being compatible with the standard model construction method. Another very popular option to describe the continuous variables is by making the assumption that the variable values are presented according a parametric probability distribution. This requires some intrinsic adap- tions of the Naive Bayesmodel in order to calculate the likelihood probability using the density distribution function. A popular solution is to use a Gaussian-like distribution. In this case, during training it is only required to calculate the mean (µ θ ) and standard deviation (σ θ ) for the corre-
Naive Bayes and Tree Augmented Naive Bayes (TAN) are probabilistic graphical models used for modeling huge datasets involving lots of uncertainties among its various interdependent feature sets. Some of the most common applications of these models are image segmentation, medical diagnosis and various other data clustering and data classification applications. A classification problem deals with identifying to which category a particular instance belongs to, based on previous knowledge acquired by analysis of various such instances. The instances are described using a set of variables called attributes or features. A Naive Bayesmodel assumes that all the attributes of an instance are independent of each other given the class of that instance. This is a very simple representation of the system, but the independence assumptions made in this model are incorrect and unrealistic. The TAN model improves on the Naive Bayesmodel by adding one more level of interaction among attributes of the system. In the TAN model, every attribute is dependent on its class and one other attribute from the feature set. Since this model incorporates the dependencies among the attributes, it is more realistic than a Naive Bayesmodel. This project analyzes the performance of these two models on various datasets. The TAN model gives better performance results if there are correlations between the attributes but the performance is almost the same as that of Naive Bayesmodel, if there are not enough
Various different types of predictive models have been designed for prediction. However, these models have some limitations and drawbacks. Existing predictive models have not been well established for TBI patients. The existing predictive models have unsatisfactory results due to unavailability of multi-class prediction. Multi-class prediction is very significant to improve the predictive models performance for TBI outcomes. Different types of predictive models are used to provide classifications and predictions such as Artificial Neural Network (ANN), AdaBoost and Support Vector Machine (SVM), Logistic Regression (LR), Bayesian Network (BN), Decision Tree (DT) Discriminant Analysis (DA) [9, 10]. Still, there is a need to develop a new predictive model for improving the existing models predictive performance. Another issue in TBI predictive model is affinity predictive model usage. The affinity is not used in TBI to develop and provide multi-class prediction. Indeed, there is a dire need to develop a new predictive model for improving the predictive model performance. In addition, the features from existing TBI predictive model need to be evaluated and approved by neurology experts for a better predictive performance.
Abstract —Bayesian filters can be made robust to outliers if the solutions are developed under the assumption of heavy-tailed distributed noise. However, in the absence of outliers, these robust solutions perform worse than the standard Gaussian assumption based filters. In this work, we develop a novel robust filter that adopts both Gaussian and multivariate t -distributions to model the outliers contaminated measurement noise. The effects of these distributions are combined within a Bayesian Model Averaging (BMA) framework. Moreover, to reduce the computational com- plexity of the proposed algorithm, a restricted variational Bayes (RVB) approach handles the multivariate t -distribution instead of its standard iterative VB (IVB) counterpart. The performance of the proposed filter is compared against a standard cubature Kalman filter (CKF) and a robust CKF (employing IVB method) in a representative simulation example concerning target tracking using range and bearing measurements. In the presence of outliers, the proposed algorithm shows a 38 % improvement over CKF in terms of root-mean-square-error (RMSE) and is computationally 2.5 times more efficient than the robust CKF.
We have proposed an empirical Bayes procedure for analysis of the data from a two-factor experiment when they are assumed to follow an Inverse Gaussian Distribution. Conjugate priors have been used. The reasons are mathematical tractibility and “objectivity” requirements as expounded in Robert . The posterior distributions have been used as the basis of any inference about the factor effects and their interactions. Though not worked there, one could have utilized various alternative priors like Jefferys’,
knowledge and identifying the goal of the process from the customer’s viewpoint. Creating a target data set which performs selecting a data set or focusing on a subset of variables or data samples on which discovery is to be performed. Data cleaning and preprocessing includes removal of noise or outliers for collecting necessary information to model or account for noise and deciding on strategies for handling missing data fields and according for time sequence information and known changes. Data reduction and projection consist of finding useful features to represent the data depending on the goal of the task. Using dimensionality reduction or transformation methods, the method has to reduce the effective number of variables or to find invariant representations for the data. The data mining task consist of
In this study we investigate the use of Bayesian Belief Networks (BBN) for developing a practical framework for machine learning process incorporating the commonsense reasoning. Bayesian Belief Networks grant a systematic and localized method for structuring probabilistic information about a situation into coherent whole. Bayesian networks have been established as a ubiquitous tool for modelling and reasoning under uncertainty. In this study we attempt to develop a graphical model that is used to represent knowledge about the uncertain domain in which the nodes are the random variables and the edges between the nodes represent probabilistic dependencies among the corresponding random variables. These conditional dependencies in the graph are often estimated by using some known statistical and computational methods. Thus developed Bayesian belief network along with joint probability distribution in the factored form can be used to evaluate all possible inference queries both predictive and diagnostic by marginalization. We experimentally developed a model for educational institutions which could be used to take decision on considering various factors link campus placement, total cost per year, academic excellence etc.
The low size of our data set made statistical mod- els perform much better than the deep learning methods. Our proposed method will take into ac- count the large number of classes by creating two different pipelines. The first one uses a Multino- mial Naive Bayes. The second model uses a Ran- dom Forest Classifier. These models were imple- mented using the package scikit-learn (Pedregosa et al., 2011). The pipelines are pre-trained be- fore they are given to the voting classifier. Then, the whole system is trained again to maximize the model performance for the dialects classification task. The data is first given into a count vectorizer then into a TF-IDF tranformer to extract meaning- ful information on word level. The voting classi- fier uses a hard voting method to select the model with the correct prediction.
Recently, variational Bayesian (VB) techniques have been applied to probabilistic matrix factor- ization and shown to perform very well in experiments. In this paper, we theoretically elucidate properties of the VB matrix factorization (VBMF) method. Through finite-sample analysis of the VBMF estimator, we show that two types of shrinkage factors exist in the VBMF estimator: the positive-part James-Stein (PJS) shrinkage and the trace-norm shrinkage, both acting on each sin- gular component separately for producing low-rank solutions. The trace-norm shrinkage is simply induced by non-flat prior information, similarly to the maximum a posteriori (MAP) approach. Thus, no trace-norm shrinkage remains when priors are non-informative. On the other hand, we show a counter-intuitive fact that the PJS shrinkage factor is kept activated even with flat priors. This is shown to be induced by the non-identifiability of the matrix factorization model, that is, the mapping between the target matrix and factorized matrices is not one-to-one. We call this model-induced regularization. We further extend our analysis to empirical Bayes scenarios where hyperparameters are also learned based on the VB free energy. Throughout the paper, we assume no missing entry in the observed matrix, and therefore collaborative filtering is out of scope.
gas disasters, adjust response options of emergency plans to make scientific decisions according to analysis and predictions of dynamic changes in uncertainty consequence of specific disasters have been key issues of coalmine sudden gas events to be researched. Such a key process is faced with the dynamic variation events with gradual increase in gas backflow scope. In view of this point, the decision plan must be real-time adjusted according to accident scenes. In coal mine emergency field, such as emergency plan, emergency information management system, emergency communication and command dispatching system, empirical emergency decision model still was remaining. Guo  proposed an emergency response plan of the coal and gas outburst and a hazard assessment emergency response model based on general regulations. Robot  provides a concise methodology for developing a comprehensive industrial program to handle major emergencies such as fires, gas leaks, and explosions, based on the expert guidance on techniques. An emergency rescue wireless communication system underground mine to implement the rescue action based was proposed . It can acquire the key information data and status information on disaster site quickly and accurately, but it did not describe how to rationally use these data and information in the rescue. Launa  studied warning messages during an emergency evacuation, which concluded that the implementation of a few relatively simple human factors principles could have improved the efficacy of warning communication systems. A management information system for managing of mine emergency resources, practicing of mine emergency program and commanding of emergency rescuer is developed on the base of mine accident emergency scheme . The system can automatically monitor the situation of rescuer personnel, rescue materials and rescuer equipments in daily, but doesn’t include the emergency rescue decision method and technology.
The CART model is a data mining technique applied in business, industry and engineering and it does not require any pre-defined underlying relationship between the dependent variable often referred to as the target and the independent variable (predictors) (Chang and Wang, 2006). CART is known to be good at handling prediction and classification problems. A CART model was developed using road accident data from Taipei, Taiwan to establish the relationship between injury severity and driver/vehicle characteristics, highway environmental variables and accident variables. Some advantages and disadvantages of using the CART model were highlighted. There is no need to specify a functional form in a CART model unlike a regression model in which a mis-specification of the model can result in an erroneous estimated relationship between the dependent and independents variables as well as the model predictions. In regression analysis, outliers are known to present a serious problem with an adverse effect on the coefficient estimates. In contrast, CART models have outliers isolated into a node resulting in no effect on splitting (risk factors) (Chang and Wang, 2006). CART deals with large data sets containing a large number of explanatory variables and can produce beneficial results from using a few important variables. The main disadvantages associated with CART models include the lack of provision of a probability level or confidence interval for the risk factors (splitters). CART models also have difficulty in conducting elasticity or sensitivity analysis and are also very unstable. They are normally used to identify important variables and then some other flexible modelling technique is used to develop the final model.
The data were analyzed by WEKA and MATLAB software, and 64 data mining models classified them. Of all 17 risk factors, 16 of them were defined as in- dependent risk factors, and one of them that was a specified type of cancer divided into Ductal and Lo- bular allocated class (dependent risk factor) tag to own. The stages of our method are shown in Fig.2. Initially, the collected breast cancer data were consi- dered as input. Secondly, the data divided into train and test kind. In third stage, train data were learned based on a special technique and produce data mining models. After that, the model changed to learned model. In fourth step, the performance of the learned model became valid by test data. Finally, the final model was pre- sented as output.
Latent Dirichlet Allocation (LDA) is a well known topic model that is often used to make inference regarding the properties of collections of text documents. LDA is a hierarchical Bayesian model, and involves a prior distribution on a set of latent topic variables. The prior is indexed by certain hyperparameters, and even though these have a large impact on inference, they are usually chosen either in an ad-hoc manner, or by applying an algorithm whose theoretical basis has not been firmly established. We present a method, based on a combination of Markov chain Monte Carlo and importance sampling, for estimating the maximum likelihood estimate of the hyperparameters. The method may be viewed as a computational scheme for implementation of an empirical Bayes analysis. It comes with theoretical guarantees, and a key feature of our approach is that we provide theoretically-valid error margins for our estimates. Experiments on both synthetic and real data show good performance of our methodology.
Artifical neural network is a complicated network composed by a lot of simple information units named nerve cell,which are used to imitate the structure and behaviour of human mind neural network.Artifical neural network not only has many excellent qualities,such as self-adapation,self-organization etc,but it has the ability of making-decision from similar,uncertain and even conflictive knowledge environment.The BP neural network model in this paper is a most widespread used one at present.It has been proved theorectically that BP neural network with 3 layers can approach any mapping relation with arbitary precision.The BP neural network with 3 layers is shown as Fig. 1. Supposing