B. Naïve Bayesian Classification In machine learning, Naive Bayesian Classification is a family of a simple probabilistic classifier based on the Bayes theorem (or Bayes’s rule) with Naive (Strong) independence assumption between the features. It is one of the most efficient and effective classification algorithms and represents a supervised learning method as well as a statistical method for classification. Naïve Bayesian classifiers assume that the effect of an attribute value on a given class is independent of the values of the other attributes. In other words Naïve Bayesian classifiers assume that there are no dependencies amongst attributes. This assumption is called class conditional independence. It is made to simplify the computations …show more content…
P(X) is the prior probability of X [20]. The naïve Bayesian classifier, or simple Bayesian classifier, works as follows: 1. Let D be a training set of tuples and their associated class labels. As usual, each tuple is represented by an n-dimensional attribute vector, X = (x1, x2... xn), depicting n measurements made on the tuple from n attributes, respectively, A1, A2... An. 2. Suppose that there are m classes, C1, C2... Cm. Given a tuple, X, the classifier will predict that X belongs to the class having the highest posterior probability, conditioned on X. That is, the naïve Bayesian classifier predicts that tuple X belongs to the class Ci if and only if P(Ci |X) > P(Cj |X) for 1 ≤ j ≤ m, j ≠ i. Thus we maximize P(Ci |X). The class Ci for which P(Ci |X) is maximized is called the maximum posteriori hypothesis. By Bayes’ theorem (Equation (6.10)), P(Ci |X) = P(X|Ci)P(Ci) /P(X) . …show more content…
Given data sets with many attributes, it would be extremely computationally expensive to compute P(XjCi). In order to reduce computation in evaluating P(XjCi), the naive assumption of class conditional independence is made. This presumes that the values of the attributes are conditionally independent of one another, given the class label of the tuple (i.e., that there are no dependence relationships among the attributes). Thus, P(X|Ci) = n ∏ k =1 P(xk|Ci) = P(x1|Ci)×P(x2|Ci)ו•• ×P(xn|Ci). We can easily estimate the probabilities P(x1|Ci), P(x2|Ci),..., P(xn|Ci) from the training tuples. Recall that here xk refers to the value of attribute Ak for tuple X. For each attribute, we look at whether the attribute is categorical or continuous-valued. For instance, to compute P(X|Ci), we consider the following (a) If Ak is categorical, then P(xkjCi) is the number of tuples of class Ci in D having the value xk for Ak, divided by jCi,Dj, the number of tuples of class Ci in D (b) If Ak is continuous-valued, then we need to do a bit more work, but the calculation is pretty straightforward. A continuous-valued attribute is typically assumed to have a Gaussian distribution with a mean μ and standard deviation s, defined
Many theories of logic use mathematical terms to show how premises lead to conclusions. The Bayesian confirmation theory relates directly to probability. When applying this theory, a logician must know the probability of a given situation, have a conditional rule, and then he or she must apply the probability when the conditional rule is applied. This theory is used to determine an outcome based on a given condition. The probability of a given situation is x, when y occurs, or the probability is z if it does not occur. If y occurs, then the outcome of the given would be x. For example, if there is a high probability that a storm will occur if a given temperature drops and there is no temperature change, then it will most likely not rain because the temperature did not change (Strevens, 2012). By using observational data such as weather patterns, a person can arrive at a logical prediction or conclusion that will most likely come true based...
ABSTRACT: My focus in this paper is on how the basic Bayesian model can be amended to reflect the role of idealizations and approximations in the confirmation or disconfirmation of any hypothesis. I suggest the following as a plausible way of incorporating idealizations and approximations into the Bayesian condition for incremental confirmation: Theory T is confirmed by observation P relative to background knowledge
First we are going to talk about probability theory, which has to do with mathematics and analysis of random phenomena. You are probably used to putting the number of outcomes over the total amount of the object or total amount what you have. An example is, if you have a normal dice and you want the probability of rolling an odd number, you would take the total amount of odd numbers (3) and put that over the total (6) amount of numbers on the dice like so 3/6 which you can also reduce it to ½ because 3 is half of 6. This theory has been around since the sixteenth century and started off as the outcome you would get in a game, which was created by Pierre de Fermat, Blaise Pascal and Gerolamo Cardano. Later on in the seventeenth century Christiaan Huygens published a book on the subject.
The combinational development of databases and AI machines that bring the new technology called as discovery in databases, The overall fields of science that discover machine learning, data visualization, knowledge recognition, computing on high performance, and expert systems but the main thing in it is data selection, data pre-processing, data converting, data mining explanation and evolution of knowledge while the data mining is the steps of knowledge discovering and is the most important one.[2]
Data mining technique can be used to overcome many health disorders. The health diseases that can be overcome are heart diseases. Palaniappan S. & Awang R. stated data mining can be done to extract all information that associated with heart disease from the database. Through this technique, this will help the physician or health practitioner to make clinical interpretation about the heart disease and help in giving a good treatment for lower cost. According to Shouman M. et al, data mining is important for determine the prognosis of the heart disease and the technique that can be used such as t...
I researched the development of the theorem and its criticism, and included my findings in this paper. Probably the most useful text in understanding the Theorem, and a definitive work supporting its use, is John Earman's work, Bayes or Bust?: A Critical Examination of Bayesian Confirmation. This book examined the relevant literature and the development of Bayesian statistics as well as defended it from its critics.
where <,> denotes an inner product between two vectors, is introduced to handle nonlinearly separable cases without any explicit knowledge of the feature mapping . The formulation (1) shows that the computational complexity of SVM training depends on the number of training data samples which is denoted as n. The computational complexity of training depends on the dimension of the input space. This becomes clear when we consider some typical kernel functions such as the linear kernel, ,
To better describe this concept, an article from Software Technology states, “This is like giving a student a set of problems and their solutions and telling that student to figure [it] out …” (2016, Panos Louridas and Christof Eber). The way the computer learns is by grouping data together. This type of method uses two different types of grouping methods to help identify possible outcomes: classification and regression algorithms.
Vicars, W., Ed.D. (1997-2013). ASL Classifiers Level 1. Lifeprint.com. Retrieved February 16, 2014, from http://www.lifeprint.com/asl101/pages-signs/classifiers/classifiers-frame.htm
Step 2: Partition the training instances in C into subsets C1, C2, ..., Cn according to the values of V.
C) Division-Classification can use more then one principle. The paper can shift from one principle to another in different parts of the paper.
[5] J.S. Fulda. Data Mining and Privacy. In R. Spinello and H. Trvani, editors, Readings in CyberEthics, pages 413-417. Jones and Barlett, Sudbury MA, 2001.
HAND, D. J., MANNILA, H., & SMYTH, P. (2001).Principles of data mining. Cambridge, Mass, MIT Press.
T. Mitchell, Generative and Discriminative Classifiers: Naive Bayes and Logistic Regression. Draft Version, 2005 download
We can tell some interesting things from looking at our confusion matrix. For one thing, the model misclassified instances that were NO almost as many times as it correctly classified these instances. On the other hand, our model did a much better job of correctly classifying instances in the YES category.