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barcode generator in vb.net BAYESIAN LEARNING in Software
CHAPTER 6 BAYESIAN LEARNING Generate QR Code JIS X 0510 In None Using Barcode creation for Software Control to generate, create Denso QR Bar Code image in Software applications. QR Code ISO/IEC18004 Reader In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. In this section we introduce the key concepts and the representation of Bayesian belief networks More detailed treatments are given by Pearl (1988), Russell and Norvig (1995), Heckerman et al (1995), and Jensen (1996) In general, a Bayesian belief network describes the probability distribution over a set of variables Consider an arbitrary set of random variables Yl Y,, where each variable Yi can take on the set of possible values V(Yi) We define the joint space of the set of variables Y to be the cross product V(Yl) x V(Y2) x V(Y,) In other words, each item in the joint space corresponds to one of the possible assignments of values to the tuple of variables (Yl Y,) The probability distribution over this joint' space is called the joint probability distribution The joint probability distribution specifies the probability for each of the possible variable bindings for the tuple (Yl Y,) A Bayesian belief network describes the joint probability distribution for a set of variables QR Code 2d Barcode Generation In C#.NET Using Barcode maker for Visual Studio .NET Control to generate, create QR image in Visual Studio .NET applications. Creating Denso QR Bar Code In VS .NET Using Barcode creator for ASP.NET Control to generate, create QR image in ASP.NET applications. 6111 Conditional Independence
Print QR Code 2d Barcode In .NET Framework Using Barcode creator for .NET framework Control to generate, create QRCode image in Visual Studio .NET applications. QR Code Generator In VB.NET Using Barcode creation for Visual Studio .NET Control to generate, create QR image in .NET framework applications. Let us begin our discussion of Bayesian belief networks by defining precisely the notion of conditional independence Let X , Y, and Z be three discretevalued random variables We say that X is conditionally independent of Y given Z if the probability distribution governing X is independent of the value of Y given a value for 2; that is, if Encoding EAN128 In None Using Barcode maker for Software Control to generate, create GS1 128 image in Software applications. Encoding Bar Code In None Using Barcode generator for Software Control to generate, create bar code image in Software applications. where xi E V(X), yj E V(Y), and z k E V(Z) We commonly write the above expression in abbreviated form as P(XIY, Z ) = P(X1Z) This definition of conditional independence can be extended to sets of variables as well We say that the set of variables X1 Xi is conditionally independent of the set of variables Yl Ym given the set of variables 2 1 Z, if Code 128 Code Set B Generator In None Using Barcode creator for Software Control to generate, create ANSI/AIM Code 128 image in Software applications. Generating DataMatrix In None Using Barcode generation for Software Control to generate, create DataMatrix image in Software applications. P ( X 1 XIJY1Ym, z Z,) = P ( X l X1]Z1 Z,) 1 Create EAN / UCC  13 In None Using Barcode printer for Software Control to generate, create GTIN  13 image in Software applications. Draw Barcode In None Using Barcode generation for Software Control to generate, create barcode image in Software applications. Note the correspondence between this definition and our use of conditional independence in the definition of the naive Bayes classifier The naive Bayes classifier assumes that the instance attribute A1 is conditionally independent of instance attribute A2 given the target value V This allows the naive Bayes classifier to calculate P ( A l , A21V) in Equation (620) as follows Encode Code 9/3 In None Using Barcode generator for Software Control to generate, create USS Code 93 image in Software applications. Data Matrix ECC200 Reader In Visual C# Using Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in .NET applications. Equation (623) is just the general form of the product rule of probability from Table 61 Equation (624) follows because if A1 is conditionally independent of A2 given V, then by our definition of conditional independence P (A1 IA2, V ) = P(A1IV) Make 2D Barcode In .NET Framework Using Barcode creator for ASP.NET Control to generate, create Matrix 2D Barcode image in ASP.NET applications. Recognize Barcode In VS .NET Using Barcode scanner for .NET framework Control to read, scan read, scan image in VS .NET applications. S,B S,B C
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FIGURE 63 A Bayesian belief network The network on the left represents a set of conditional independence assumptions In particular, each node is asserted to be conditionally independent of its nondescendants, given its immediate parents Associated with each node is a conditional probability table, which specifies the conditional distribution for the variable given its immediate parents in the graph The conditional probability table for the Campjire node is shown at the right, where Campjire is abbreviated to C , Storm abbreviated to S, and BusTourGroup abbreviated to B 6112 Representation
A Bayesian belief network (Bayesian network for short) represents the joint probability distribution for a set of variables For example, the Bayesian network in Figure 63 represents the joint probability distribution over the boolean variables Storm, Lightning, Thunder, ForestFire, Campjre, and BusTourGroup In general, a Bayesian network represents the joint probability distribution by specifying a set of conditional independence assumptions (represented by a directed acyclic graph), together with sets of local conditional probabilities Each variable in the joint space is represented by a node in the Bayesian network For each variable two types of information are specified First, the network arcs represent the assertion that the variable is conditionally independent of its nondescendants in the network given its immediate predecessors in the network We say Xjis a descendant of , Y if there is a directed path from Y to X Second, a conditional probability table is given for each variable, describing the probability distribution for that variable given the values of its immediate predecessors The joint probability for any desired assignment of values ( y l , , y,) to the tuple of network variables (YI Y,) can be computed by the formula ~ ( Y I , , yd = n p ( y i ~ p a r e n t s ( ~ i ) ) where Parents(Yi) denotes the set of immediate predecessors of Yi in the netParents(Yi)) are precisely the values stored in the work Note the values of P(yiJ conditional probability table associated with node Yi To illustrate, the Bayesian network in Figure 63 represents the joint probability distribution over the boolean variables Storm, Lightning, Thunder, Forest

