BAYESIAN LEARNING in Software
CHAPTER 6 BAYESIAN LEARNING Create QRCode In None Using Barcode generator for Software Control to generate, create QR Code 2d barcode image in Software applications. Recognize QRCode In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. ordering of variable dependencies in the actual network The program succeeded in reconstructing the correct Bayesian network structure almost exactly, with the exception of one incorrectly deleted arc and one incorrectly added arc Constraintbased approaches to learning Bayesian network structure have also been developed (eg, Spirtes et al 1993) These approaches infer independence and dependence relationships from the data, and then use these relationships to construct Bayesian networks Surveys of current approaches to learning Bayesian networks are provided by Heckerman (1995) and Buntine (1994) Paint QR Code In Visual C#.NET Using Barcode printer for Visual Studio .NET Control to generate, create QR Code JIS X 0510 image in .NET applications. QR Code ISO/IEC18004 Generation In VS .NET Using Barcode generation for ASP.NET Control to generate, create Quick Response Code image in ASP.NET applications. 612 THE EM ALGORITHM
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Creating Code128 In None Using Barcode generation for Software Control to generate, create Code128 image in Software applications. Encode GS1128 In None Using Barcode drawer for Software Control to generate, create USS128 image in Software applications. The easiest way to introduce the EM algorithm is via an example Consider a problem in which the data D is a set of instances generated by a probability distribution that is a mixture of k distinct Normal distributions This problem setting is illustrated in Figure 64 for the case where k = 2 and where the instances are the points shown along the x axis Each instance is generated using a twostep process First, one of the k Normal distributions is selected at random Second, a single random instance xi is generated according to this selected distribution This process is repeated to generate a set of data points as shown in the figure To simplify our discussion, we consider the special case where the selection of the single Normal distribution at each step is based on choosing each with uniform probability, where each of the k Normal distributions has the same variance a2,and where a2 is known The learning task is to output a hypothesis h = (FI, pk) that describes the means of each of the k distributions We would like to find EAN 13 Encoder In None Using Barcode printer for Software Control to generate, create GS1  13 image in Software applications. UPCA Supplement 5 Creation In None Using Barcode generation for Software Control to generate, create GS1  12 image in Software applications. FIGURE 64 Instances generated by a mixture of two Normal distributions with identical variance aThe instances are shown by the points along the x axis If the means of the Normal distributions are unknown, the EM algorithm can be used to search for their maximum likelihood estimates Drawing I2/5 In None Using Barcode printer for Software Control to generate, create ANSI/AIM I2/5 image in Software applications. UPCA Scanner In Visual C#.NET Using Barcode decoder for .NET framework Control to read, scan read, scan image in .NET framework applications. a maximum likelihood hypothesis for these means; that is, a hypothesis h that maximizes p ( D lh) Note it is easy to calculate the maximum likelihood hypothesis for the mean x2, of a single Normal distribution given the observed data instances X I , , xm drawn from this single distribution This problem of finding the mean of a single distribution is just a special case of the problem discussed in Section 64, Equation (66), where we showed that the maximum likelihood hypothesis is the one that minimizes the sum of squared errors over the m training instances Restating Equation (66) using our current notation, we have Barcode Printer In Java Using Barcode generator for Java Control to generate, create bar code image in Java applications. UPC A Drawer In Visual C# Using Barcode generator for VS .NET Control to generate, create UPC A image in VS .NET applications. Generate Data Matrix In Visual Basic .NET Using Barcode encoder for VS .NET Control to generate, create Data Matrix ECC200 image in Visual Studio .NET applications. EAN 13 Drawer In None Using Barcode generation for Font Control to generate, create EAN13 image in Font applications. Printing EAN 13 In .NET Framework Using Barcode maker for Reporting Service Control to generate, create EAN13 image in Reporting Service applications. Making Code 39 Extended In Java Using Barcode generator for Java Control to generate, create ANSI/AIM Code 39 image in Java applications. 
