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Can we devise effective algorithms for learning Bayesian belief networks from training data This question is a focus of much current research Several different settings for this learning problem can be considered First, the network structure might be given in advance, or it might have to be inferred from the training data Second, all the network variables might be directly observable in each training example, or some might be unobservable In the case where the network structure is given in advance and the variables are fully observable in the training examples, learning the conditional probability tables is straightforward We simply estimate the conditional probability table entries just as we would for a naive Bayes classifier In the case where the network structure is given but only some of the variable values are observable in the training data, the learning problem is more difficult This problem is somewhat analogous to learning the weights for the hidden units in an artificial neural network, where the input and output node values are given but the hidden unit values are left unspecified by the training examples In fact, Russell et al (1995) propose a similar gradient ascent procedure that learns the entries in the conditional probability tables This gradient ascent procedure searches through a space of hypotheses that corresponds to the set of all possible entries for the conditional probability tables The objective function that is maximized during gradient ascent is the probability P(D1h) of the observed training data D given the hypothesis h By definition, this corresponds to searching for the maximum likelihood hypothesis for the table entries java gs1-128 Java GS1-128 (UCC/EAN-128) Barcodes Generator for Java
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ZXing does support GS1 - 128 (formerly called EAN - 128 ) but ... is an open source Java barcode generator which supports EAN - 128 / GS1 - 128 . The gradient ascent rule given by Russell et al (1995) maximizes P(D1h) by following the gradient of In P(D Ih) with respect to the parameters that define the conditional probability tables of the Bayesian network Let wi;k denote a single entry in one of the conditional probability tables In particular, let wijk denote the conditional probability that the network variable Yi will take on the value yi, given that its immediate parents Ui take on the values given by uik For example, if wijk is the top right entry in the conditional probability table in Figure 63, then Yi is the variable Campjire, Ui is the tuple of its parents (Stomz,BusTourGroup), yij = True, and uik = (False, False) The gradient of In P(D1h) is given by the derivatives for each of the toijkAs we show below, each of these derivatives can be calculated as method (Listing 11-11) 10:1 sheet, and the debugger console should produce logging results similar to Listing 11-12 java ean 128 Generating a GS1 - 128 (formerly EAN - 128 ) barcode using ZXing ...
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Java EAN 128 Generator library to generate GS1 128 barcode in Java class, JSP , Servlet. Download Free Trial Package | Developer Guide included | Detailed ... For example, to calculate the derivative of In P(D1h) with respect to the upperrightmost entry in the table of Figure 63 we will have to calculate the quantity P(Campf ire = True, Storm = False, BusTourGroup = Falseld) for each training example d in D When these variables are unobservable for the training example d , this required probability can be calculated from the observed variables in d using standard Bayesian network inference In fact, these required quantities are easily derived from the calculations performed during most Bayesian network inference, so learning can be performed at little additional cost whenever the Bayesian network is used for inference and new evidence is subsequently obtained Below we derive Equation (625) following Russell et al (1995) The remainder of this section may be skipped on a first reading without loss of continuity To simplify notation, in this derivation we will write the abbreviation Ph(D) to represent P ( D J h ) Thus, our problem is to derive the gradient defined by the set of derivatives for all i , j, and k Assuming the training examples d in the data set D are drawn independently, we write this derivative as 4,608 11: 4,608 = 1ax W can now f(~) This last step makes use of the general equality introduce the values of the variables Yi and Ui = Parents(Yi), by summing over their possible values yijl and uiu Figure 11-18 1,536 Listing 11-10 This last step follows from the product rule of probability, Table 61 Now consider the the rightmost sum in the final expression above Given that W i j k = Ph(yijl~ik), is nonzero is the term for which j' = j and only term in this sum for which i' = i Therefore 11,520 #import <UIKit/UIKith> @interface AlertsProgressViewController : UIViewController <UIActionSheetDelegate> { } - (IBAction) removeAll: (id) sender; @end Thus, we have derived the gradient given in Equation (625) There is one more item that must be considered before we can state the gradient ascent training procedure In particular, we require that as the weights wijk are updated they must remain valid probabilities in the interval [0,1] We also require that the sum wijk remains 1 for all i , k These constraints can be satisfied by updating weights in a two-step process First we update each wijkby gradient ascent 5,400 Listing 11-11 13,824 java gs1 128 EAN 128 in Java - OnBarcode
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