Example of Real AdaBoosting The training data index x value y value 0 0 1 1 1 1 2 2 1 3 3 1 4 4 1 5 5 1 6 6 1 7 7 1 8 8 1 9 9 1 The weak learner produces hypotheses of the form x v or x v The threshold v is determined to minimize the probability of error over the entire data No sampling Classifier smoothing is performed with 0 00001 Running the algorithm We start with the following probabilities p0 0 1 p1 0 1 p2 0 1 p3 0 1 p4 0 1 p5 0 1 p6 0 1 p7 0 1 p8 0 1 p9 0 1 Iteration 1 h1 I x 2 5 G1 0 3464 c c 1 0 1438 1 5 1545 Z1 0 6946 pi 0 001 0 001 0 001 0 125 0 125 0 125 0 166 0 166 0 166 0 125 fT xi 5 154 5 154 5 154 0 144 0 144 0 144 0 144 0 144 0 144 0 144 ET 0 3 Bound 0 6945523449743416 Iteration 2 h2 I x 5 5 G2 0 2799 c c 2 0 69311 2 2 50334 Z2 0 5598374 pi 0 018 0 018 0 018 0 018 0 018 0 018 0 148 0 148 0 148 0 445 fT xi 2 651 2 651 2 651 2 647 2 647 2 647 0 549 0 549 0 549 0 549 ET 0 1 Bound 0 3888 Iteration 3 h3 I x 8 5 G3 0 16530791883827795 c c 3 1 1065266302597234 3 5 35211775762808 Z3 0 3327263392704587 pi 0 018 0 018 0 018 0 166 0 166 0 166 0 148 0 148 0 148 0 006 fT xi 3 758 3 758 3 758 1 541 1 541 1 541 1 656 1 656 1 656 4 803 ET 0 0 Bound 0 12937610768453509 Iteration 4 h4 I x 5 5 G4 0 2169587316594253 c c 4 1 1084319671449605 4 2 1220492864707183 Z4 0 4339174963707576 pi 0 126 0 126 0 126 0 126 0 126 0 126 0 041 0 041 0 041 0 122 fT xi 2 649 2 649 2 649 2 649 2 649 2 649 3 778 3 778 3 778 2 681 ET 0 0 Bound 0 056138556736667 Iteration 5 h5 I x 2 5 G5 0 2471935882250572 c c 5 5 269832144753351 5 0 7042779787620895 Z5 0 49633095855592646 pi 0 001 0 001 0 001 0 125 0 125 0 125 0 166 0 166 0 166 0 122 fT xi 7 919 7 919 7 919 3 353 3 353 3 353 3 074 3 074 3 074 3 385 ET 0 0 Bound 0 027863303677056195
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