Noisy-Or Classifier

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Logistic discrimination The fundamental assumption of logistic discrimination: log P M (C = 0 | A = a) 1 − P M (C = 0 | A = a) which implies P M (C = 0 | A = a) = = β 0 + ∑ j A data vector a is classified to C = 1 provided β j · a j = β 0 + ∑ β j , j:a j =1 exp(β 0 + ∑ j:a j =1 β j ) 1 + exp(β 0 + ∑ j:a j =1 β j ) . log P M (C = 0 | A = a) 1 − P M (C = 0 | A = a) < 0 .
<strong>Noisy</strong>-or revisited log P M (C = 0 | A = a) = ∑ j = ∑ j:a j =0 = ∑ j log P M (A ′ j = 0 | A j = a j ) p j (0) + p j (0) + ∑ j:a j =1 = r 0 + ∑ r j . j:a j =1 ∑ j:a j =1 p j (1) p j (1) − p j (0) Let r 0 = β 0 − log(1 + exp(β 0 + ∑ j:a j =1 β j )) and r j = β j , j = 1, . . . , k. P M (C = 0 | A = a) = exp(r 0 + ∑ r j ) = exp(β 0 + ∑ j:a j =1 β j ) 1 + exp(β j:a j =1 0 + ∑ j:a j =1 β j ) . This is the formula used in logistic discrimination.
Page 1 and 2: Noisy-Or Classifier Jiří Vomlel L
Page 3 and 4: Learning from the training data - I
Page 5: A ′ 1 A ′ 2 C B . . . A ′ k E
Page 9 and 10: Reuters text collection We have use
Page 11 and 12: Microaverage precision and recall 1
Page 13: Conclusions and future work • Noi

Noisy-Or Classifier

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