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| Both sides previous revisionPrevious revisionNext revision | Previous revisionLast revisionBoth sides next revision | ||
| data_mining:neural_network:loss_functions [2019/11/10 00:10] – [Binary cross entropy] phreazer | data_mining:neural_network:loss_functions [2019/11/10 00:31] – [Binary cross entropy] phreazer | ||
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| $-(y log(\hat{y}) + (1-y) log(1-\hat{y})$ | $-(y log(\hat{y}) + (1-y) log(1-\hat{y})$ | ||
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| + | or | ||
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| + | $-1/N \sum_{i=1}^N (y_i log(\hat{y_i}) + (1-y_i) log(1-\hat{y_i})$ | ||
| (Negative log, since log in [0,1] is < 0) | (Negative log, since log in [0,1] is < 0) | ||
| Line 34: | Line 38: | ||
| For an algo we need to find closes $p$ for $q$ by minimizing cross-entropy. | For an algo we need to find closes $p$ for $q$ by minimizing cross-entropy. | ||
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| + | In training we have $N$ samples. For one particular example the distribution is known to which class it belongs. The loss function should minimize the average cross-entropy. | ||