Difference between revisions of "Binary cross-entropy loss"
KevinYager (talk | contribs) (Created page with "The binary cross-entropy loss is given by: :<math> L = - \frac{1}{m} \sum_{i=1}^{m} \left[ y_i \cdot \log{ (\hat{y_i}) } + (1-y_i) \cdot \log{ (1-\hat{y_i}) } \right] </math>...") |
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L = - \frac{1}{m} \sum_{i=1}^{m} \left[ y_i \cdot \log{ (\hat{y_i}) } + (1-y_i) \cdot \log{ (1-\hat{y_i}) } \right] | L = - \frac{1}{m} \sum_{i=1}^{m} \left[ y_i \cdot \log{ (\hat{y_i}) } + (1-y_i) \cdot \log{ (1-\hat{y_i}) } \right] | ||
</math> | </math> | ||
| − | for <math>m</math> training examples (indexed by <math>i</math>) where <math>y_i</math> is the class label (0 or 1) and <math>\hat{y_i}</math> is the prediction for that example (i.e. the predicted probability that it is a positive example). Thus <math>1-\hat{y_i}</math> is the probability that it is a negative example. | + | for <math>m</math> training examples (indexed by <math>i</math>) where <math>y_i</math> is the class label (0 or 1) and <math>\hat{y_i}</math> is the prediction for that example (i.e. the predicted probability that it is a positive example). Thus <math>1-\hat{y_i}</math> is the probability that it is a negative example. Note that we are adding |
Revision as of 15:37, 3 February 2023
The binary cross-entropy loss is given by:
![{\displaystyle L=-{\frac {1}{m}}\sum _{i=1}^{m}\left[y_{i}\cdot \log {({\hat {y_{i}}})}+(1-y_{i})\cdot \log {(1-{\hat {y_{i}}})}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2cc7893dd2d25f4f49ccea803f1a1a99b4940bc9)
for training examples (indexed by ) where is the class label (0 or 1) and is the prediction for that example (i.e. the predicted probability that it is a positive example). Thus is the probability that it is a negative example. Note that we are adding
