Submissions are evaluated using a weighted multi-class logarithmic loss. The overall effect is such that each class is roughly equally important for the final score.
Each object has been labeled with one type. For each object, you must submit a set of predicted probabilities (one for every category). The formula is then
$$\text{Log Loss} = - \left( \frac{\sum^{M}_{i=1} w_{i} \cdot \sum_{j=1}^{N_{i}} \frac{y_{ij}}{N_{i}} \cdot \ln  p_{ij} }{\sum^{M}_{i=1} w_{i}} \right)$$
where N is the number of objects in the class set, M is the number of classes,  \\(ln\\) is the natural logarithm, \\(y_{ij}\\) is 1 if observation (i) belongs to class (j) and 0 otherwise, \\(p_{ij}\\) is the predicted probability that observation \\(i\\) belongs to class \\(j\\).
The submitted probabilities for a given object are not required to sum to one because they are rescaled prior to being scored (each row is divided by the row sum). In order to avoid the extremes of the log function, predicted probabilities are replaced with \\(max(min(p,1-10^{-15}),10^{-15})\\).
## Submission File
For each object ID in the test set, you must predict a probability for each of the different possible classes. The file should contain a header and have the following format:


    object_id,class_6,class_15,class_16,class_42,class_52,class_53,class_62,class_64,class_65,class_67,class_88,class_90,class_92,class_95,class_99
    13,0,0.1,0,0.1,0,0.3,0,0,0,0,0,0.5,0,0,0
    14,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0
    17,0.75,0.23,0,0,0.01,0,0,0,0,0.01,0,0,0,0,0
    etc.