The goal of this task is to forecast the collaboration between pairs of volunteers on a monthly basis over a 6-month period, ranging from August 2021 to February 2022.

## Submission Format

- The file should contain two columns named `Id` and `Predicted`.
- The `Id` column should consist of three hyphen-connected elements. These elements represent pairwise volunteers and a timestep `i` ranging from 0 to 5, indicating the prediction for the next `i-th` month.
- Each `Predicted` value in the file represents the probability of collaboration between the corresponding two participants.

The file should contain a header and have the following format. Also, a sample submission form is given at [Data](https://www.kaggle.com/competitions/MLSP2023-volunteers-02/data?select=sample_submission_collaboration_multistep.csv) Page. 
```
Id,Predicted
122028-204227-0,0.7
185807-155353-3,0.3
185807-155353-5,0.4
```

## Area Under Receiver Operating Characteristic Curve (AUC-ROC Curve)

The evaluation metric for this competition is the [Area Under Receiver Operating Characteristic Curve (AUC-ROC Curve)](https://towardsdatascience.com/understanding-auc-roc-curve-68b2303cc9c5). The AUC-ROC curve is a graphical representation of the performance of a binary classification model. It plots the True Positive Rate (TPR) against the False Positive Rate (FPR) for different classification thresholds. The area under this curve, known as AUC-ROC, is commonly used as a metric to evaluate the model's performance.

### Formula

The TPR and FPR are calculated using the following formulas:

TPR = TP / (TP + FN)

FPR = FP / (FP + TN)

Where:
- TP (True Positives): The number of positive instances correctly classified as positive.
- FN (False Negatives): The number of positive instances incorrectly classified as negative.
- FP (False Positives): The number of negative instances incorrectly classified as positive.
- TN (True Negatives): The number of negative instances correctly classified as negative.

### Properties

- The AUC-ROC value ranges between 0 and 1, where a higher value indicates better performance. An AUC-ROC of 0.5 suggests a random classifier, while an AUC-ROC of 1 indicates a perfect classifier.
- The curve is generated by varying the classification threshold and calculating the corresponding TPR and FPR values.
- The AUC-ROC curve is commonly used in machine learning to compare different models or to optimize classification thresholds.
- AUC-ROC is insensitive to class imbalance, making it a suitable metric when dealing with imbalanced datasets.
- The AUC-ROC curve is a useful tool for visualizing the trade-off between sensitivity and specificity in a classification model.

### Interpretation

By examining the AUC-ROC curve, you can determine how well your model is performing across different classification thresholds. The curve's shape can provide insights into the model's behavior and its ability to discriminate between positive and negative instances.

A model with a curve closer to the top-left corner indicates higher overall accuracy, while a curve closer to the diagonal line suggests poor performance.

Remember that the AUC-ROC curve is just one tool for evaluating model performance, and it should be used in conjunction with other metrics and domain knowledge to make informed decisions.