Logistic Regression

Distinguish the model that calculates probabilities from the criterion that triggers the final alarm to adjust the costs of misses and false alarms.

Starting conditions

The inputs are the provided 12×2 synthetic features; samples whose two features sum to more than 1 belong to Class 1.

Procedure

1. Run the code while distinguishing the values passed to BCEWithLogitsLoss from those after applying Sigmoid.
2. For each sample, record the two features, ground truth, logit, probability, and decision at .5 in a table.
3. Plot the loss curve and show the classes in the 2-dimensional data.

Results to retain

• A 12-row output table and plots of the loss and data.

Starting conditions

Apply Threshold=.35,.5,.65 to the probabilities from the same trained model.

Procedure

1. Calculate TP, FP, FN, and TN separately.
2. Calculate Accuracy, Precision, and Recall, and define how to display cases with a denominator of 0.
3. Choose a threshold for a sensor alarm scenario where you want to reduce missed detections, and explain your reasoning.

Results to retain

• A table of 3 conditions and 3 sentences explaining your choice.

Starting conditions

Assign a weight of 3 to the training loss of Class 1 samples and compare with the baseline model. Keep the inputs, initial seed, and epochs the same.

Procedure

1. Set weights to 3 for Class 1 and 1 for Class 0.
2. Compare decisions at .5 for the weighted model with decisions at .35 for the baseline model.
3. Explain how weighting the training loss differs from changing the decision threshold.

Results to retain

• A comparison table of the two approaches and a brief interpretation.