What is log loss?

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🔹 What is Log Loss?

Log Loss is a performance metric for classification models that output probabilities instead of just class labels.

It measures how far the predicted probability is from the actual label.

• A perfect prediction (probability = 1 for the correct class) gives Log Loss = 0.

• Wrong predictions with high confidence get very high Log Loss.

👉 In short: Log Loss penalizes false predictions more when the model is confident but wrong.

🔹 Formula for Binary Classification

$$\text{Log Loss} = -\frac{1}{N} \sum_{i=1}^{N} \Big( y_i \log(p_i) + (1-y_i) \log(1-p_i) \Big)$$

Where:

• $N$ = number of samples

• $y_i$ = actual label (1 or 0)

• $p_i$ = predicted probability of being class 1

🔹 Example

Suppose we have one sample:

• Actual = 1 (positive class)

• Predicted probability = 0.9

$$\text{Log Loss} = - [1 \cdot \log(0.9)] = 0.105$$

✅ Very low (good prediction).

Now if predicted probability = 0.1 (model is confident in the wrong class):

$$\text{Log Loss} = - [1 \cdot \log(0.1)] = 2.302$$

❌ Much higher penalty.

🔹 Interpretation

• Lower Log Loss = Better model.

• 0 = perfect predictions.

• Values increase as predictions diverge from actual labels.

🔹 Why is it useful?

• Unlike accuracy (which just counts correct/incorrect), Log Loss evaluates the quality of probability estimates.

• Helps in comparing models that output probabilities (like Logistic Regression, Neural Nets, XGBoost).

✅ In short:

Log Loss measures how well a model predicts probabilities. It heavily penalizes confident wrong predictions and rewards well-calibrated probabilities.

Read more :

What is a confusion matrix?

Explain ROC curve and AUC.

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