Debug Binary Logistic Regression Training Code

Question

The candidate is asked to debug a binary logistic regression training code, identifying and correcting errors in the gradient computation and other related functions.

Codemia · Accepted Answer

In this task, I will identify and debug the key issues present in the binary logistic regression training code. The main focus will be on the gradient computation, as it is critical for the model's training process. I will also discuss the implications of these errors on the overall model performance.

The primary bug in the code is in the gradient calculation. The correct formula for the gradient of the cross-entropy loss with respect to the weights is:

$$
abla_w L = \frac{1}{m} X^T (h - y)$$

Where:
- $h$ is the predicted probability from the sigmoid function.
- $y$ is the true label.

In the provided code, the gradient was incorrectly computed as `grad = X.T @ h / m`, which completely ignores the true labels. This oversight would lead to incorrect updates to the weights during training.

To correct the gradient calculation, I would modify the `compute_gradient` function as follows:

```python
import numpy as np

def compute_gradient(X, y, w):
    m = len(y)
    h = sigmoid(X @ w)
    grad = (1 / m) * (X.T @ (h - y))
    return grad
```

This adjustment ensures that the gradient reflects the difference between the predicted probabilities and the actual labels, which is essential for effective model training.

If the gradient is incorrectly calculated, the model will not converge properly during training, leading to poor performance. The weights may oscillate or diverge rather than settling into a minimum loss configuration. This highlights the importance of accurately implementing mathematical formulations in machine learning algorithms.

In summary, debugging the logistic regression code involves careful examination of the gradient calculation and ensuring it aligns with theoretical principles. By correcting the gradient computation, the model will be able to learn effectively from the training data, leading to improved accuracy in predictions.

Debug Binary Logistic Regression Training Code

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