Python Divide by Zero Encountered in Log – Logistic Regression
In logistic regression, the sigmoid function, which predicts the probability of an event occurring, utilizes the natural logarithm. A divide by zero error during this calculation can arise, leading to model training failures.
Understanding the Problem
The logistic regression model’s core function is the sigmoid function, defined as:
| Sigmoid(z) = 1 / (1 + exp(-z)) |
|---|
Where ‘z’ represents a linear combination of features and their respective coefficients. During the model training process, the algorithm attempts to optimize these coefficients. The optimization process relies on gradient descent, which involves calculating derivatives of the cost function.
Where the Error Occurs
The error occurs when the sigmoid function encounters a value of ‘z’ that results in ‘exp(-z)’ being zero. This leads to a divide-by-zero error during the computation of the sigmoid function.
Causes
- Data Issues: Highly skewed data where a feature exhibits extreme values, leading to ‘z’ becoming excessively large or small.
- Feature Scaling: Insufficient or incorrect scaling of features can result in large magnitude values in ‘z’.
- Numerical Precision: The floating-point representation of numbers in computers has limitations, leading to near-zero values being treated as zero.
Solutions
- Data Preprocessing:
- Feature scaling (e.g., standardization or normalization) can mitigate extreme values.
- Handling outliers using techniques like Winsorization or trimming.
- Regularization: L1 or L2 regularization can prevent overfitting and reduce the impact of extreme values.
- Numerical Stability:
- Using numerical libraries like NumPy with advanced numerical stability features.
- Employing techniques like adding a small constant (epsilon) to the denominator to avoid division by zero.
- Debugging and Analysis: Examining the values of ‘z’ and identifying potential causes of extreme values can guide troubleshooting.
Example and Solution
Consider a dataset with a feature ‘feature1’ exhibiting extreme values.
Example Code
import numpy as np from sklearn.linear_model import LogisticRegression X = np.array([[1, 100000], [2, 5], [3, 10], [4, 150000]]) y = np.array([0, 1, 0, 1]) model = LogisticRegression() model.fit(X, y)
This code might encounter a divide by zero error during model training. To address this, we can scale the feature ‘feature1’.
Solution Code
import numpy as np from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import StandardScaler X = np.array([[1, 100000], [2, 5], [3, 10], [4, 150000]]) y = np.array([0, 1, 0, 1]) scaler = StandardScaler() X_scaled = scaler.fit_transform(X) model = LogisticRegression() model.fit(X_scaled, y)
Scaling ‘feature1’ using StandardScaler helps mitigate extreme values and prevent the divide by zero error.
Conclusion
Encountering a divide by zero error in logistic regression typically stems from issues with data preprocessing and feature scaling. Addressing these concerns through appropriate techniques can ensure the successful training of your logistic regression model.