Which of the following conditions can lead to logistic regression overfitting the training data?

Question

BlackTom AI · Accepted Answer

Starting with what's given, we need to evaluate the prompt: 'Which of the following conditions can lead to logistic regression overfitting the training data?'

First, note that the provided answer list contains a single item: 'A large number of features relative to the number of training examples.' This aligns with a common understanding in machine learning: when the feature dimensionality is high compared to the number of samples, models like logistic regression can fit noise in the training data, leading to overfitting. The intuition is that with many features, there are more pathways to exactly or nearly perfectly separate or fit the training labels, even if those patterns do not generalize.

Next, consider the nature of overfitting in logistic regression. Overfitting occurs when the model capacity is too large for the amount of data, allowing it to memorize training examples rather than learn generalizable patterns. A high feature-to-sample ratio increases model complexity and the risk of fitting to idiosyncratic noise, which harms performance on unseen data.

If we think about the alternative factors that could influence overfitting (even though they aren’t listed here), such as insufficient regularization, extremely small regularization strength (low C in logistic regression), or noisy labels, these would also contribute to overfitting. Conversely, a reasonable number of features relative to samples and proper regularization tend to mitigate overfitting.

Addressing the prompt’s structure: with only one option provided, we can focus on explaining why that particular condition can lead to overfitting. The reasoning highlights the core concept of model capacity relative to data, the role of feature count, and the generalization risk inherent in high-dimensional spaces.

In summary, recognizing that a large feature count compared to the number of training examples expands the hypothesis space of the model, making it easier to capture noise rather than signal, helps justify why this condition is associated with overfitting in logistic regression.

Note: If there were additional options, we would evaluate each for their potential to cause overfitting, including considerations like regularization strength, data noise, and sample size, to provide a comparative analysis.

COMP90049_2025_SM2 Lecture 8 Gradient Descent & Logistic Regression Practice Quiz

Which of the following conditions can lead to logistic regression overfitting the training data?

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