Naive Bayes vs Logistic Regression
THE VERDICT
Both are linear-ish, fast text baselines. Naive Bayes trains in one counting pass and shines with tiny training sets; logistic regression needs a bit more data but produces better-calibrated probabilities and tolerates correlated features that break the independence assumption. Start with NB to smoke-test the pipeline in minutes, ship logistic regression once you have a few thousand labelled examples.
[ 01 ] Side by side
| Dimension | Naive Bayes | Logistic Regression |
|---|---|---|
| Family | Classification | Classification |
| Interpretability | High | High |
| Training speed | Fast | Fast |
| Data needed | Small | Small |
| Complexity | Low | Low |
| Training cost | O(n·d) - one counting pass | O(n·d) per iteration |
| Inference cost | O(d), effectively instant | O(d) |
[ 02 ] When to choose each
Choose Naive Bayes when…
- Text classification
- Spam filtering
- Real-time prediction
…but not when
- You need well-calibrated probabilities (NB is famously over-confident - its winner is right, its 0.9999 is not)
- Feature interactions carry the signal ("not good" vs "good")
- Dense correlated numeric features - Gaussian NB gets outclassed fast
How it works: Flip prediction around with Bayes’ rule: how likely would this input be under each class? Assume every feature contributes independently (the "naive" part - obviously false, surprisingly harmless), multiply the per-feature likelihoods with the class prior, and pick the winner. For word counts, this is a few additions per document.
Full Naive Bayes dossier →Choose Logistic Regression when…
- Binary classification
- When probability scores needed
- Interpretable predictions
…but not when
- Decision boundary is strongly non-linear and feature crosses cannot fix it
- Classes are perfectly separable - weights diverge without regularisation
- You have millions of sparse one-hot features but need interactions - trees handle those natively
How it works: Linear regression squeezed through a sigmoid: compute a weighted score, then map it to a probability between 0 and 1. The decision boundary is still a straight line - what changes is that the output is a calibrated "how sure am I", and the weights are trained to make observed labels as likely as possible.
Full Logistic Regression dossier →[ 03 ] Quick answers
Q.01When should I use Naive Bayes instead of Logistic Regression?
Naive Bayes is the better choice for: Text classification; Spam filtering; Real-time prediction. Avoid it when: You need well-calibrated probabilities (NB is famously over-confident - its winner is right, its 0.9999 is not)
Q.02When should I use Logistic Regression instead of Naive Bayes?
Logistic Regression is the better choice for: Binary classification; When probability scores needed; Interpretable predictions. Avoid it when: Decision boundary is strongly non-linear and feature crosses cannot fix it
Q.03Is Naive Bayes or Logistic Regression easier to interpret?
Naive Bayes: high interpretability. Logistic Regression: high interpretability. Both are linear-ish, fast text baselines.