# Q1d · Sentiment with logistic regression

Subject: Natural Language Processing

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/nlp/#tee/papers/legacy-f22/q1d

Canonical: https://deep-learning-study-room.vercel.app/read/nlp/tee/papers/legacy-f22--q1d/

Previous examination · complete worked answers

**Question. Explain sentiment analysis using logistic regression with an example.** [5 marks]

### Answer

Binary logistic regression maps text features x to a probability:



$$
z=w^Tx+b,\qquad P(y=1\mid x)=\sigma(z)=\frac{1}{1+e^{-z}}
$$



Use positive-word count and negative-word count as an illustrative feature vector. With x=(2,1), w=(1,−1), b=0: z=1×2+(−1)×1=1; P(positive)=1/(1+e⁻¹)=0.731059. A declared 0.5 threshold predicts positive. Fit weights from labelled reviews by minimizing cross-entropy; the hand-chosen weights here only illustrate the computation.

Labelled reviews → Tokenize / vectorize → Fit logistic weights → Probability → Threshold / class