# Sentiment Analysis and Logistic Regression

Suppose we want to classify a review as good ($$1$$) or bad ($$0$$). We have a training data set of $$10,000$$ reviews. Also suppose we have a vocabulary of $$100,000$$ words $$w_1, \dots, w_{100,000}$$. So the data is a matrix of dimension $$100,000 \times 10,000$$. Let's represent each of the words in the reviews using a bag-of-words approach over tf-idf values. Also we normalize the rows such that they sum to $$1$$. In a logistic regression approach would we have $$10,000$$ different logistic regression models as follows:

$$\log \left(\frac{p}{1-p} \right)_{1} = \beta_{0_{1}} + \beta_{1_{1}}w_{11} + \dots + \beta_{100,000_{1}}w_{100,000} \\ \vdots \\ \log \left(\frac{p}{1-p} \right)_{10,000} = \beta_{0_{10,000}} + \beta_{1_{10,000}}w_{11} + \dots + \beta_{100,000_{10,000}}w_{100,000}$$

So are we estimating $$100,000 \times 10,000$$ coefficients?