Score calculation (what the model computes)

• The model first computes a score for an input by taking a weighted sum of features plus a bias.

• This score is a single number that tells the model how “positive” or “negative” the input looks.

  $$ \begin{align*} \text{score}(x) &= w_0 + w_1 x_1 + w_2 x_2 + \dots + w_p x_p \end{align*} $$

• Here $x_i$ are the feature values and $w_i$ are the weights (coefficients).

  

What is $x_i$ (feature value)

• $x_i$ is the numeric value of the $i^{th}$ feature.
• Example in a sentiment model: a feature could be the count (or presence) of the word “awesome” in a review. Then $x_{\text{awesome}}$ = number of times “awesome” appears (or 0/1 for presence).
• Features can be counts, binary flags, normalized numbers, etc.

What is $w_i$ (weight / coefficient)

• $w_i$ is the importance the model gives to feature $x_i$.
• If $w_i > 0$, that feature pushes the score toward the positive class.
• If $w_i < 0$, that feature pushes the score toward the negative class.
• If $w_i \approx 0$, that feature has little effect.

Examples:

• “amazing” → $w_{\text{amazing}}$ = +2.5 (strong positive)
• “awful” → $w_{\text{awful}}$ = -3.1 (strong negative)