Generalized Additive Models (GAMs) can be applied to classification problems where the response variable $Y$ is qualitative. Assuming a binary response where $Y$ takes values 0 or 1, let $p(X) = Pr(Y = 1 \mid X)$ be the conditional probability that the response equals one given the predictors. The standard logistic regression model is $\log\left(\frac{p(X)}{1-p(X)}\right) = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \dots + \beta_p X_p$. With GAMs, each linear component $\beta_j X_j$ is replaced by a non-linear function $f_j(X_j)$, resulting in the model: $\log\left(\frac{p(X)}{1-p(X)}\right) = \beta_0 + f_1(X_1) + f_2(X_2) + \dots + f_p(X_p)$.