A couple of mistakes in chapter 12.7 Generative linear classifiers

[davidevecchi]

Hello, I found a couple of potential mistakes in the chapter 12.7 about Generative linear classifiers.

• Page 151, at the end:

  $\displaystyle \prod^{K}_{k=1}$ : $x_j$ is a discrete variable with $k$ possible values

  There's a little typo, it should be " $K$ possible values".

• Page 152, at the beginning:

  $θ_{ky_i}$ parameter of the kth value for $y_i$ class. It is the probability that feature $k$ of $x_j$ is true given $y_i$. In essence $θ_{ky_i}$ is raised to the power of $1$ when $x_j$ has the kth feature, otherwise $θ_{ky_i}$ is raised to the power of $0$. (Figure 12.12)

  From my understanding, $k$ is not a feature. Instead, it represents the index of a value within a set of $K$ possible states that the actual feature $x_j$ can take. Therefore, the statement should be revised as:

  $θ_{ky_i}$ parameter of the $k$-th value for $y_i$ class. It is the probability that the feature $x_j$ takes the $k$-th value given $y_i$. In essence $θ_{ky_i}$ is raised to the power of $1$ when $x_j$ is equal to the $k$-th value, otherwise $θ_{ky_i}$ is raised to the power of $0$. (Figure 12.12)

Thank you guys for creating this handbook. I truly appreciate your efforts, and I'm grateful for the excellent outcome.

[StefanoGenettiUniTN]

Thank you for your valuable comment; it is much appreciated. Unfortunately, we do not have the time in this period to update the document due to other obligations. If you'd like, you can make a pull request, and I will gladly accept it to include your suggested modifications.