= (X_{i1},...,X_{ip})$ represents the $p$ features of the $i$-th observation along with indicator variables $D_i = (D_{ij})_{j=1}^p $ such that $$\label{eq:d}
D_{ij} = \begin{cases}
             0, & \text{$X_{ij}$ is missing}\\
             1, & \text{otherwise}.
         \end{cases}$$ Without loss of generality, we can assume for each $i$, the observation $X_i = (X_{ij})_{j=1}^p$ contains $p_0$ categorical features for $j \in \{1,2,...,p_0\}$ and $p_1$ continuous features for $j \in \{p_0+1,...,p_0+p_1\}$ such that $p_0 + p_1 = p$. Let the $j$-th categorical feature contain $k_j$ different values and the $j$-th continuous variable representing the $(p_0 + j)$-th feature of $X_i$, indexed by $j\in\{1,...,p_1\}$ take values from a continuous set $C_j \subset \mathbb{R}$. For each of the categorical features, we can map the $k_j$ different values to the first $k_j$ natural numbers, such that $X \in \{1,...,k_1\} \times ... \times \{1,...,k_{p_0}\} \times C_1 \times ... \times C_{p_1} \subset \mathbb{R}^p$.

In this setting, we can assume that $\{(X_i, Y_i)\}_{i=1}^n$ satisfy the model $$\label{eq:class}
Y_i = g(X_i), \quad i=1, 2,..., n,$$ where $g(.)$ is an unknown function mapping a $p$-dimensional number (belonging to a subspace of $\mathbb{R}^p$) to a discrete set $\mathscr{G}$ representing the class labels and $Y_i \in \mathscr{G}$. We assume that $\mathscr{G}$ contains $m$ values and thus the 