$\mathcal{I}_{n}^{-1}(p)=r$. Moreover, as each agent $n$ is only interested in reconstructing the states of agents in its interest set, the estimate at agent $n$, $\mathbf{x}_{n}(t)\in\mathbb{R}^{\left|\mathcal{I}_{n}\right|},~\forall~t$. At every time instant $t$, an agent $n$ simultaneously fuses information received from the neighbors and the latest sensed information to update its parameter estimate. However, as the interest set of agents in the neighborhood might not be the same as that of the agent itself, the information received from the neighbors needs censoring. Let the message received from agent $l$ at time $t$ be denoted by $\mathbf{x}_{l}(t)\in\mathbb{R}^{\left|\mathcal{I}_{l}\right|}$, where $l\in\Omega_{n}$. The censored message processed by agent $n$, $\mathbf{x}_{l,n}^{r}(t)\in\mathbb{R}^{\left|\mathcal{I}_{n}\right|}$ is generated as follows: [$$\begin{aligned}
            \label{eq:cens_1}
            \mathbf{e}_{j}^{\top}\mathbf{x}_{l,n}^{r}(t)=
            \begin{cases}
            \mathbf{e}_{\mathcal{I}_{l}^{-1}\left(\mathcal{I}_{n}(j)\right)}^{\top}\mathbf{x}_{l}(t) & \mathcal{I}_{n}(j)\in\mathcal{I}_{l}\\
            0 & \mbox{otherwise},
            \end{cases}
            \end{aligned}$$]{} where $\mathbf{e}_{j}$ and $\mathbf{e}_{\mathcal{I}_{l}^{-1}\left(\mathcal{I}_{n}(j)\right)}$ are canonical vectors with $\mathbf{e}_{j}\in\mathbb{R}^{\left|\mathcal{I}_{n}\right|}$ and $\mathbf{e}_{\mathcal{I}_{l}^{-1}\left(\mathcal{I}_{n}(j)\right)}\in\mathbb{R}^{\left|\mathcal{I}_{l}\right|}$. Agent $n$ only wants to use estimates of those states from an agent in its neighborhood which are common to their interest sets. Formally, with agent $l$, agent $n$ only wants to use estimates of the states in the set $\mathcal{I}_{n}\cap\mathcal{I}_{l}$. Similarly, while using the obtained estimate states from the neighbors, only those states in the set $\mathcal{I}_{n}\cap\mathcal{I}_{l}$ are updated. We also define the transformed estimate $\mathbf{x}_{l,n}^{s}(t)\in\mathbb{R}^{\left|\mathcal{I}_{n}\right|}$ at agent $n$, 