The network function \(w : \mathbb{R}^5\to\mathbb{R}\) from Lund and Hansen, 2018
For each penalty model \(\lambda_k\), \(k\in\{1,\ldots,10\}\), the above visualizes the mean aggregated estimate of the network function \(w\). The left column shows the (mean aggregated) estimate of the time aggregated \(w\) given by \[\bar w(x,y,x',y') := \int_{-\tau}^0w(x,y,x',y',t)dt.\] In particular, the top left plot shows the estimate of \(\bar w(\cdot,\cdot,x_m,y_n)\) i.e. the time aggregated effects going out from \((x_m,y_n)\). Note that \((x_m,y_n)\) is indicated with a white dot. Similarly the bottom left plot shows the estimate of \(\bar w(x_m,y_n,\cdot,\cdot)\) i.e. the time aggregated effects going in to \((x_m,y_n)\).
The right column shows the network function \(w\) for a particular delay \(t_l\). The top right plot shows \(w(\cdot,\cdot, x_m,y_n, t_l)\) i.e. the time aggregated effects going out from \((x_m,y_n)\) with delay \(t_l\). The bottom right plot shows \(w(x_m,y_n,\cdot,\cdot, t_l)\) i.e. the time aggregated effects going in to \((x_m,y_n)\) with delay \(t_l\).