Figure 1

The LASSO-Kalman smoother tracker. Top row: parallel architecture of the tracker. The tracking is performed for each gene separately to find its incoming edges. The connectivity matrix $\mathit{A}\left(k\right)=[{\mathit{a}}_1^t;\cdots ;{\mathit{a}}_p^t]$. Bottom row: the LASSO-Kalman smoother: the prior estimate is predicted to give a_k|k-1. The filter is updated with the observations to give the unconstrained estimate a_k|k. The projection operator projects this estimate to enforce the constraint. This procedure is repeated for all time steps k=1,⋯,n. Then, a forward-backward smoother is applied to reduce the covariance of the estimate and lead to the final constrained and smoothed estimate.