Abstract
BackgroundMost existing algorithms for modeling and analyzing molecular networks assume a static or time-invariant network topology. Such view, however, does not render the temporal evolution of the underlying biological process as molecular networks are typically “re-wired” over time in response to cellular development and environmental changes. In our previous work, we formulated the inference of time-varying or dynamic networks as a tracking problem, where the target state is the ensemble of edges in the network. We used the Kalman filter to track the network topology over time. Unfortunately, the output of the Kalman filter does not reflect known properties of molecular networks, such as sparsity.ResultsTo address the problem of inferring sparse time-varying networks from a set of under-sampled measurements, we propose the Approximate Kernel RecONstruction (AKRON) Kalman filter. AKRON supersedes the Lasso regularization by starting from the Lasso-Kalman inferred network and judiciously searching the space for a sparser solution. We derive theoretical bounds for the optimality of AKRON. We evaluate our approach against the Lasso-Kalman filter on synthetic data. The results show that not only does AKRON-Kalman provide better reconstruction errors, but it is also better at identifying if edges exist within a network. Furthermore, we perform a real-world benchmark on the lifecycle (embryonic, larval, pupal, and adult stages) of the Drosophila Melanogaster.ConclusionsWe show that the networks inferred by the AKRON-Kalman filter are sparse and can detect more known gene-to-gene interactions for the Drosophila melanogaster than the Lasso-Kalman filter. Finally, all of the code reported in this contribution will be publicly available.
Highlights
Most existing algorithms for modeling and analyzing molecular networks assume a static or time-invariant network topology
Results we present an empirical analysis of the Approximate Kernel RecONstruction (AKRON)-KF and its smoother, including comparisons to other approaches proposed for detecting the relationships between different genes in a molecular network
Results on synthetic data Synthetic time-varying networks are simulated to evaluate the efficacy of the proposed AKRON-KF(S) on data that we have complete control over
Summary
We present an empirical analysis of the AKRON-KF and its smoother, including comparisons to other approaches proposed for detecting the relationships between different genes in a molecular network. Our experiments make use of the following algorithms for a sparse reconstruction of a time-varying network:. Α needs to be close to one to achieve a high accuracy at edge detection (i.e., (3) will place a large weight on the l1 penalty and a small weigh on the error) Given these results, we choose α = 0.2 for the remainder of the experiments since this value provides a reasonable trade-off between the different statistics that were assessed. These statistics are shown, which again shows the benefit of using the AKRON-KF over the l1-KF. Notice that AKRON used less points and found more correct interactions
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