The potential downside of relying on a single set of exemplars to estimate state probabilities is that it may yield overly sparse state probability vectors.
Going beyond LocARNA, which sparsifies based on base pair probabilities, SPARSE additionally sparsifies based on conditional probabilities of bases and base pairs within loops (Otto et al., 2014).
For very sparse projections, the probability of at least one false-negative increases with the number of injections (Fig. 5 B).
Applying a classical forward model selection to the features ranked by these selection probabilities, sparse loadings vectors that are parameter estimation consistent as well as model selection consistent can be identified.
The new sensing matrix guarantees unique sparse reconstruction with high probability for sparse signals with uniformly distributed supports.
The similar compact sensing matrix has low coherence, which guarantees a perfect reconstruction of the sparse vector with high probability.
Fortunately, optimization algorithms, such as the basic matching pursuit (MP) [19] and orthogonal matching pursuit (OMP) [20], can exactly recover sparse signals with high probability.
Our analysis shows that when the number of one-bit measurements is sufficiently large, with a high probability the sparse signal can be recovered with an error decaying linearly with the ℓ2-norm of the difference between the quantization thresholds and the original unquantized measurements.
Specifically, a single-injection approach can 1) detect all but the most sparse projections with high probability, 2) provide a reasonable estimate of the connection weight of each pathway (generally within an order of magnitude), and 3) identify some of the sparse connections that are statistically likely to be inconsistent across multiple injections.
In the future, CDMS will allow the user to upload a sparse matrix of conditional probabilities so the calculation of EESN and EESP can be readily modified dynamically using empirically derived conditional probabilities during the tree search as needed.
