To overcome this limitation, we reformulate the problem of unconstrained optimization into a biologically justified constrained (conditional) optimization problem.
To estimate edge set E ^, we have to determine the node neighborhoods of all nodes in V. To achieve this goal, we solve a sparsity constrained conditional maximum likelihood estimation problem: (8) min U, W ∑ s ∈ V ℓ s (U, W ; D ) + α (Reg (U ) + Reg (W ) ).
When this occurs, a negative binomial model, which does not constrain the conditional variance to equal the mean, is preferred over a Poisson Model [ 29, 30].
This is a generalization of EM algorithm where the E step remains the same butthe M step is replaced by CM (constrained or conditional maximization) step.
Partial correlations can be estimated assuming that the observations follow a graphical Gaussian model, in which (Sigma) is constrained by the conditional independence described by a graph (see e.g. [13]).
The most promising approach was constraining migrant contributions while maximizing the conditional probability that two alleles randomly chosen from the offspring population are not identical by descent, given that both descend from native founders.
We instead use conditional entropy constrained scalar quantizers (CEC-SQ), designed by modifying the algorithm in [27] to accommodate a conditional entropy constraint similar to CEC-TCQ approach above.
For practical implementation of SP-DTCs, the idea of using conditional entropy constrained (CEC) quantizers followed by Slepian-Wolf coding is explored.
In order practically implement this approach, we introduce the idea of designing conditional entropy constrained TCQ (CEC-TCQ) based on analytically found bit-allocations.
When we compared T1 and T2 profiles with those obtained with T1 and T2 models constrained to have baseline conditional health indicator probabilities, the concordance in how individuals are grouped reaches 90% at T1, and 88% at T2.
