Pairwise InPhyNet

What is the pairwise algorithm?

The inphynet(D, constraints, namelist) function will always provide valid output so long as the networks in constraints are valid semi-directed, level-1 networks. The main InPhyNet algorithm attempts to utilize all of the data in D and constraints simultaneously, but when there are more than 2 constraint networks, this process occassionally fails. InPhyNet still returns a valid network because, when this process fails, a backup version of the InPhyNet algorithm is run that works as follows:

1. Instead of merging all constraints simultaneously, merge constraints[1] and constraints[2] into a new intermediate network Nhat12 (using the portions of D and namelist that pertain only to these constraints).
2. Remove constraints[1] and constraints[2] from the list of constraints.
3. Add Nhat12 to the list of constraints.
4. Repeat until constraints has only 1 network remaining: this network is the final inferred network.

The main InPhyNet algorithm is guaranteed to return a valid network when 2 constraints are provided, so this "pairwise" algorithm is thereby also guaranteed to return a valid network. This algorithm is implemented in the internal function InPhyNet.inphynetpairwise.

Example where the pairwise algorithm is needed

Here, we provide an example where a merge conflict would arise without inphynetpairwise. A visual depiction and deeper explanation of this example is given in the Appendices of the InPhyNet manuscript (see here for a citation containing a URL to the manuscript).

To load the data for this example, you can use the loadconflictexample function as follows:

using InPhyNet
loadconflictexample()
inphynet(D, constraints, namelist; refuse_pairwise=true)	# this will give an error
inphynet(D, constraints, namelist)							# this will return a network

Checking whether the pairwise algorithm was used

In some cases, it may be desirable to know whether or not the pairwise algorithm was needed as a fallback. For example, failure of the main algorithm may indicate that the pairwise distance matrix D and the networks in constraints do not align very well with one another. For analyses only seeking to infer a single network, this is straightforward and can be conducted as shown in the code snippet above. For larger studies, though, this approach is wasteful as both calls to inphynet will run the initial algorithm before falling back to the pairwise algorithm. In such a case, the following more efficient strategy may be preferred:

global used_pairwise = false
global Nhat
try
	global Nhat = inphynet(D, constraints, namelist; refuse_pairwise=true)
catch
	global used_pairwise = true
	global Nhat = InPhyNet.inphynetpairwise(D, constraints, namelist)
end

In the example we circumvent the need to redo the work of the initial InPhyNet algorithm by calling the internal function InPhyNet.inphynetpairwise directly.