Link Reversals
Suppose P and C are
or
nodes within a net, and that P is a
of C. Since there is a link going from P to C, the table for the
two nodes is expressed as probabilities for the states of C,
on the states of P (or a function providing C’s value in terms of P’s
value if the node is deterministic). But sometimes you might want
to know what the probabilities for the states of P are, conditioned on
the states of C.
You can achieve that by doing a net
transform known as link reversal,
which reverses the link from P to C. When that link is reversed,
the other links and the
of C and P are adjusted in such a way that any done after the reversal will yield exactly the same
results as before the reversal. In other words, the of the net does not change when a
link is reversed. The global relationship between the nodes remains
the same; just the local expressions of it have been changed (as is the
case with node absorption). Link
reversal is the probabilistic generalization of function inversion , and
is a good example of Bayes
rule in action.
Adds Links:
During the reversal, Netica may add links to C from the parents
of P, and/or add links to P from the parents of C, which will increase
the complexity of the net (all links added will be confined to P and its
). When links are added, the size of CPTs may
grow significantly, and sometimes enormously. The size of the tables
is the product of the number of states of all the parents, so the size
of each table can grow exponentially. When link reversals result
in a node having many parents, the operation may be slow, or Netica may
report that there is not enough memory available.
Removes Links: Occasionally,
during a reversal, Netica may remove links to C from the parents of P,
and/or remove links to P from the parents of C, resulting in a simpler
net. For example, if reversing a link added other links, then reversing
it again will remove them (assuming all the nodes have nondegenerate CPTs,
and that there are no major rounding inaccuracies).
Simpler Net: Usually when
a net is simpler due to the direction of its links, it provides a better
model of the world. For example: it usually represents true causality
more accurately, it may be better at generalizing, and of course it allows
for faster computation. Sometimes link reversals can be used to
search for more simple nets, given a net that was originally learned from
data. In that case Netica might not always automatically remove
links that should be removed, because although these links will be ,
they will not be completely ineffectual (perhaps because the probability
tables learned are not “exact”). You would have to remove these
weak links by hand.
How To: To
reverse a link you
it and choose Modify →
Reverse Links, or click the
toolbar button. If
a node is
when you click the button, Netica will do all the link reversals necessary
to make all links involving the node point to it. Alternately, you
can
on a link, and choose Reverse
from the menu. Right-clicking on an __unselected__ node gives the
options Links →
Reverse So All Incoming
and Links →
Reverse So All Outgoing, which
will do all the reversals necessary to achieve the stated effect. If
all links are made to point away from the node, then many extra links
may have to be added between the ancestors of the node (not just its Markov
boundary), and Netica may report that there is not enough memory available.
Several Links:
If you have several links to reverse, you can select them all (e.g.
by ctrl-clicking
on them), and then click the button.
The amount of time and memory required to reverse a set of links
depends greatly on the order in which they are reversed. Unless
you know a good order to do the reversals, you should reverse them all
at once rather than one-by-one so that Netica can choose a good order
to do them.
See also Disconnecting
and Reconnecting Links