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appearance. A series of eight objects l =1 ,..., 8 yields the probability of success
P k for object k
8
π l 16 ( t )
P k ( t )=
O kl
·
k
∈{
1 ,..., 8
}
.
(5)
l =1
So, P k
is the final probability the model picks the correct button if object k is
shown.
Before the next learning step, we weight the state probability vectors of all
objects
l ( t ) with the probability to confuse the current object k with object l
π
l update = O kl π
l +(1
l
π
O kl )
π
l =1 ,..., 8and k
∈{
1 ,..., 8
}
.
(6)
We have to consider the chance that the current object k already was confused,
which is the element O kl
O kl for 'confusion'. This
ensures that all state probability vectors are updated even if just object k is
shown since object k might be confused with all other objects. In case of a
perfect recall of objects this step does not change the state probability vectors
since O kl =0if k
for 'no confusion' and 1
= l and O kl =1if k = l .
Figure 2 shows the workflow of the model. Briefly summarised, for every single
object we model a learning process through 16 possible states. The state space is
given by the experimental set up. The state transitions are given by the assumed
policy a subject follows. Further we added three parameters to the model. Each
controls a typical mistake that might occur during trial and error learning in the
experiment. These parameters are: (i) the success recall probability p suc giving
the chance to confuse 'success' and 'failure', (ii) the state recall probability p sr
representing the models ability to remember its previous actions on an object
and (iii) the object recall probability p or indicating the chance to remember the
current object in a later trial.
Figure 3 shows the learning curves of the model for each object in a series of
eight. In this simulation eight objects are shown to the model. The objects are
presented for ten cycles. That is, every single object is shown once per cycle,
Fig. 2. Workflow of the Markov model
 
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