Information Technology Reference
In-Depth Information
Table 12.3
Valid hypotheses per iteration
Number of valid hypotheses
Without learning
With learning
Iteration
Formed
Matched
Formed
Matched
1
41
20
42
40
2
21
21
24
22
3
7
7
3
3
4
1
1
0
0
5
0
0
1
1
By training the system prior to running, the probabilistic values of the generating
hypothesis tends to increase more rapidly compared to its non-training counterpart.
This provides vital information on how to resolve the problem of two hypotheses
competing against one another.
If we have two competing hypotheses (say A and B) and if A increases at a greater
rate compared to B, then A is the most likely hypothesis. It doesn't matter if A has
a lower probabilistic value since its rate of change will cause it to close its gap on B
and eventually will surpass B at some point.
However, it is important to note that since both A and B are competing against one
another, they are really two representations or manifestations of the same thing. The
behavior provided by the trained system merely pinpoints the generating hypothesis
based on experience and the criteria for validation.
Another result is that the generating hypothesis tends to be more stable than
related hypotheses. For example, the trained system where the intended hypothesis
is a factorial, we noticed that the behavior of the factorial hypothesis is stable.
However, there are two other hypotheses where their behavior fluctuates. This would
suggest that the inappropriate hypotheses are either unstable or their confidence level
decrease over time.
The second set of experiments shows the difference between a system with no
learning and one with learning. The table below gives the results of running the system
for 85 samples. The first experiment performs a running assessment calculated on
each sequence and the running probability obtained together with the probability
values in the density-table used to rank concepts. In both cases, the system managed
to generate hypotheses for 70 out of the 85 samples (Table
12.3
).
We ran two experiments on each sample. In the first, we did not employ any
training and learning at all. A predefined ranking of concepts was used and the
system merely traversed the list to build a hypothesis. The iteration is the number
of times it has to traverse the list before a hypothesis was successfully found. The
result shows that it manages to build hypothesis from the first concept in the list for
41 samples, 21 samples have their hypotheses constructed from the second concept,
etc. However, the result also shows a disappointing 20 out of 41 hypotheses actually
matched with the intended (generating) hypothesis.
