A method for comparing hypotheses in explanatory-based reasoning: *

We prefer the hypothesis or explanation that ***expects* more observations.
If both explanations expect the same observations, then the simpler of the
two is preferred (because the unnecessary terms of the more complicated
explanation do not add to the predictive power).*

*Why are expected events so important?* They are a measure of 1) explanatory
power and 2) predictive power. The more predictive and the more explanatory
a hypothesis is, the more likely the hypothesis is when compared to a
competing hypothesis.

Here are two case studies I've been analyzing from sensory perception of
simplified visual input:
The goal of the case studies is to answer the following: How do you generate
the most likely motion hypothesis in a way that is general and applicable to
*Case Study 1)* Here is a link to an example: animated gif of two black
squares move from left to right<http://practicalai.org/images/CaseStudy1.gif>.
*Description: *Two black squares are moving in unison from left to right
across a white screen. In each frame the black squares shift to the right so
that square 1 steals square 2's original position and square two moves an
equal distance to the right.
*Case Study 2) *Here is a link to an example: the interrupted
*Description:* A single square is moving from left to right. Suddenly in the
third frame, a single black square is added in the middle of the expected
path of the original black square. This second square just stays there. So,
what happened? Did the square moving from left to right keep moving? Or did
it stop and then another square suddenly appeared and moved from left to

*Here is a simplified version of how we solve case study 1:
*The important hypotheses to consider are:
1) the square from frame 1 of the video that has a very close position to
the square from frame 2 should be matched (we hypothesize that they are the
same square and that any difference in position is motion).  So, what
happens is that in each two frames of the video, we only match one square.
The other square goes unmatched.
2) We do the same thing as in hypothesis #1, but this time we also match the
remaining squares and hypothesize motion as follows: the first square jumps
over the second square from left to right. We hypothesize that this happens
over and over in each frame of the video. Square 2 stops and square 1 jumps
over it.... over and over again.
3) We hypothesize that both squares move to the right in unison. This is the
correct hypothesis.

So, why should we prefer the correct hypothesis, #3 over the other two?

Well, first of all, #3 is correct because it has the most explanatory power
of the three and is the simplest of the three. Simpler is better because,
with the given evidence and information, there is no reason to desire a more
complicated hypothesis such as #2.

So, the answer to the question is because explanation #3 expects the most
observations, such as:
1) the consistent relative positions of the squares in each frame are
2) It also expects their new positions in each from based on velocity
3) It expects both squares to occur in each frame.

Explanation 1 ignores 1 square from each frame of the video, because it
can't match it. Hypothesis #1 doesn't have a reason for why the a new square
appears in each frame and why one disappears. It doesn't expect these
observations. In fact, explanation 1 doesn't expect anything that happens
because something new happens in each frame, which doesn't give it a chance
to confirm its hypotheses in subsequent frames.

The power of this method is immediately clear. It is general and it solves
the problem very cleanly.

*Here is a simplified version of how we solve case study 2:*
We expect the original square to move at a similar velocity from left to
right because we hypothesized that it did move from left to right and we
calculated its velocity. If this expectation is confirmed, then it is more
likely than saying that the square suddenly stopped and another started
moving. Such a change would be unexpected and such a conclusion would be

I also believe that explanations which generate fewer incorrect expectations
should be preferred over those that more incorrect expectations.

The idea I came up with earlier this month regarding high frame rates to
reduce uncertainty is still applicable. It is important that all generated
hypotheses have as low uncertainty as possible given our constraints and
resources available.

I thought I'd share my progress with you all. I'll be testing the ideas on
test cases such as the ones I mentioned in the coming days and weeks.


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