I've been trying to figure out how to score hypotheses. Do you guys have any
constructive ideas about how to define the way you score hypotheses like
these a little better? I'll define the problem below in detail. I know Abram
mentioned MDL, which I'm about to look into. Does that even apply to this
sort of thing?
I came up with a hypothesis scoring idea. It goes as follows
*Rule 1:* Hypotheses are compared only 1 at a time.
*Rule 2:* If hypothesis 1 predicts/expects/anticipates something, then you
add (+1) to its score and subtract (-1) from hypothesis 2 if it doesn't also
anticipate the observation. (Note:When comparing only 2 hypotheses, it may
actually not be necessary to subtract from the competing hypothesis I
guess.)
*Here is the specific problem I'm analyzing: *Let's say that you have two
window objects that contain the same letter, such as the letter "e". In
frame 0, the first window object is visible. In frame 1, window 1 moves a
bit. In frame 2 though, the second window object appears and completely
occludes the first window object. So, if you only look at the letter "e"
from frame 0 to frame 2, it looks like it never disappears and it just
moves. But that's not what happens. There are two independent instances of
the letter "e". But, how do we get the algorithm to figure this out in a
general way? How do we get it to compare the two possible hypotheses (1
object or two objects) and decide that one is better than the other? That is
what the hypothesis scoring method is for.
*Algorithm Description and Details*
*Hypothesis 1:* there are two separate objects... there are two separate
instances of the letter "e"
*Hypothesis 2:* there is only one letter object... only one letter "e" that
occurs in all the frames of the video.
*Time 0: object 1*
*Time 1: "e" moves rigidly with object 1*
H1: +1 compared to h2 because we expect the e to move rigidly with the
first object, rather than independently from the first object.
H2: -1 compared to h1 because we don't expect the first object to move
rigidly with "e" but h1 does.
*Time 2: object 2 appears and completely occludes object 1. Object 1 and 2
both have the letter "e" on them. So, to a dumb algorithm, it looks as if
the "e" moved between the two frames of the video.*
H1: -1 compared to h2 because we don't expect what h2 expects.
H2: +1 compared to h1 "e" moves independently of the first window
*Time 3: "e" moves rigidly with object 2*
H1: +1 compared to h2 "e" moves with second object.
H2: -1 compared to h1
*Time 4: "e" moves rigidly with object 2*
H1: +1 compared to h2 "e" moves with second object.
H2: -1 compared to h1
*Time 5: "e" moves rigidly with object 2*
H1: +1 compared to h2 "e" moves with second object.
H2: -1 compared to h1
*After 5 video frames the score is: *
H1: +3
H2: -3
Dave
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agi
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