CalTech machine learning video 5 note , training vs. testing
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start CalTech machine learning, video 5
training vs testing
7:14 2014-09-23
training => testing
7:44 2014-09-23
key notion: break point
7:45 2014-09-23
final examination: training => testing
7:47 2014-09-23
this guarantee is not a guarantee at all:
M is too big!
7:55 2014-09-23
they could be independent which means they
could be proportionally overlapping
7:59 2014-09-23
where did the M come from?
7:59 2014-09-23
the overlap is so significant
8:00 2014-09-23
can we improve on M?
bad events are very overlapping
8:06 2014-09-23
Ein // in-sample error
8:12 2014-09-23
What are we going to replace with?
8:13 2014-09-23
What can we replace M with?
8:15 2014-09-23
input space
8:15 2014-09-23
the count should reflect the strength
of the hypothesis set.
8:18 2014-09-23
dichotomies // dichotomy
8:19 2014-09-23
Dichotomies: mini-hypotheses
8:23 2014-09-23
dichotomies are also hypotheses, but the domain
are not the full input space, just a few points
8:24 2014-09-23
why dichotomies?
#hypotheses |H| can be infinite,
#dichotomies can be FINITE
8:28 2014-09-23
the growth function:
the growth function counts the most dichotomies
8:30 2014-09-23
I give you the N budgts, you choose where to
put the points
8:31 2014-09-23
mH(N) // growth functions
counts the most number of dichotomies
8:36 2014-09-23
perceptron dichotomy
8:38 2014-09-23
positive rays
8:46 2014-09-23
positive intervals
9:01 2014-09-23
can we shatter this set?
9:13 2014-09-23
What we're trying to do is to replace M.
replace M by mH(N)
9:15 2014-09-23
once you declare that the hypotheses set
has a polynomial growth function, we can
declare that learning is feasible using that
hypotheses set.
9:18 2014-09-23
growth function is polynomial => good // learning is feasible
9:19 2014-09-23
with probability assurance
9:19 2014-09-23
key point: break point
9:20 2014-09-23
break point of H: // break point of a hypothses set
Definition:
If no data set of size k can be shattered by H.
then k is a break point for H.
9:22 2014-09-23
just view "break point" as the capability of H(hypothese set)
9:22 2014-09-23
"data set" can be "shattered" by "hypotheses set"
9:23 2014-09-23
main results:
no break point => exp(2, n)
any break point => polynomial
9:31 2014-09-23
this is a remarkable result
training vs testing
7:14 2014-09-23
training => testing
7:44 2014-09-23
key notion: break point
7:45 2014-09-23
final examination: training => testing
7:47 2014-09-23
this guarantee is not a guarantee at all:
M is too big!
7:55 2014-09-23
they could be independent which means they
could be proportionally overlapping
7:59 2014-09-23
where did the M come from?
7:59 2014-09-23
the overlap is so significant
8:00 2014-09-23
can we improve on M?
bad events are very overlapping
8:06 2014-09-23
Ein // in-sample error
8:12 2014-09-23
What are we going to replace with?
8:13 2014-09-23
What can we replace M with?
8:15 2014-09-23
input space
8:15 2014-09-23
the count should reflect the strength
of the hypothesis set.
8:18 2014-09-23
dichotomies // dichotomy
8:19 2014-09-23
Dichotomies: mini-hypotheses
8:23 2014-09-23
dichotomies are also hypotheses, but the domain
are not the full input space, just a few points
8:24 2014-09-23
why dichotomies?
#hypotheses |H| can be infinite,
#dichotomies can be FINITE
8:28 2014-09-23
the growth function:
the growth function counts the most dichotomies
8:30 2014-09-23
I give you the N budgts, you choose where to
put the points
8:31 2014-09-23
mH(N) // growth functions
counts the most number of dichotomies
8:36 2014-09-23
perceptron dichotomy
8:38 2014-09-23
positive rays
8:46 2014-09-23
positive intervals
9:01 2014-09-23
can we shatter this set?
9:13 2014-09-23
What we're trying to do is to replace M.
replace M by mH(N)
9:15 2014-09-23
once you declare that the hypotheses set
has a polynomial growth function, we can
declare that learning is feasible using that
hypotheses set.
9:18 2014-09-23
growth function is polynomial => good // learning is feasible
9:19 2014-09-23
with probability assurance
9:19 2014-09-23
key point: break point
9:20 2014-09-23
break point of H: // break point of a hypothses set
Definition:
If no data set of size k can be shattered by H.
then k is a break point for H.
9:22 2014-09-23
just view "break point" as the capability of H(hypothese set)
9:22 2014-09-23
"data set" can be "shattered" by "hypotheses set"
9:23 2014-09-23
main results:
no break point => exp(2, n)
any break point => polynomial
9:31 2014-09-23
this is a remarkable result
0 0
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