The Training Example Lie Bracket
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The Training Example Lie Bracket
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Re: The Training Example Lie Bracket
#2Could this be used for batch filtering?
Re: The Training Example Lie Bracket
#3Could this be used for batch filtering?
Lie brackets are bi-linear so whatever you do per example automatically carries over to sums, the bracket for the batch is just the pairwise brackets for elements in the batch, i.e. {a + b + c, d} = {a, d} + {b, d} + {c, d}. Similarly for the second component.
Re: The Training Example Lie Bracket
#4Eventually ML folks will discover fiber bundles.
Re: The Training Example Lie Bracket
#5Eventually ML folks will discover fiber bundles.
But what bastard "new" name will they give them?
Re: The Training Example Lie Bracket
#6Was hoping for a tournament bracket of best lies found in training data :(
Re: The Training Example Lie Bracket
#7> An ideal machine learning model would not care what order training examples appeared in its training process. From a Bayesian perspective, the training dataset is unordered data and all updates based on seeing one additional example should commute with each other.
One of Andrew Gelman's favorite points to make about science 'as practiced' is that researchers fail to behave this way. There's a gigantic bias in favor of whatever information is published first.
Re: The Training Example Lie Bracket
#8Could this be used for batch filtering?
Lie brackets are bi-linear so whatever you do per example automatically carries over to sums, the bracket for the batch is just the pairwise brackets for elements in the batch, i.e. {a + b + c, d} = {a, d} + {b, d} + {c, d}. Similarly for the second component.
> Similarly for the second component.
Hmm.
{a + b, c + d} = {a, c + d} + {b, c + d} = {a, c} + {a, d} + {b, c} + {b, d}.
{a + b + c, x + y + z} = {a, x + y + z} + {b, x + y + z} + {c, x + y + z} = (a sum of nine direct brackets).
This doesn't look like it will scale well.
Re: The Training Example Lie Bracket
#9Earlier quoted context omitted.
Lie brackets are bi-linear so whatever you do per example automatically carries over to sums, the bracket for the batch is just the pairwise brackets for elements in the batch, i.e. {a + b + c, d} = {a, d} + {b, d} + {c, d}. Similarly for the second component.
> Similarly for the second component. Hmm. {a + b, c + d} = {a, c + d} + {b, c + d} = {a, c} + {a, d} + {b, c} + {b, d}. {a + b + c, x + y + z} = {a, x + y + z} + {b, x + y + z} + {c, x + y + z} = (a sum of nine direct brackets). This doesn't look like it will scale well.
Then don't use the Lie bracket. All bilinear forms scale the same way.
Re: The Training Example Lie Bracket
#10Eventually ML folks will discover fiber bundles.
Sooner if you explain why.