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Hybrid Monte
Carlo can only take small steps because
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the energy
surface is curved.
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With a single
layer of hidden units, it is possible to use
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alternating parallel Gibbs sampling.
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Step
1: each student-t hidden
unit picks a variance
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from
the posterior distribution over variances given
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the
violation produced by the current datavector. If the
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violation
is big, it picks a big variance
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This is
equivalent to picking a Gaussian from an infinite
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mixture of
Gaussians (because thats what a student-t is).
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With
the variances fixed, each hidden unit defines a
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one-dimensional
Gaussians in the dataspace.
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Step
2: pick a visible vector
from the product of all the
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one-dimensional
Gaussians.
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