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Products of
Experts multiply probabilities together. This
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is equivalent to
adding log probabilities.
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Mixture models add contributions in the
probability
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domain.
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Product
models add contributions in the log
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probability
domain. The contributions are energies.
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In a mixture
model, the only way a new component can
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reduce the
density at a point is by stealing mixing
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proportion.
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In a product
model, any expert can veto any point by
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giving that
point a density of zero (i.e. an infinite energy)
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So
its important not to have overconfident experts in a
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product
model.
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Luckily,
vague experts work well because their
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product
can be sharp.
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