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If each of the M
experts is a Gaussian with the
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same variance,
the product is a Gaussian with a
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variance of 1/M on each dimension.
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But a product of
lots of Gaussians is just a
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Gaussian
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Adding Gaussians allows us to create
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arbitrarily
complicated distributions.
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Multiplying Gaussians doesn’t.
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So
we need to multiply more complicated
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“experts”.
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