Singular Learning Theory (2)
Here, we will clarify a road returning from algebraic geometry to statistical learning theory. (1) By the resolution theorem, it is proved that the Gelfand zeta function is meromorphic. (2) The inverse Mellin transform of the zeta function is the state density function. (3) The Laplace transform of the state density function is the partition function. (4) Finally, we elucidate the marginal likelihood using empirical process theory.
Here, we will clarify a road returning from algebraic geometry to statistical learning theory. (1) By the resolution theorem, it is proved that the Gelfand zeta function is meromorphic. (2) The inverse Mellin transform of the zeta function is the state density function. (3) The Laplace transform of the state density function is the partition function. (4) Finally, we elucidate the marginal likelihood using empirical process theory.
This is the road from algebraic geometry to singular learning theory. The inverse Mellin transform of the zeta function is the state density function, whose Laplace transform is the partition function.
This is the road from algebraic geometry to singular learning theory. The inverse Mellin transform of the zeta function is the state density function, whose Laplace transform is the partition function.
The log likelihood function can be understood as an empirical process defined on algebraic variety, which converges to a Gaussian process in distribution.
The log likelihood function can be understood as an empirical process defined on algebraic variety, which converges to a Gaussian process in distribution.
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