Learning Stationary Time Series using Gaussian Processes with Nonparametric Kernels [ 1 ]
نویسندگان
چکیده
a0 exp ✓ c0 + b 2 0 4a0 ◆ (1) Z R exp a1⌧ 1 a2⌧ 2 + b12⌧1⌧2 + b1⌧1 + b2⌧2 + c1 d⌧ = 2⇡ p 4a1a2 b12 exp ✓ c1 + a1b 2 1 + a2b 2 2 + b1b12b2 4a1a2 b12 ◆ (2) where a0, a1, a2 > 0 and b0, b1, b2, b12, c0, c1 2 R are constants. 1 Derivation of the kernel K f |h — given the filter function h The covariance function K f |h(t1, t2) of the random variable f |h, t 2 R is given by K f |h(t1, t2) = E [f(t1)f(t2)|h] = E Z R2 h(t1 ⌧1)h(t2 ⌧2)x(⌧1)x(⌧2)d⌧1⌧2 h
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