A 2D sampling example
We show a 2D sampling example. The dimension of the model space is 2. We assume the ground truth is at the origin and the initial error range is R1 = (8, 2).
Let delta=1.7, sigmamax=1000.
Based on equation (11) in the paper, we have:
R1 = (8, 2) Sigma1 = (4.71 1000)
R2=(2.77 2.00) Sigma2 = (1.63 1.63)
R3=(0.96 0.96) Sigma3 = (0.56 0.56)
The plot of feasible regions defined by R1(black) , R2(red), and R3(green).
The level 1 sampling results. R1 = (8, 2) and Sigma1 = (4.71 1000). The target function q1(C|I) is the normal distribution N(0, Sigma1). The sampling density function is the gradient magnitude of q1(C|I). The metropolis sampling is used to sample training examples.
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The plot of q1(C|I) | The gradient magnitude of q1(C|I) | The sampled points using Metropolis algorithm. |
The level 2 sampling results. R2 = (2.77 2.00) and Sigma2 = (1.63 1.63). The target function q2(C|I) is the normal distribution N(0, Sigma2). The sampling density function is the gradient magnitude of q2(C|I). The metropolis sampling is used to sample training examples.
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The plot of q2(C|I) | The gradient magnitude of q2(C|I) | The sampled points using Metropolis algorithm. |
The level 3 sampling results. R3 = (0.96 0.96) and Sigma3 = (0.56 0.56). The target function q3(C|I) is the normal distribution N(0, Sigma3). The sampling density function is the gradient magnitude of q3(C|I). The metropolis sampling is used to sample training examples.
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The plot of q3(C|I) | The gradient magnitude of q3(C|I) | The sampled points using Metropolis algorithm. |