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We broke the least-squares error into three separate terms:

$$
\mathbf{E}\left[\left(y-f_\theta(x)\right)^2\right]=\mathbf{E}\left[(y-h(x))^2\right]+\mathbf{E}\left[\left(h(x)-f_\theta(x)\right)^2\right]+\mathbf{E}\left[\left(f_\theta(x)-\mathbf{E}\left[f_\theta(x)\right]\right)^2\right]
$$

where $y=h(x)+\epsilon, h(x)$ is the true model and $\epsilon$ is zero-mean noise. For each of the following terms, indicate its usual interpretation in the bias variance trade-off:

 

Column 1Column 2
(i) $\mathbf{E}\left[(y-h(x))^2\right]$a. Bias
(ii)$\mathbf{E}\left[\left(h(x)-f_\theta(x)\right)^2\right]$b. Variance
(iii) $\mathbf{E}\left[\left(f_\theta(x)-\mathbf{E}\left[f_\theta(x)\right]\right)^2\right]$c. Noise
  1. (i)-c, (ii)-b, (iii)-a
  2. (i)-c, (ii)-a, (iii)-b
  3. (i)-b, (ii)-c, (iii)-a
  4. (i)-c, (ii)-a, (iii)-b

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