Epsilon Hat

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Note that since AdamOptimizer uses the formulation just before Section 21 of the Kingma and Ba paper rather than the formulation in Algorithm 1 the “epsilon” referred to here is “epsilon hat” in the paper.

$Cov(\hat{\epsilon})$ in a linear regression model Cross

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Is the residual, e, an estimator of the error, $\epsilon

Since X and f ^ are assumed to be fixed and “independent” of ϵ E () pretty much treats them like a constant That means that E [ 2 ϵ ( f ( X) − f ^ ( X))] = E ( ϵ) 2 ( f ( X) − f ^ ( X)) The second thing applies linearity of expectation again The assumption that ϵ has zero mean means that E ( ϵ) equals zero.