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5 votes

What conditions are there on the exponent $p$ such that $\underset{\mu}{\arg\min}\left\{\mathbb E\left\vert X-\mu\right\vert^p\right\} $ must exist?

The choice $p=0$ is the only one such that the arg min in question always exists. For any $p>0$ we can find a distribution $F$ such that $\mathbb{E} \vert X - \mu \vert^p$ does not exist for any $\...
picky_porpoise's user avatar
2 votes

What conditions are there on the exponent $p$ such that $\underset{\mu}{\arg\min}\left\{\mathbb E\left\vert X-\mu\right\vert^p\right\} $ must exist?

Generally, for $E[\vert X-\mu \vert^p]$ to be finite, it is necessary and sufficient that $E[\vert X \vert^p] < \infty$, i.e. that $X \in L^p$ (I think you forgot the expectation in your question), ...
jacques's user avatar
  • 337
1 vote

Why does Bayesian Optimization perform poorly in more than 20 Dimensions?

I think you really want to ask is that, how does standard GP perform, compare to all those HDBO methods. We actually found that Standard BO performs great in High dimensional benchmarks (Standard ...
XZT's user avatar
  • 11
1 vote

How can I determine what values of alpha and kappa to use for Bayesian Optimization?

I would suggest using a Cauchy distribution, if a equals one as you want to analyse the function there is various types of strategy that could be pursued..In such a situation looking at the wave and ...
Vilhjalmur Halldorson's user avatar

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