MathJax

Wednesday, July 22, 2015

Concentration of measure

To characterize the deviation of a random quantity (typically a general function of weakly correlated variables) from it's mean.  

One can look at
  • the tail end probability (moment method and chernoff's bound)
  • the stability about it's mean (i.e. \mathbb{P}\{ \left| \frac{Z}{\mathbb{E}Z} -1 \right| > \epsilon\})
  • the bounded difference (\mathbb{P}[ | Z - \mathbb{E}Z | > t ])

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