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Results tagged with pr.probability
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user 41082
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
7
votes
1
answer
2k
views
Exponential tail bounds without the moment generating function
As an exercise, I thought I would try to prove some classical Chernoff bounds without ever using the moment generating function, but then found myself getting stuck in certain places. Before I state m …
- 231
3
votes
Exponential tail bounds without the moment generating function
Ok, I figured out the answer to my own question, though without the $\ln(ep K^2/\sigma^2)$ in the denominator. I'll see whether I can get that later (or maybe someone else sees it?). We can assume wit …
- 231
2
votes
bilinear form tail bound
The Hanson-Wright inequality says
$$
\mathop{\mathbb{P}}_{u,v}(|u^T A v| > t) \le C\cdot \max\left\{e^{-c t^2/\|A\|_F^2}, e^{-c t/\|A\|}\right\}
$$
where $\|\cdot\|$ is the largest singular value and …
- 231
1
vote
bound the tail distribution
Exponential tail bounds automatically imply moment bounds and vice versa. That is to say, $(a)$ is equivalent to $(A)$ for $a\in \{j,k,l\}$ below where $X$ is a nonnegative random variable and $\|X\|_ …
- 231