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Results tagged with approximation-theory
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user 29697
Approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.
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vote
Accepted
Good UPPER bounds for $\log(\sum_{i=1}^n p_ie^{z_i})-\sum_{i=1}^np_iz_i$ where $(p_i)_i$ is ...
One answer - subgaussian variables generalize this property.
Let $\mu = \sum_i p_i z_i$, then the distribution is considered $\sigma^2$-subgaussian if for all $\lambda \in \mathbb{R}$,
$$ \log\left …
- 4,529
4
votes
The relative error of approximating a binomial
Don't forget that far out in the left tail, the Binomial CDF is multiplicatively approximated by the PMF, because terms grow geometrically.
Example. For $t \leq \frac{np}{2}$, we claim $\Pr[X = t] \le …
- 4,529