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coolname11
coolname11
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I am trying to understand few of the mathematical steps I have encountered in a paper, there are two of them

(a) $\sum_{m=0}^{\lfloor xs\rfloor} 2 \binom{s}{m} p^m (1-p)^{s-m} \leq 2\exp{\left(-\frac{2(\lfloor xs\rfloor - sp)^2}{s}\right)}$

(b) $\sum_{m= \lfloor xs \rfloor + 1}^s \left(\frac{p}{x}\right)^m \left(\frac{1-p}{1-x}\right)^{s-m} \leq p\exp{\left(-sd(x,p)\right)}$, herewhere $d(\cdot,\cdot)$ is KL Divergence$d(a,b) = a\log{\frac{a}{b}} + (1-a)\log{\frac{1-a}{1-b}}$.

I have searched and tried a lot but could not figure out it. If some one can help or point out some relevant reference it would be helpful.

I am trying to understand few of the mathematical steps I have encountered in a paper, there are two of them

(a) $\sum_{m=0}^{\lfloor xs\rfloor} 2 \binom{s}{m} p^m (1-p)^{s-m} \leq 2\exp{\left(-\frac{2(\lfloor xs\rfloor - sp)^2}{s}\right)}$

(b) $\sum_{m= \lfloor xs \rfloor + 1}^s \left(\frac{p}{x}\right)^m \left(\frac{1-p}{1-x}\right)^{s-m} \leq p\exp{\left(-sd(x,p)\right)}$, here $d(\cdot,\cdot)$ is KL Divergence

I have searched and tried a lot but could not figure out it. If some one can help or point out some relevant reference it would be helpful.

I am trying to understand few of the mathematical steps I have encountered in a paper, there are two of them

(a) $\sum_{m=0}^{\lfloor xs\rfloor} 2 \binom{s}{m} p^m (1-p)^{s-m} \leq 2\exp{\left(-\frac{2(\lfloor xs\rfloor - sp)^2}{s}\right)}$

(b) $\sum_{m= \lfloor xs \rfloor + 1}^s \left(\frac{p}{x}\right)^m \left(\frac{1-p}{1-x}\right)^{s-m} \leq p\exp{\left(-sd(x,p)\right)}$, where $d(a,b) = a\log{\frac{a}{b}} + (1-a)\log{\frac{1-a}{1-b}}$.

I have searched and tried a lot but could not figure out it. If some one can help or point out some relevant reference it would be helpful.

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coolname11
coolname11
  • 141
  • 6

Why is $\sum_{m=0}^x^{\lfloor xs\rfloor} 2 \binom{s}{m} p^m (1-p)^{s-m} \leq 2\exp{\left(-\frac{2(x\lfloor xs\rfloor - sp)^2}{s}\right)}$?

I am trying to understand few of the mathematical steps I have encountered in a paper, there are two of them

(a) $\sum_{m=0}^x 2 \binom{s}{m} p^m (1-p)^{s-m} \leq 2\exp{\left(-\frac{2(x - sp)^2}{s}\right)}$$\sum_{m=0}^{\lfloor xs\rfloor} 2 \binom{s}{m} p^m (1-p)^{s-m} \leq 2\exp{\left(-\frac{2(\lfloor xs\rfloor - sp)^2}{s}\right)}$

(b) $\sum_{m= \lfloor xs \rfloor + 1}^s \left(\frac{p}{x}\right)^m \left(\frac{1-p}{1-x}\right)^{s-m} \leq p\exp{\left(-sd(x,p)\right)}$, here $d(\cdot,\cdot)$ is KL Divergence

I have searched and tried a lot but could not figure out it. If some one can help or point out some relevant reference it would be helpful.

Why is $\sum_{m=0}^x 2 \binom{s}{m} p^m (1-p)^{s-m} \leq 2\exp{\left(-\frac{2(x - sp)^2}{s}\right)}$?

I am trying to understand few of the mathematical steps I have encountered in a paper, there are two of them

(a) $\sum_{m=0}^x 2 \binom{s}{m} p^m (1-p)^{s-m} \leq 2\exp{\left(-\frac{2(x - sp)^2}{s}\right)}$

(b) $\sum_{m= \lfloor xs \rfloor + 1}^s \left(\frac{p}{x}\right)^m \left(\frac{1-p}{1-x}\right)^{s-m} \leq p\exp{\left(-sd(x,p)\right)}$, here $d(\cdot,\cdot)$ is KL Divergence

I have searched and tried a lot but could not figure out it. If some one can help or point out some relevant reference it would be helpful.

Why is $\sum_{m=0}^{\lfloor xs\rfloor} 2 \binom{s}{m} p^m (1-p)^{s-m} \leq 2\exp{\left(-\frac{2(\lfloor xs\rfloor - sp)^2}{s}\right)}$

I am trying to understand few of the mathematical steps I have encountered in a paper, there are two of them

(a) $\sum_{m=0}^{\lfloor xs\rfloor} 2 \binom{s}{m} p^m (1-p)^{s-m} \leq 2\exp{\left(-\frac{2(\lfloor xs\rfloor - sp)^2}{s}\right)}$

(b) $\sum_{m= \lfloor xs \rfloor + 1}^s \left(\frac{p}{x}\right)^m \left(\frac{1-p}{1-x}\right)^{s-m} \leq p\exp{\left(-sd(x,p)\right)}$, here $d(\cdot,\cdot)$ is KL Divergence

I have searched and tried a lot but could not figure out it. If some one can help or point out some relevant reference it would be helpful.

Source Link
coolname11
coolname11
  • 141
  • 6

Why is $\sum_{m=0}^x 2 \binom{s}{m} p^m (1-p)^{s-m} \leq 2\exp{\left(-\frac{2(x - sp)^2}{s}\right)}$?

I am trying to understand few of the mathematical steps I have encountered in a paper, there are two of them

(a) $\sum_{m=0}^x 2 \binom{s}{m} p^m (1-p)^{s-m} \leq 2\exp{\left(-\frac{2(x - sp)^2}{s}\right)}$

(b) $\sum_{m= \lfloor xs \rfloor + 1}^s \left(\frac{p}{x}\right)^m \left(\frac{1-p}{1-x}\right)^{s-m} \leq p\exp{\left(-sd(x,p)\right)}$, here $d(\cdot,\cdot)$ is KL Divergence

I have searched and tried a lot but could not figure out it. If some one can help or point out some relevant reference it would be helpful.