Timeline for Concentration of Sample Mode
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 3, 2019 at 5:21 | comment | added | Chandramouli | I am looking for a bound that depends on $\epsilon, n, L$ and preferably not on $f$ | |
| Sep 3, 2019 at 5:02 | comment | added | Chandramouli | Let $X_{1}, X_{2}, X_{3}, \cdots $ are i.i.d with probability mass function $f:\{1,2,\cdots, L\} \rightarrow [0,1]$. Suppose that $f$ has a unique mode i.e there exists unique $m$ such that $p_m=\displaystyle\max^{L}_{i=1}p_i$. Let $E^{i}_{n}=\{k: X_k=i, 1\leq k\leq n \}$. Let $M_n$ be sample mode of $n$ samples i.e. $M_{n}:=\displaystyle\arg\max^L_{i=1}|E^{i}_{n}|$ (if there is a tie we take the smaller index). Is there a result that bounds $Pr(|M_n-m|>\epsilon)$ interms of $\epsilon$? | |
| Aug 31, 2019 at 5:26 | comment | added | Yuval Peres | Can you state a precise version of your question? | |
| Aug 31, 2019 at 1:19 | comment | added | Chandramouli | $f$ is a discrete distribution. Could you direct me to some type of mode concentration results? I will try to figure out if they can be modified to my problem | |
| Aug 30, 2019 at 13:15 | comment | added | Iosif Pinelis | How do you define the sample mode? Is the underlying distribution, from which you sample, discrete? Even if so, what other conditions on that distribution are known? In view of re-scaling, it is easy to see that without additional conditions no concentration bound on the sample mode exists. | |
| Aug 30, 2019 at 8:38 | history | asked | Chandramouli | CC BY-SA 4.0 |