Smallest set (typical set)
up vote
0
down vote
favorite
Given the following table of sequences, I'm trying to find the smallest set with probability $p = 0.9$.
The smallest set consists of some sequences from the table, which probability (column 3) should add up to $p$, while the length (found in the second column) is being minimized.
I'm struggling to find a good approach to find the smallest set, without just trying a lot of options and checking their length. Therefore I was wondering if there exists a fast approach to find the smallest set, given such a table.
information-theory
asked Nov 22 at 11:52
Steven Raaijmakers
1175
add a comment |
up vote
0
down vote
favorite
Given the following table of sequences, I'm trying to find the smallest set with probability $p = 0.9$.
The smallest set consists of some sequences from the table, which probability (column 3) should add up to $p$, while the length (found in the second column) is being minimized.
I'm struggling to find a good approach to find the smallest set, without just trying a lot of options and checking their length. Therefore I was wondering if there exists a fast approach to find the smallest set, given such a table.
information-theory
asked Nov 22 at 11:52
Steven Raaijmakers
1175
what you call length is unclear to me. do you mean hamming weight? And why would you minimize it?
– kodlu
Nov 24 at 0:25
And what is the probability parameter in the binomial distribution? You use $p=0.9$ but this is not the $p$ in the equations generating column 3, that looks more like $papprox 15/25,$ judging by the peak in the binomial distribution.
– kodlu
Nov 24 at 0:27
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Given the following table of sequences, I'm trying to find the smallest set with probability $p = 0.9$.
The smallest set consists of some sequences from the table, which probability (column 3) should add up to $p$, while the length (found in the second column) is being minimized.
I'm struggling to find a good approach to find the smallest set, without just trying a lot of options and checking their length. Therefore I was wondering if there exists a fast approach to find the smallest set, given such a table.
information-theory
asked Nov 22 at 11:52
Steven Raaijmakers
1175
Given the following table of sequences, I'm trying to find the smallest set with probability $p = 0.9$.
The smallest set consists of some sequences from the table, which probability (column 3) should add up to $p$, while the length (found in the second column) is being minimized.
I'm struggling to find a good approach to find the smallest set, without just trying a lot of options and checking their length. Therefore I was wondering if there exists a fast approach to find the smallest set, given such a table.
information-theory
information-theory
asked Nov 22 at 11:52
Steven Raaijmakers
1175
asked Nov 22 at 11:52
Steven Raaijmakers
1175
asked Nov 22 at 11:52
Steven Raaijmakers
1175
asked Nov 22 at 11:52
Steven Raaijmakers
1175
asked Nov 22 at 11:52
Steven Raaijmakers
1175
1175
what you call length is unclear to me. do you mean hamming weight? And why would you minimize it?
– kodlu
Nov 24 at 0:25
And what is the probability parameter in the binomial distribution? You use $p=0.9$ but this is not the $p$ in the equations generating column 3, that looks more like $papprox 15/25,$ judging by the peak in the binomial distribution.
– kodlu
Nov 24 at 0:27
add a comment |
what you call length is unclear to me. do you mean hamming weight? And why would you minimize it?
– kodlu
Nov 24 at 0:25
And what is the probability parameter in the binomial distribution? You use $p=0.9$ but this is not the $p$ in the equations generating column 3, that looks more like $papprox 15/25,$ judging by the peak in the binomial distribution.
– kodlu
Nov 24 at 0:27
what you call length is unclear to me. do you mean hamming weight? And why would you minimize it?
– kodlu
Nov 24 at 0:25
what you call length is unclear to me. do you mean hamming weight? And why would you minimize it?
– kodlu
Nov 24 at 0:25
And what is the probability parameter in the binomial distribution? You use $p=0.9$ but this is not the $p$ in the equations generating column 3, that looks more like $papprox 15/25,$ judging by the peak in the binomial distribution.
– kodlu
Nov 24 at 0:27
And what is the probability parameter in the binomial distribution? You use $p=0.9$ but this is not the $p$ in the equations generating column 3, that looks more like $papprox 15/25,$ judging by the peak in the binomial distribution.
– kodlu
Nov 24 at 0:27
add a comment |
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
The smallest set should be (obviously?) formed by picking the most probable sequences.
For that, you should add to your sheet that column (probability of each sequence). In this case, because $p>0.5$, it should be clear that the most probable sequences are in the last rows (greater $k$, greater probability).
Hence you should acummulate the (total) probability of those sequences, until you get your total desired probability.
answered Nov 24 at 1:22
leonbloy
39.9k645107
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
The smallest set should be (obviously?) formed by picking the most probable sequences.
For that, you should add to your sheet that column (probability of each sequence). In this case, because $p>0.5$, it should be clear that the most probable sequences are in the last rows (greater $k$, greater probability).
Hence you should acummulate the (total) probability of those sequences, until you get your total desired probability.
answered Nov 24 at 1:22
leonbloy
39.9k645107
add a comment |
up vote
1
down vote
accepted
The smallest set should be (obviously?) formed by picking the most probable sequences.
For that, you should add to your sheet that column (probability of each sequence). In this case, because $p>0.5$, it should be clear that the most probable sequences are in the last rows (greater $k$, greater probability).
Hence you should acummulate the (total) probability of those sequences, until you get your total desired probability.
answered Nov 24 at 1:22
leonbloy
39.9k645107
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
The smallest set should be (obviously?) formed by picking the most probable sequences.
For that, you should add to your sheet that column (probability of each sequence). In this case, because $p>0.5$, it should be clear that the most probable sequences are in the last rows (greater $k$, greater probability).
Hence you should acummulate the (total) probability of those sequences, until you get your total desired probability.
answered Nov 24 at 1:22
leonbloy
39.9k645107
The smallest set should be (obviously?) formed by picking the most probable sequences.
For that, you should add to your sheet that column (probability of each sequence). In this case, because $p>0.5$, it should be clear that the most probable sequences are in the last rows (greater $k$, greater probability).
Hence you should acummulate the (total) probability of those sequences, until you get your total desired probability.
answered Nov 24 at 1:22
leonbloy
39.9k645107
answered Nov 24 at 1:22
leonbloy
39.9k645107
answered Nov 24 at 1:22
leonbloy
39.9k645107
answered Nov 24 at 1:22
leonbloy
39.9k645107
39.9k645107
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3009042%2fsmallest-set-typical-set%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
what you call length is unclear to me. do you mean hamming weight? And why would you minimize it?
– kodlu
Nov 24 at 0:25
And what is the probability parameter in the binomial distribution? You use $p=0.9$ but this is not the $p$ in the equations generating column 3, that looks more like $papprox 15/25,$ judging by the peak in the binomial distribution.
– kodlu
Nov 24 at 0:27