Show that $sup_x_1, dots, x_n in mathscrX|mathscrF(x_1, dots, x_n)|=S(mathscrA, n)$ The 2019 Stack Overflow Developer Survey Results Are InShow that the posterior density of ($mu$, $tau$) is equal to $f(mu, tau | x_1, …, x_n) = f(mu| tau, x_1,…,x_n)f(tau|x_1,…x_n)$Show that $T$ is a sufficient statistic.How to calculate the probability that $X_n$ is not the largest observation in the sample?Is it correct to say $textmax(x_1,x_2,dots,x_n)=lim_p to infty fracx_1^p+x_2^p+dots+x_n^px_1^p-1+x_2^p-1+dots+x_n^p-1$Show that X_1,…,X_n are independent.What is the expectation of norm of $[X_1,ldots, X_n]$ where $X_i$ are indpendent complex Gaussian random variablesFind expectation of $fracX_1 + cdots + X_mX_1 + cdots + X_n$ when $X_1,ldots,X_n$ are i.i.dDerive the maximum likelihood equation when only $I[X_1>5], I[X_2 > 5], … , I[X_n > 5]$ are observed.$X_1, X_2, cdots, X_n$ : i.i.d. $sim textBernoulli(p)$. Then $barx$ is an unbiased estimator of $p$.distribution of $sum_i=1^n (X_i-X_n+i)^2$ where $X_1,X_2,dots,X_2n$ are iid $N(mu,sigma^2)$
How come people say “Would of”?
Why does the nucleus not repel itself?
What is this sharp, curved notch on my knife for?
Is it ok to offer lower paid work as a trial period before negotiating for a full-time job?
What does Linus Torvalds mean when he says that Git "never ever" tracks a file?
What is the meaning of Triage in Cybersec world?
The phrase "to the numbers born"?
Why is this code so slow?
Is it ethical to upload a automatically generated paper to a non peer-reviewed site as part of a larger research?
Alternative to の
Can we generate random numbers using irrational numbers like π and e?
How do you keep chess fun when your opponent constantly beats you?
What information about me do stores get via my credit card?
What do I do when my TA workload is more than expected?
Why can I use a list index as an indexing variable in a for loop?
What is the most efficient way to store a numeric range?
Why did Peik say, "I'm not an animal"?
Is there a way to generate a uniformly distributed point on a sphere from a fixed amount of random real numbers?
Are there any other methods to apply to solving simultaneous equations?
What does もの mean in this sentence?
What could be the right powersource for 15 seconds lifespan disposable giant chainsaw?
How did passengers keep warm on sail ships?
Match Roman Numerals
Finding the area between two curves with Integrate
Show that $sup_x_1, dots, x_n in mathscrX|mathscrF(x_1, dots, x_n)|=S(mathscrA, n)$
The 2019 Stack Overflow Developer Survey Results Are InShow that the posterior density of ($mu$, $tau$) is equal to $f(mu, tau | x_1, …, x_n) = f(mu| tau, x_1,…,x_n)f(tau|x_1,…x_n)$Show that $T$ is a sufficient statistic.How to calculate the probability that $X_n$ is not the largest observation in the sample?Is it correct to say $textmax(x_1,x_2,dots,x_n)=lim_p to infty fracx_1^p+x_2^p+dots+x_n^px_1^p-1+x_2^p-1+dots+x_n^p-1$Show that X_1,…,X_n are independent.What is the expectation of norm of $[X_1,ldots, X_n]$ where $X_i$ are indpendent complex Gaussian random variablesFind expectation of $fracX_1 + cdots + X_mX_1 + cdots + X_n$ when $X_1,ldots,X_n$ are i.i.dDerive the maximum likelihood equation when only $I[X_1>5], I[X_2 > 5], … , I[X_n > 5]$ are observed.$X_1, X_2, cdots, X_n$ : i.i.d. $sim textBernoulli(p)$. Then $barx$ is an unbiased estimator of $p$.distribution of $sum_i=1^n (X_i-X_n+i)^2$ where $X_1,X_2,dots,X_2n$ are iid $N(mu,sigma^2)$
$begingroup$
Show that $$sup_x_1, dots, x_n in mathscrX|mathscrF(x_1, dots, x_n)|=S(mathscrA, n)$$
where $S(mathscrA, n)$ denotes the n-th shattering number of the class
$$mathscrA=A_f: f in mathscrF$$
where
$$A_f = x in mathscrX: f(x) = 1$$
I don't quite understand how to approach this problem. Any help will be highly appreciated.
statistics machine-learning
asked Mar 24 at 7:32
acrob4t1acrob4t1
41
$endgroup$
add a comment |
$begingroup$
Show that $$sup_x_1, dots, x_n in mathscrX|mathscrF(x_1, dots, x_n)|=S(mathscrA, n)$$
where $S(mathscrA, n)$ denotes the n-th shattering number of the class
$$mathscrA=A_f: f in mathscrF$$
where
$$A_f = x in mathscrX: f(x) = 1$$
I don't quite understand how to approach this problem. Any help will be highly appreciated.
statistics machine-learning
asked Mar 24 at 7:32
acrob4t1acrob4t1
41
$endgroup$
$begingroup$
What does $|mathscrF(x_1,dots, x_n)|$ stand for?
$endgroup$
– stochasticboy321
Mar 24 at 22:57
$begingroup$
Having thought a little - I'm guessing $mathscrF(x)$ is the set $(f(x_1), dots, f(x_n) ), f in mathscrF,$ and the $f$ are $0,1$-valued. In addition, you define the shattering number in the set-inclusion sense. If this is the case, argue pointwise - fix a set of inputs $X = x_1, dots, x_n$, and consider the map $varphi: mathscrA(X) to mathscrF(X), (A_f cap X) mapsto (f(x_1), dots, f(x_n) ).$ Argue that this is a bijection (this is almost trivial), to get that for any $X$, $mathscrA(X)$ and $mathscrF(X)$ are of equal size. The conclusion then follows.
$endgroup$
– stochasticboy321
Mar 24 at 23:37
add a comment |
$begingroup$
Show that $$sup_x_1, dots, x_n in mathscrX|mathscrF(x_1, dots, x_n)|=S(mathscrA, n)$$
where $S(mathscrA, n)$ denotes the n-th shattering number of the class
$$mathscrA=A_f: f in mathscrF$$
where
$$A_f = x in mathscrX: f(x) = 1$$
I don't quite understand how to approach this problem. Any help will be highly appreciated.
statistics machine-learning
asked Mar 24 at 7:32
acrob4t1acrob4t1
41
$endgroup$
Show that $$sup_x_1, dots, x_n in mathscrX|mathscrF(x_1, dots, x_n)|=S(mathscrA, n)$$
where $S(mathscrA, n)$ denotes the n-th shattering number of the class
$$mathscrA=A_f: f in mathscrF$$
where
$$A_f = x in mathscrX: f(x) = 1$$
I don't quite understand how to approach this problem. Any help will be highly appreciated.
statistics machine-learning
statistics machine-learning
asked Mar 24 at 7:32
acrob4t1acrob4t1
41
asked Mar 24 at 7:32
acrob4t1acrob4t1
41
asked Mar 24 at 7:32
acrob4t1acrob4t1
41
asked Mar 24 at 7:32
acrob4t1acrob4t1
41
asked Mar 24 at 7:32
acrob4t1acrob4t1
41
41
$begingroup$
What does $|mathscrF(x_1,dots, x_n)|$ stand for?
$endgroup$
– stochasticboy321
Mar 24 at 22:57
$begingroup$
Having thought a little - I'm guessing $mathscrF(x)$ is the set $(f(x_1), dots, f(x_n) ), f in mathscrF,$ and the $f$ are $0,1$-valued. In addition, you define the shattering number in the set-inclusion sense. If this is the case, argue pointwise - fix a set of inputs $X = x_1, dots, x_n$, and consider the map $varphi: mathscrA(X) to mathscrF(X), (A_f cap X) mapsto (f(x_1), dots, f(x_n) ).$ Argue that this is a bijection (this is almost trivial), to get that for any $X$, $mathscrA(X)$ and $mathscrF(X)$ are of equal size. The conclusion then follows.
$endgroup$
– stochasticboy321
Mar 24 at 23:37
add a comment |
$begingroup$
What does $|mathscrF(x_1,dots, x_n)|$ stand for?
$endgroup$
– stochasticboy321
Mar 24 at 22:57
$begingroup$
Having thought a little - I'm guessing $mathscrF(x)$ is the set $(f(x_1), dots, f(x_n) ), f in mathscrF,$ and the $f$ are $0,1$-valued. In addition, you define the shattering number in the set-inclusion sense. If this is the case, argue pointwise - fix a set of inputs $X = x_1, dots, x_n$, and consider the map $varphi: mathscrA(X) to mathscrF(X), (A_f cap X) mapsto (f(x_1), dots, f(x_n) ).$ Argue that this is a bijection (this is almost trivial), to get that for any $X$, $mathscrA(X)$ and $mathscrF(X)$ are of equal size. The conclusion then follows.
$endgroup$
– stochasticboy321
Mar 24 at 23:37
$begingroup$
What does $|mathscrF(x_1,dots, x_n)|$ stand for?
$endgroup$
– stochasticboy321
Mar 24 at 22:57
$begingroup$
What does $|mathscrF(x_1,dots, x_n)|$ stand for?
$endgroup$
– stochasticboy321
Mar 24 at 22:57
$begingroup$
Having thought a little - I'm guessing $mathscrF(x)$ is the set $(f(x_1), dots, f(x_n) ), f in mathscrF,$ and the $f$ are $0,1$-valued. In addition, you define the shattering number in the set-inclusion sense. If this is the case, argue pointwise - fix a set of inputs $X = x_1, dots, x_n$, and consider the map $varphi: mathscrA(X) to mathscrF(X), (A_f cap X) mapsto (f(x_1), dots, f(x_n) ).$ Argue that this is a bijection (this is almost trivial), to get that for any $X$, $mathscrA(X)$ and $mathscrF(X)$ are of equal size. The conclusion then follows.
$endgroup$
– stochasticboy321
Mar 24 at 23:37
$begingroup$
Having thought a little - I'm guessing $mathscrF(x)$ is the set $(f(x_1), dots, f(x_n) ), f in mathscrF,$ and the $f$ are $0,1$-valued. In addition, you define the shattering number in the set-inclusion sense. If this is the case, argue pointwise - fix a set of inputs $X = x_1, dots, x_n$, and consider the map $varphi: mathscrA(X) to mathscrF(X), (A_f cap X) mapsto (f(x_1), dots, f(x_n) ).$ Argue that this is a bijection (this is almost trivial), to get that for any $X$, $mathscrA(X)$ and $mathscrF(X)$ are of equal size. The conclusion then follows.
$endgroup$
– stochasticboy321
Mar 24 at 23:37
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
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%2f3160241%2fshow-that-sup-x-1-dots-x-n-in-mathscrx-mathscrfx-1-dots-x-n%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
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%2f3160241%2fshow-that-sup-x-1-dots-x-n-in-mathscrx-mathscrfx-1-dots-x-n%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
$begingroup$
What does $|mathscrF(x_1,dots, x_n)|$ stand for?
$endgroup$
– stochasticboy321
Mar 24 at 22:57
$begingroup$
Having thought a little - I'm guessing $mathscrF(x)$ is the set $(f(x_1), dots, f(x_n) ), f in mathscrF,$ and the $f$ are $0,1$-valued. In addition, you define the shattering number in the set-inclusion sense. If this is the case, argue pointwise - fix a set of inputs $X = x_1, dots, x_n$, and consider the map $varphi: mathscrA(X) to mathscrF(X), (A_f cap X) mapsto (f(x_1), dots, f(x_n) ).$ Argue that this is a bijection (this is almost trivial), to get that for any $X$, $mathscrA(X)$ and $mathscrF(X)$ are of equal size. The conclusion then follows.
$endgroup$
– stochasticboy321
Mar 24 at 23:37