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pages of very, very dense math. Without a page number and/or clarification, the reference provides no value- reading an advanced textbook to guess what is meant when a short definition would suffice is unreasonably onerous. I have a copy of the text, and I'd be happy to rewrite the section/reference if the editor can add more detail. Otherwise, I propose removing the formula entirely as it provides no information beyond the reference- simply saying that the reference contains a derivation for the general case would be clearer.
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2215:. Surely, that cannot be an intended part of the definition of this distribution: viz, that it consists almost entirely of empty tables, at which it becomes impossible/forbidden to sit? And heaven help us, if this is correct, then can the article be amended to make it clear that there will be forbidden tables? And state what the fraction of forbidden tables are over time? Personally, I suspect that the definition is just-plain-wrong, but its hard to guess what the correct, intended definition should be.
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1553:{\displaystyle {\begin{aligned}\Pr(B_{2}=B)&={\dfrac {(\theta )_{|B|,0}}{(\theta +1)_{1,1}}}\prod _{b\in B}(1)_{|b|-1,1}={\dfrac {\theta }{\prod _{i=0}^{1}(\theta +1+i)}}\cdot (1)_{1,1}=\\&={\dfrac {\theta }{(\theta +1)(\theta +2)}}\prod _{i=0}^{0}(1+i)=\\&={\dfrac {\theta }{(\theta +1)(\theta +2)}}=\\&\neq {\dfrac {1}{\theta +2}},\end{aligned}}}
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2282:. However the result of this process does not care about table numbering, so assigning customers in this way is equivalent to assigning them to the next empty table. The formal definition is written this way because "the next empty table" is a much more complicated thing to formally define than "table n."
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I am a mathematics graduate and it is not obvious to me why the given formula holds. I think that a derivation of the simple, non-generalized case belongs here. I hate it when people say that something "follows immediately" when, in fact, it requires half a hour's thought and a half-page derivation.
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The current formula for the generalized CRP uses the notation of the gamma function extensively, but then notes that the gamma notation is not the usual gamma function without elaboration. The reference is Jim Pitman's "Combinatorial
Stochastic Processes", and while it is a great text it is also 250
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I think it should be noted that the names "Chinese restaurant" and "Indian buffet" are rather problematic, and seem to stem from stereotypes in the 1980s. Is there any reason for this to be called a "Chinese restaurant process" and not simply a "restaurant process"? Of course, I understand if
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This is not "a
Chinese restaurant process" but "the Chinese Restaurant Process". Knowledge cannot rename this process because that is how it is known in the literature. I'm not sure which stereotypes from the 80s you are referring to. The Knowledge article on
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The formulate is indeed wrong. Instead of |B| it should read |B|-1 in the above quoted section. Since this is properly the most important thing to get right I hope it is okay that I correct the text, see for instance formula 16 of pitmanns paper:
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There is some mistake with the expected number of tables. First, it doesn't depend on alpha. Second, it should go to alpha * log n as n increases, and when theta=1, and that doesn't happen. I think there is somewhere a theta instead of an alpha.
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1076:{\displaystyle \Pr(B_{1}=B)={\dfrac {(\theta )_{|B|,0}}{(\theta +1)_{0,1}}}\prod _{b\in B}(1)_{|b|-1,1}={\dfrac {(\theta )_{1,0}}{(\theta +1)_{0,1}}}\cdot (1)_{0,1}={\dfrac {\prod _{i=0}^{0}\theta }{1}}\cdot 1=\theta \neq 1}
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When the discount parameter is not zero, the number of expected tables is not O(log(n)) but a power law, which is the defining characteristic of the Pitman-Yor
Process that is integrated out to get the two parameter CRP.
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anyone might be interested in studying this process. If there is any heuristic or intuitive way to understand the process, it should be mentioned as a non-rigorous way of gaining some insight into its significance.
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I found that the second explanation, in "definition", was easier to understand than the first explanation in the introduction, so I essentially swapped them around. Hope this helps.
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there is exactly zero probability that anyone will ever sit at that table. That is, once a table is skipped, it will stay unoccupied, forever. Viz. at time
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mathematicians (or anyone else) might be interested in this particular process would still be helpful; the "Applications" section offers a scant few clues.
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is the notation inconsistent? for example: n_k is the number of elements in the n-th block... but... |b| is also the number of elements in a block.
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is stated explicitly in the article. Therefore I was surprised by the question above. But now I've made it more explicit by adding a link to
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claims the name of the process comes from the custom as practiced in restaurants in Hong Kong, Taiwan, and parts of China.
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The article, as currently written, is either just-plain wrong, or is deeply misleading. The core problem is that it uses
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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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https://web.archive.org/20110411124712/http://users.cecs.anu.edu.au/~xzhang/pubDoc/notes/dirichlet_process.pdf
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The process and related distribution seem to be essentially the same topic and so are best covered together.
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I see this comment has been here for several weeks. I just saw it. I'll look at it later this afternoon.
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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with
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before doing mass systematic removals. This message is updated dynamically through the template
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Thank you, the change does somewhat improve the article. However, an expanded explanation of
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Forgive me, I don't know much about the notations used here. But even using the convention
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to count both time-steps, and the number of "occupied" tables. It states that, at time
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It is not "immediate" that the probability assigned to a particular partition is ...
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The intro to this article currently fails to comply with the
Knowledge policy
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tables. Most of those tables will end up being empty. Specifically, table
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after the link to keep me from modifying it. Alternatively, you can add
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http://users.cecs.anu.edu.au/~xzhang/pubDoc/notes/dirichlet_process.pdf
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The intro to this article is currently too technical for most readers
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to keep me off the page altogether. I made the following changes:
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http://www.springerlink.com/content/k175tg8150441520/fulltext.pdf
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The above criticism is still valid. The article should explain
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Expected number of tables in general case needs clarification
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The definition is correct. The distribution will distribute
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When you have finished reviewing my changes, please set the
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that the second person sit at the same table as the first.
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wikipedia is not the right forum for such discussions.
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and that otherwise, the probability of sitting at table
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I have just added archive links to one external link on
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article needs discussion of meaning of this distribution
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1796:Chinese restaurant process
1791:Hello fellow Wikipedians,
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65:Chinese restaurant process
38:Chinese restaurant process
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1994:
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1969:
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1649:
1648:Michael Hardy
1645:
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1634:Michael Hardy
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653:Michael Hardy
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619:doesnt it :)
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163:Find sources:
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150:Verifiability
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48:its talk page
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2368:— Preceding
2364:
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1870:source check
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59:This is the
27:
2217:14.0.170.34
1660:guess not.
669:—Preceding
635:80.41.36.60
188:free images
71:not a forum
43:its history
2432:Categories
1769:Reify-tech
1725:Reify-tech
305:Statistics
296:statistics
268:Statistics
32:page were
2344:complete.
2314:Andrew D.
1890:this tool
1883:this tool
1743:Grabigail
128:if needed
111:Be polite
61:talk page
2370:unsigned
2286:unsigned
1896:Cheers.—
1806:cbignore
1683:unsigned
1086:or with
683:contribs
671:unsigned
662:notation
597:unsigned
96:get help
69:This is
67:article.
2416:Cswitch
2347:Klbrain
1906::Online
1835:checked
1800:my edit
572:Cswitch
351:Mistake
332:on the
239:C-class
194:WP refs
182:scholar
2342:Merger
2047:where
1814:nobots
621:Anlace
245:scale.
166:Google
34:merged
209:JSTOR
170:books
124:Seek
36:into
2420:talk
2399:talk
2378:talk
2351:talk
2318:talk
2294:talk
2221:talk
1839:true
1773:talk
1747:talk
1729:talk
1691:talk
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1623:talk
679:talk
605:talk
576:talk
202:FENS
176:news
113:and
2009:is
1954:is
1864:RfC
1826:to
1765:why
1720:why
566:.
526:log
324:Low
216:TWL
2434::
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
