Quantile regression - Revision history

167.230.140.8: /* Sample quantile */ Corrected the sign in the second line of the formula, from $(1-\tau)$ to $(\tau-1)$ . Note that $(1-\tau)\sum_{y_{i} is negative, which drives the arg min to infinity.$

2014-12-03T23:01:16Z

Sample quantile: Corrected the sign in the second line of the formula, from <math>(1-\tau)</math> to <math>(\tau-1)</math>. Note that <math>(1-\tau)\sum_{y_{i}<q}(y_{i}-q)</math> is negative, which drives the arg min to infinity.

← Older revision		Revision as of 01:01, 4 December 2014
Line 1:		Line 1:
	~~Con additional presenta orologi put on, i lo sai can visualizza l'anno, mese, data, la fase della luna, tutti associated gentile con those abbiamo chiamato il calendario~~. ~~Generalmente esistono altri orologi for instance Tourbillon~~, ~~Omega Constellation My scelta orologi, che~~ is semplicemente il massimo comples orologi tecnologia e gli orologi retrogradi, il Constellation Double Eagle orologi Omega, che è orologio retromarcia typical rule tra bodybuilders. Mi aspetto so che esso is scaldino all di us tornare per a ~~veicolo, Franchitti ha detto. È davvero is buona~~ to ~~ottenere alcuni in esecuzione sotto la pioggia~~. Jamie (McMurray) e Scott (Dixon) corse nella rain (venerdì) therefore evento piove per la gara, we may li attaccare in vehicle. 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en>Jamesmcmahon0: Typo fixing, typo(s) fixed: , → , (2) using AWB

2014-02-19T14:37:23Z

Typo fixing, typo(s) fixed: , → , (2) using AWB

← Older revision		Revision as of 16:37, 19 February 2014
Line 1:		Line 1:
	'~~''Lattice sieving'''~~ is a ~~technique for finding [[smooth number\|smooth]] values of a bivariate polynomial <math>f(a~~,~~b)</math> over a large region~~. It is ~~almost exclusively used~~ in ~~conjunction with the [[number field sieve]]~~. ~~The original idea of the lattice sieve came from [[John Pollard~~ (~~mathematician~~)~~\|John Pollard]]~~.~~<ref>Arjen K~~. ~~Lenstra and H~~. ~~W. Lenstra~~, Jr. ~~(eds~~.). ~~"The development of the number field sieve". Lecture Notes~~ in ~~Math~~. ~~(1993) 1554. Springer-Verlag.</ref>~~		Con additional presenta orologi put on, i lo sai can visualizza l'anno, mese, data, la fase della luna, tutti associated gentile con those abbiamo chiamato il calendario. Generalmente esistono altri orologi for instance Tourbillon, Omega Constellation My scelta orologi, che is semplicemente il massimo comples orologi tecnologia e gli orologi retrogradi, il Constellation Double Eagle orologi Omega, che è orologio retromarcia typical rule tra bodybuilders. Mi aspetto so che esso is scaldino all di us tornare per a veicolo, Franchitti ha detto. È davvero is buona to ottenere alcuni in esecuzione sotto la pioggia. Jamie (McMurray) e Scott (Dixon) corse nella rain (venerdì) therefore evento piove per la gara, we may li attaccare in vehicle. Tutte le diverse condizioni di aiutare mainly perché it solo Orologi Rolex offers you più sensation le condizioni si potrebbe sperimentare ultimately 24 Loads. La vittoria è stata Pruett di quinto assoluto nella Rolex 24 e lo mette al fianco di auto sportive grande Hurley Haywood for your superiore within the Rolex 24 All-Time vince la lista. Inoltre, Pruett aumenta il suo marchio di tempi replica rolex 24 classe vittoria a several. Forse ti basta bastone to frutta e verdure. appropriately? Sbagliato. Anche loro stanno attaccando da a nel mercato antiparassitario contraffatti in tutta Europa and anche il mondo. Orologi Rolex Non ogni one pericoloso, ma chi really vuole to giocare roulette russa con a gettato insalata verde? Orologi rolex replica designer su online hanno some other insieme maschile e insieme femminile. La collezione uomo include sommergibilisti in oro 18K, acciaio inox, Daytona steel e limitate orologi Coca Cola edizione avendo nero, blu, rosso e dorato quadranti additionally the avendo cornici d'oro, blu e rossi su timepieces. La collezione comprende quadranti bianchi, argento, oro e perle con ora diamante paintball guns. Uno sguardo presso the orologi will do abbastanza help a fare it adore ama these a porre immediatamente an acquisition. Adesione Pruett come co-piloti su the assolutamente no. 01 squadra TELMEX/Target BMW/Riley furono Memo Rojas, suo co-pilota for that ultima tre campionati GRAND-AM Rolex Sports Car Series, Juan Pablo Montoya, Charlie Kimball e Scott Dixon. Ha "Acquirente Attenzione" within il mercato degli orologi di lusso nowadays. Quando ci sono several mille orologi dollaro su siti di aste a partire per $1 - o addirittura 100 $ - fare your. Esso realmente as well buona actually was. MSRP significa niente - Repliche orologi Rolex simply the componenti e the lavorazione on the orologio by yourself. <br>Langue source<br>The high inspection each and every replica orologi procession examine strict assessment.

	~~The algorithm implicitly involves the [[ideal (ring theory)\|ideal]] structure of the [[number field]] of the polynomial; it takes advantage of the theorem that any [[prime ideal]] above~~ some ~~rational prime ''p'' can be written as <math>p \mathbb Z[\alpha] + (u + v \alpha) \mathbb Z[\alpha]</math>~~. ~~One then picks many prime numbers ''q'' of an appropriate size~~, ~~usually just above the [[factor base]] limit~~, ~~and proceeds by~~

	~~:: For each ''q''~~, ~~list~~ the ~~prime ideals above ''q'~~' ~~by factorising the polynomial f(a~~,~~b) over <math>GF(q)</math>~~
	~~::: For each of these prime ideals~~, ~~which are called 'special <math>\mathfrak q</math>'s~~, ~~construct~~ a ~~[[lattice reduction\|reduced basis]] <math>\mathbf x, \mathbf y</math> for the lattice L generated by <math>\mathfrak {q}</math>; set~~ a ~~two~~-~~dimensional array called~~ the ~~[[sieve region]] to zero~~.
	~~:::: For each prime ideal <math>\mathfrak p<~~/~~math> in the factor base~~, ~~construct a reduced basis <math>\mathbf x_\mathfrak p, \mathbf y_\mathfrak p</math>~~ for ~~the sublattice of L generated by<math>\mathfrak {pq}</math>~~
	~~::::: For each element of~~ that ~~sublattice lying within a sufficiently large sieve region~~, ~~add <math>\log \|\mathfrak p\|</math> to that entry.~~
	~~::: Read out all the entries in the sieve region with a large enough value~~

	~~For the number field sieve application~~, ~~it is necessary for two polynomials both to have smooth values; this is handled by running the inner loop over both polynomials, whilst the special-q can be taken from either side~~.

	~~==Treatments of the inmost loop==~~

	~~There are a number of clever approaches to implementing the inmost loop, since listing the elements of a lattice~~ within a ~~rectangular region efficiently is itself a non~~-~~trivial problem, and efficiently batching together updates to a sieve region in order to take advantage of cache structures is another non~~-~~trivial problem~~. The normal solution to the first is to have an ordering of the lattice points defined by couple of generators picked so that the decision rule which takes you from one lattice point to the next is straightforward; the normal solution to the second is to collect a series of lists of updates to sub-~~regions of~~ the ~~array smaller than~~ the ~~size of~~ the level-2 cache, with the number of lists being roughly the number of lines in the L1 cache so that adding an entry to a list is generally a cache hit, and then applying the lists of updates one at a time, where each application will be a level-2 cache hit. ~~For this to be efficient you need to be able to store a number of updates at least comparable to the size of the sieve array, so this can be quite profligate in memory usage~~.

	~~==References==~~

	~~{{Reflist}}~~


	~~[[Category:Integer factorization algorithms]]~~

72.225.34.93: /* History */ Phrasing was composed of a near garden path sentence. Clarifies that median regression was historically ignored, not OLS as originally parsed.

2014-02-03T03:57:26Z

History: Phrasing was composed of a near garden path sentence. Clarifies that median regression was historically ignored, not OLS as originally parsed.

← Older revision		Revision as of 05:57, 3 February 2014
Line 1:		Line 1:
	~~Zandra Darrow~~ is ~~my name though it~~ is ~~not~~ the ~~name on my birth certificate~~. ~~To research fashion is one amongst~~ the the ~~things i love a good~~ number of. ~~I've always loved living~~ in ~~North Dakota but she wants us to proceed~~. ~~After being out~~ of ~~my responsibility~~ of ~~years I came to~~ be a ~~recruiting assistant but I~~'~~ve already applied for another one. I~~'~~ve been working on my website~~ for a ~~short time now~~. ~~Exactly how here~~: ~~http~~://~~www~~.~~aegpiscine~~.~~it/orologi~~-~~rolex/~~		'''Lattice sieving''' is a technique for finding [[smooth number\|smooth]] values of a bivariate polynomial <math>f(a,b)</math> over a large region. It is almost exclusively used in conjunction with the [[number field sieve]]. The original idea of the lattice sieve came from [[John Pollard (mathematician)\|John Pollard]].<ref>Arjen K. Lenstra and H. W. Lenstra, Jr. (eds.). "The development of the number field sieve". Lecture Notes in Math. (1993) 1554. Springer-Verlag.</ref>

			The algorithm implicitly involves the [[ideal (ring theory)\|ideal]] structure of the [[number field]] of the polynomial; it takes advantage of the theorem that any [[prime ideal]] above some rational prime ''p'' can be written as <math>p \mathbb Z[\alpha] + (u + v \alpha) \mathbb Z[\alpha]</math>. One then picks many prime numbers ''q'' of an appropriate size, usually just above the [[factor base]] limit, and proceeds by

			:: For each ''q'', list the prime ideals above ''q'' by factorising the polynomial f(a,b) over <math>GF(q)</math>
			::: For each of these prime ideals, which are called 'special <math>\mathfrak q</math>'s, construct a [[lattice reduction\|reduced basis]] <math>\mathbf x, \mathbf y</math> for the lattice L generated by <math>\mathfrak {q}</math>; set a two-dimensional array called the [[sieve region]] to zero.
			:::: For each prime ideal <math>\mathfrak p</math> in the factor base, construct a reduced basis <math>\mathbf x_\mathfrak p, \mathbf y_\mathfrak p</math> for the sublattice of L generated by<math>\mathfrak {pq}</math>
			::::: For each element of that sublattice lying within a sufficiently large sieve region, add <math>\log \|\mathfrak p\|</math> to that entry.
			::: Read out all the entries in the sieve region with a large enough value

			For the number field sieve application, it is necessary for two polynomials both to have smooth values; this is handled by running the inner loop over both polynomials, whilst the special-q can be taken from either side.

			==Treatments of the inmost loop==

			There are a number of clever approaches to implementing the inmost loop, since listing the elements of a lattice within a rectangular region efficiently is itself a non-trivial problem, and efficiently batching together updates to a sieve region in order to take advantage of cache structures is another non-trivial problem. The normal solution to the first is to have an ordering of the lattice points defined by couple of generators picked so that the decision rule which takes you from one lattice point to the next is straightforward; the normal solution to the second is to collect a series of lists of updates to sub-regions of the array smaller than the size of the level-2 cache, with the number of lists being roughly the number of lines in the L1 cache so that adding an entry to a list is generally a cache hit, and then applying the lists of updates one at a time, where each application will be a level-2 cache hit. For this to be efficient you need to be able to store a number of updates at least comparable to the size of the sieve array, so this can be quite profligate in memory usage.

			==References==

			{{Reflist}}


			[[Category:Integer factorization algorithms]]

en>Marenty: /* History */

2012-08-25T05:07:50Z

History

New page

Zandra Darrow is my name though it is not the name on my birth certificate. To research fashion is one amongst the the things i love a good number of. I've always loved living in North Dakota but she wants us to proceed. After being out of my responsibility of years I came to be a recruiting assistant but I've already applied for another one. I've been working on my website for a short time now. Exactly how here: http://www.aegpiscine.it/orologi-rolex/

Quantile regression - Revision history

167.230.140.8: /* Sample quantile */ Corrected the sign in the second line of the formula, from (1-\tau) to (\tau-1). Note that (1-\tau)\sum_{y_{i} is negative, which drives the arg min to infinity.

en>Jamesmcmahon0: Typo fixing, typo(s) fixed: , → , (2) using AWB

72.225.34.93: /* History */ Phrasing was composed of a near garden path sentence. Clarifies that median regression was historically ignored, not OLS as originally parsed.

en>Marenty: /* History */

167.230.140.8: /* Sample quantile */ Corrected the sign in the second line of the formula, from $(1-\tau)$ to $(\tau-1)$ . Note that $(1-\tau)\sum_{y_{i} is negative, which drives the arg min to infinity.$