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Uae r cxg. A Z X ҂ł́A R s A C x g ̊J n ɂȂ ܂ C x g n ܂ 1 x ȏ 퓬 Ă A C x g J n C g 2 x ȏ ʉ߂. Where S(z;r) = sign(z)maxfjzj r;0gis the softthresholding function, a = W2 ij W iiW jj, b = S ij W ij wTi Dw j, and c = X ij D ij The main cost is in computing wT i Dw j Instead, we maintain U = DW after each coordinate updates, and then compute wT i u j only O(p) ops per updates. D v s > ù û ÿ ÷ ä Ý Ê Â É Ê » ­ ­ ¦ ¡ § ¤ Ž x g w e h i m q t x u d r a k n u b m k f \ s m n o s p r q o n p n v ` c b.

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1 Prove that VCER, Ja E R and functions f and g such that lim f(x) = 0, lim g(x) = 0, lim f(x) g(x) = C xa Xa xa 0 This is how you show that 0 is an indeterminate form ю 00, and o ♡ are also 1 2 Prove the same way that indeterminate forms 3 Prove that 1º,0°, and 00° are indeterminate forms (You will only get c > 0 this time). E4 CS I VeU Z=g eJ 4hw e^ L G. .

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R ^ > Ä ò t s h t x z r w O s Ú E A É U l h S f R ~ > a V T ü s b \ q U O A p K { é $ t x z ¤ « » U G ¶ Ö ¼ t b ð J r w O t Ý Ý ` o M h T q M O q z é $ s S f U ¤ « » t r w O t R ^ > Ä ò q s l h T q M O t £ è ` o ü. R_latin_01R ß°R ß°BOOKMOBI) ø#’ P S /K 0O 0‡ 1{ 2“ 3{ 4K 4_ 5_ 6C 6G ìô = •"= Á$= å&= ( MOBIø ýé5 †q. Title Microsoft Word ATSTP class descriptions and notes Author SHAWNBODKIN Created Date 1/17/19 PM.

6 t \ ® t S M a a ¯ r « p V b {Í t µ å Å ^ d b { ¶ q s b { ² t ¾ V Z ` b { Í < í y ¶ Ì Í < í y ¶ Ì ä 7 ç Û1( 4( 7 é ¿ « r { Ñ å ý Ä s ò リシェント 玄関ドア3 採風タイプ リシェント 勝手口ドア ) w K ò. U ú s M M Þ S Ä « \ Æ Þ ÿ b q z A ¨ 8 s r w Ú E U !. CS174 Lecture 10 John Canny Chernoff Bounds Chernoff bounds are another kind of tail bound Like Markoff and Chebyshev, they bound the total amount of probability of some random variable Y that is in the “tail”, ie far from the mean Recall that Markov bounds apply to any nonnegative random variableY and have the form PrY ≥ t ≤Y.

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î ì ñ ï î ì ô ~ î í í í ì ó ï ó î í ì í í ì ó r W X Z X W } ~W o µ } v t o ( d µ ' } µ } ( / v µ } v ~/ v P u µ U u À o } v v d o } u u µ v } v v P P / } / /. Where S(z;r) = sign(z)maxfjzj r;0gis the softthresholding function The key computational bottleneck here is in computing the terms wT i Dw j, which take O(p2) time when implemented naively To address this, 9 proposed to store and maintain U = DW, which reduced the cost to O(p) flops per update However, this is not a strategy we can use when. ¨ lDD µt r } rt 4z r } rz 4 t l v v P W ó l í ì l î ì î ìt r } rt 4 W } u D } v Z ¨ í X ó î ï r î X ó 9 r î ð X ï 9K o Z P í ô í r í X í 9 í î rD } v Z ¨ î X ð ì ó r ì X î 9 r í X í 9 ' Z P ó ñ r ì X ó 9.

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R ` t @ N g I C X g A. § Ù Ä t L8 ³. Theorem 6 (Constrained optimization) Let f A ⊂ Rn → R be a continuously differentiable function, where A is an open set Let g A ⊂ Rn → R also be a continuously differentiable function For c ∈ R, let S = g−1(c) = {x g(x) = c} If, among all points in S, the function f has an extreme point at p 0, then ∇f(p.

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> a g r w õ > > P N P N 0 U > Ù ¼ Ï ¨ w ­ Ï x > > > > > > > > v Ú ä Ï x ß H w { Ö W H x Ê v ° % ½ â ù O J E â s w ù _ x Æ ¥ Á Ï í v Ü Á æ f _ l c b _ > g l l m t _ r g m l > a g r w w & f g a w ú ö I ô ö I õ x Ì f. BASIC STATISTICS 1 SAMPLES,RANDOMSAMPLING ANDSAMPLESTATISTICS 11 Random Sample The random variables X1,X2,, are called a random sample of size n fromthe populationf(x)if X1,X2,, are mutuallyindependent random variablesand themar ginal probability density function of each Xi is the same function of f(x) Alternatively, X1,X2,, are called independent and identically. Name Address 12 The total amount ofcontributions received dllling D the preceding 12 months or I& the preceding fiscal year $3,453,(1 0} 13 The total amount paid to commercial telephone solicitors dllling Othe preceding.

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