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Title Microsoft Word FSN07VIKING14_VikingSubscriberSoftware1GeneralReleasedocx Author lorikowal Created Date 7/13/ AM. R ∞ −∞ g(x,θ) dx < ∞, then, the following equality holds, d dθ Z ∞ −∞ f(x,θ) dx = Z ∞ −∞ ∂ ∂θ f(x,θ) dx The conditions say that the first derivative of the function must be bounded by another function whose integral is finite Now, we are ready to prove the following theorem. L ЎR C x g 쎖 d b ł̂ ₢ 킹 TEL k C s H 2 2 2 9.

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> 4 r V @ > r V @ ¥ k k x 4 q k f 4 { s ¥ 4 e ¥ i Y j Y j y k a > $ 0 9 3 0 B « «. ¨»n¤ª· µª· ¥µ«µ­ ¦r¡ºÊ µ ¨³ · «µ­ ¦r 31 CR ¨»n¤ª· µ ´ ´ ­µ µ 56 CR ¨n»¤ª· µÁ¨º° ­µ µt 15 CR ¦ª¤ ¦µ¥ª· µÂ 50 CR oX j` 4 1 ;. 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.

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Search the world's information, including webpages, images, videos and more Google has many special features to help you find exactly what you're looking for. 0310 try W i/100 ~150mm @ Copyright(C) HIROYUKI YAMADA All Rights Reserved. .

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. 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.

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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). S t \ E R y \ ̓` F S t B Ŋy C x g 񖞍ځb ` F S t F y R X F { F y s ԉ ` F S t F y R X ӂ. Cheree ` F D ̂ ܂ @ @ @ @ @ @ @ @ @ pico&cotto lucklin b N 킹 ̎ ĂĂ ܂.

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. 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. ٧ Y XW V U T S R Q P O N M L f e d c b a ` _ ^ \ Z q p on m l k j i h g ٨ g f e d c b a ` _ ^ \ r qp o n m l k j i h ~ } { z y x wv u ts.

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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. U ú s M M Þ S Ä « \ Æ Þ ÿ b q z A ¨ 8 s r w Ú E U !. Z À õ l í ñ l î ì î ì } d o } v WWZ dZ E^D/^^/KE KW Z > ^ µ } Z o d v u } v K } v o v v P µ Z } Ç Á Z } v } o v X.

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. D ڍ R d ݒn Ɍ _ ˎs 斀 R 22. ªü®‰ yP žTõ !ÁŠ¡š_úÔ\cá·vÒêt´à 3qÈ°à pN ¶ ”$ò•` ø“ø À‚q¡ óHÖ&™?.