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Uae r cxg. ³ µ Â Ü K V o M h M \ s M t ¦ µ µ Ý b p t H w 0 t E « C ?. 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). 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.

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(r n− 1 n 2,r n n2) ≤ X∞ n=1 m (r n− 1 n2,r n 1 n2) = X∞ n=1 2 n. § Ù Ä t L8 ³. 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.

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. R } v v À ( } u Z yD> E/^d ^W ô ì ì r ñ ï } v } o ~ v Æ & v ' U o } Z E/^d E } v o s µ o v o Ç ~Es W Z W l l v À X v X P } À l ô ì ì r ñ ï. Title Microsoft Word 0224_Jak wypeÅ niÄ wniosek_nabór_IIdocx Author AleksandraJablonska Created Date 3/3/ PM.

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Cheree ` F D ̂ ܂ @ @ @ @ @ @ @ @ @ pico&cotto lucklin b N 킹 ̎ ĂĂ ܂. 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. 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.

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³ µ Â Ü x K U C ?. 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. D ˜Ô{¦ù«š /Ð* r—RÁ Á÷´¶eN wmR™P£y‡¢ !Eü ™pE‰ž€R JÖ¯Ù$ê°ˆW$õN©¸kV6¸ ´éz ~p&¤†*n Ô>¥ YÓx Øç± “Ø?.

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. E4 ( , ) ¨n»¤ª· µ­´ ¤«µ­ ¦r3 (®oµ¤ 23xxxxx) p X c;. 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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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. The Fokker CX was a Dutch biplane scout and light bomber designed in 1933 It had a crew of two (a pilot and an observer). ^ W ŊJ Â C x g ŁA Ɏ t ⏤ i A ւ̗U A p t b g 𗈏 ҂ɔz z T v O Ȃǂ s ܂ B R p j I ̑u ₩ ȏΊ Ɛg ̂ Ȃ C x g 𐷂 グ A N I e B ߂܂ B Ǘ f B N ^ A ؂ȏ i 薣 ͓I ɓ` MC A Ƃ̃C W A b v EPR ɒ l ނ 񋟒v ܂ B ̑ A u X ̎{ H E ݉c ̊ E ܂ B.