Consider the following problem of L1-regularization, i.e., minimize for i=1 to n
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- 3. Try to obtain a closed form for the following recurrence equation: 1 if n 4. if n = 3,Consider the following problem of Ll-regularization, i.e., minimize for i=1 to n * 2 LR(0; ) = H;¡ (0; – 0; ) +a | 0; | where all H;; > 0, `11 * and a is the L1 regularization cọnstant. Find the smallest value of a (in terms of H;; and 0; ) so that the optimal regularized solution to the given minimization problem, 0; = 0 for all i. 14 -Question : Prove L = {apbm : p,m\epsilonN} Note: Use Pumping lemma to solve this.
- (1) Find a tight bound solution for the following recurrence: T(m) = T(4) + T(쓱) + cn2 (cis a positive constant) That is, find a function g(n) such that T(n) e O(g(n)). For convenience, you may assume that n is a power of 2, i.e., n=2k for some positive integer k. Justify your answer. [Note: Read question 4-(2) first before writing your answer]3. (i) Solve the following recurrence relation by expansion (substitution): for n ≥ 2, n a power of 2 T(n) = 8T() + n², T(1) = 1 (ii) Express T(n) in order, i.e., T(n) = (f(n)) for n ≥ 1, n a power of 2. (iii) Check your solution by plugging it back into the recurrence relation.1. Using the pumping lemma and contradiction, prove that L = (ab² n>=0} is not regular. 2. Using the pumping lemma and contradiction, prove that L = {a"bm n> m} is not regular. 3. Using the pumping lemma and contradiction, prove that L = (aºb nPlease answer it correctly.Consider the following code:> x <- matrix(rnorm(n = 500), ncol = 5)> varx <- var(x)Starting with varx, use two applications of the sweep() function, one dividing each row of the matrix andthe other dividing each column, of a covariance matrix to obtain R, the correlation matrix.(1) Show the solution of following recurrence relation T(n) is O (nlogn) by using substitution method If n = 0 T (n) = T (n- 1) + logn If n >0Recommended textbooks for youDatabase System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill Education
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