[SOLVED] Machine Learning Homework 5-Theory + SVM

HW5 – Theory + SVM

1.

1. Let 𝐾, 𝐿 be two kernels (operating on the same space) and let 𝛼, 𝛽 be two

   positive scalars.

   Prove that 𝛼𝐾 + 𝛽𝐿 is a kernel.

2. Provide (two different) examples of non-zero kernels 𝐾, 𝐿 (operating on the

   same space), so that:
   i. 𝐾−𝐿isakernel.

   ii. 𝐾−𝐿isnotakernel. Prove your answers.

2. Use Lagrange Multipliers to find the maximum and minimum values of the function subject to the given constraints:

   Function:𝑓(𝑥,𝑦,𝑧)= 𝑥0 +𝑦0 +𝑧0.Constraint:𝑔(𝑥,𝑦,𝑧)= 23 +53 +73 =1, 43 63 63

   where𝛼> 𝛽>0

3. Let𝑋=R=.Let

   𝐶 = 𝐻 = {h(𝑎, 𝑏, 𝑐) = {(𝑥, 𝑦, 𝑧) 𝑠. 𝑡 |𝑥| ≤ 𝑎, |𝑦| ≤ 𝑏, |𝑧| ≤ 𝑐} 𝑠. 𝑡. 𝑎, 𝑏, 𝑐 ∈ RL} the set of all origin centered boxes. Describe a polynomial sample complexity algorithm 𝐿

   that learns 𝐶 using 𝐻. State the time complexity and the sample complexity of your suggested algorithm. Prove all your steps.