Problem 1.3 Question Please Help

[jewelltaylor9430]

Question 1.3 A: Let p = min(1=<n=<N) y(n)(w*Yx(n)). Show that p > 0.

(For lack of any other notation I use brackets to represent subscripts, sorry)

Question 1.3 B: Show that wT(t)w* >= wT(t-1)w* + p, and conclude that wT(t)w* >= tp

My Questions:
- I understand p is defined in A but I am not familiar with the notation and I do not know what it represents. What is the min expression getting at? Is it the fact the value of p such that the value of n is minimized? Can you give me intuition behind what p actually is?

- How does the the RHS of the first inequality relate to the RHS of the second inequality in B? My understanding is t represents the iteration number of the perceptron algorithim. Is this the case or am I mistaken? Does tp somehow equal wT(t-1)w* + p and if so where the heck does it come from? I am so confused

Any help would be much appreciated, I have been stumped on this question for too long

[htlin]

Originally Posted by jewelltaylor9430

Question 1.3 A: Let p = min(1=<n=<N) y(n)(w*Yx(n)). Show that p > 0.

(For lack of any other notation I use brackets to represent subscripts, sorry)

Question 1.3 B: Show that wT(t)w* >= wT(t-1)w* + p, and conclude that wT(t)w* >= tp

My Questions:
- I understand p is defined in A but I am not familiar with the notation and I do not know what it represents. What is the min expression getting at? Is it the fact the value of p such that the value of n is minimized? Can you give me intuition behind what p actually is?

- How does the the RHS of the first inequality relate to the RHS of the second inequality in B? My understanding is t represents the iteration number of the perceptron algorithim. Is this the case or am I mistaken? Does tp somehow equal wT(t-1)w* + p and if so where the heck does it come from? I am so confused

Any help would be much appreciated, I have been stumped on this question for too long

represents the distance from the closest to the boundary represented by if the latter is reasonably nromalized.

If you can prove that the inner product increases at least by in each iteration, then after iterations the inner product naturally increases by which is what you need to prove in B.

Hope this helps.