Question

5. Parameter Estimation. Given a time-dependent model with parameter vector f(t;p) and data r = = [1,2,...) a times tu, ta, ...tn (a) [10 pts) write down the squared-error function, E(p). (b) (10 pts) Write down in general and describe in words the hill-climbing algorithm equation. (c) (20 pts) Letting ft;p) = P(3)? +p(2)t + P(1), write down the specific hill-climbing algorithm equation.

Answer 1

a 1 The Hill Clinting algorithms are a generally class of hewrisake oftimization algorithmg that deal with the optimization problem. there is a frite Set & of possible Configurations. Eeach configration is assigned non-negatine, real number called cost, or, in other words, a cost function is define as fix R for each configration & EX a set of neighbors nwex is defined aim of the search is find Xmm EX minimizing the lost function fexy. a) same error = The mean sumused estoy tells you have close a regression line is to a. set of beint, gt drees this by taking the distance from the bonds to the regression line is necessary to remove any negatine signs. It also gives more weight to larger differences. It as called guine assor. and squating

fells C Stel 1 take tarihle. and survived caros tos the folkeuring for of values-- C43,41), 099,152,648,45), (16,97),(17,19) Find the regression fine. I used pers online calculator and got the. -e)27-5519-1 Отс y = 9.2 +0.8x Step 2 and the new y values 9.2 + O'8093) 2936 9.2 +08694) = 44.4 9.2 + 0-81452 2452 9.2 +08 (40)2 46 9.74 0.8 047 1 2 46.8 Ima the furres cy-Y) 41 43.6= -2.6 95 44.4 = 0.6 49 45.2 = 3.8 47 - 46 44 468 = -2.8 Square the errors (€ 2.62 = 6.76 Stars add all suured 0.36 Coror up = 6.76 +0.36 .tg4.44 +1 +7.89 14.94 230.4 V stab see 4 stepe (6.62 (3812 12 (7.872 2 7.84

for mo, Genoval formulation of hill cemtimy algorithms Xhest x D Set the outto loop While Stepfimy coiterier med medte Counter Kko while K<K do M-1 do generate a neighbour YEM(x) with Probability Yk (x4) Confuse the cost function fcy) of the Candidate if Rk (x4) flyg-f(x) then х<- A accept the more if f(x) <forest) then best Configration and if and if and for 2 A store the best К<- K+ ) And while and while