*ANSWER* q5

[arcticblue]

I got Q5 wrong and don't know where I've gone wrong. My code is below and I believe my partial derivatives are correct. I believe eta and the starting values are correct. I then loop through using the weights to calculate the new weights. The same weights are used for both partial derivatives and then both weights are updated at the end of the iteration. I then get the results at the bottom. I end up with iteration 17 being when the error drops below 10e-14 (which is the wrong number of iterations). To calculate the error I'm summing the square of the differences and then taking the sqrt. (Refer to print statement in code).

So can someone point out what I've done wrong, I'm sure it's obvious to someone who got the answer right but it's not to me. Alternatively if anyone has some code that works then please post it and I'll try and work out how mine is different.

Thank you.

def derWRTu(u,v):
    result = Decimal(2)*(Decimal.exp(v) + Decimal(2) * v * Decimal.exp(-u)) * (u * Decimal.exp(v) - Decimal(2)*v*Decimal.exp(-u))
    return result

def derWRTv(u,v):
    result = Decimal(2)*(u*Decimal.exp(v) - Decimal(2) * Decimal.exp(-u)) * (u * Decimal.exp(v) - Decimal(2)*v*Decimal.exp(-u))
    return result

eta = Decimal(0.1)
weight1 = Decimal(1.0)
weight2 = Decimal(1.0)

for i in range(1,20):
        temp1 = Decimal(weight1 - eta * derWRTu(weight1,weight2))
        temp2 = Decimal(weight2 - eta * derWRTv(weight1,weight2))
        print i, temp1, temp2, math.sqrt((temp1 - weight1)**2 + (temp2 - weight2)**2)
        weight1 = temp1
        weight2 = temp2

Results
iteration newWeight1 newWeight2 error

1 -0.369542993196839967955794109 0.2139205536245797574025398844 1.5791038301
2 0.0305206903512627734316713927 -0.5079340454438062055203607077 0.825302982601
3 0.1075231141989984274494072585 -0.1222102555735032213170381668 0.393334737025
4 0.06564482581488226125563096705 -0.0151665598769331032201461945 0.114944090002
5 0.04784117062171890279998341002 0.01848989922674513542330801974 0.038075285654
6 0.04499946309943379128005628962 0.02349925169679327305149255062 0.00575924594121
7 0.04475601902934555265991082578 0.02392429647039781800619960613 0.000489824534736
8 0.04473774604067714316407965262 0.02395617479661382948530576517 3.67441124156e-05
9 0.04473639081750715769541853207 0.02395853892224864452997465102 2.72501740502e-06
10 0.04473629039778214055992344406 0.02395871409914178947550918280 2.01918461425e-07
11 0.04473628295735141684956930350 0.02395872707857492077823017572 1.49608052512e-08
12 0.04473628240606795227909993835 0.02395872804025939239070240562 1.10849018094e-09
13 0.04473628236522174893968490660 0.02395872811151340584997873671 8.21312776066e-11
14 0.04473628236219533441993488016 0.02395872811679282384392635644 6.08534626789e-12
15 0.04473628236197109852827296072 0.02395872811718399134381489950 4.50881079752e-13
16 0.04473628236195448423608868001 0.02395872811721297408644352622 3.34070961782e-14
17 0.04473628236195325323465204219 0.02395872811721512150250060613 2.47522933467e-15

[Kekeli]

why are you taking the square root of the Ein?

[arcticblue]

As E is a vector I took the error to be the difference between two iterations. So based on that I took the difference of u/u' and v/v' then summed the square of these values and took the square root to get the combined length, taking this to be the error.

I see if I remove the sqrt and just take the error as the sum of the differences squared then I get the correct answer.

Have I just misunderstood how to calculate an error in gradient descent? If I have then if someone could point out the particular slide or section of the lecture to re-watch I would be grateful. Alternatively if this is just something I should have known then a link to something explaining how to calculate the error would be great.

Thank you.

[Ziad Hatahet]

You should use the given error equation: instead of the one you are using.

[arcticblue]

Of course, it's so obvious now that you've pointed it out and I've re-read the question. Thank you.