Facit til forløbet "Cambridge Analytica skandalen - matematik"
NoteFacit – opgave 1
\(\textrm{Vm}(\sigma)=]0,1[\)
NoteFacit – opgave 2
| Vægt | Feature | Værdi |
|---|---|---|
| \(w_0\) | bias |
\(-3.666\) |
| \(w_1\) | likes_art_culture |
\(0.05245\) |
| \(w_2\) | likes_science_tech |
\(0.03711\) |
| \(w_3\) | likes_travel_nature |
\(0.02928\) |
| \(w_4\) | likes_entertainment |
\(0.003369\) |
| \(w_5\) | likes_sports |
\(-0.01699\) |
| \(w_6\) | likes_political_social |
\(0.04105\) |
\(R^2=0.5976\)
RMSE = \(0.0746\)
NoteFacit – opgave 3
Vægtet sum: \(-2.207\)
Prædikteret openness-score: \(0.099\)
NoteFacit – opgave 4
Sebastians openness-score: \(0.300\)
Bettinas openness-score: \(0.420\)
Viggas openness-score: \(0.266\)
NoteFacit – opgave 5
\[ \frac{\partial}{\partial w_1} (w_0 + w_1 \cdot x_1 + w_2 \cdot x_2 + \cdots + w_6 \cdot x_6) = x_1 \]
\[ \frac{\partial}{\partial w_1} \sigma (w_0 + w_1 \cdot x_1 + w_2 \cdot x_2 + \cdots + w_6 \cdot x_6) = o \cdot (1-o) \cdot x_1 \]
hvor
\[ o = \sigma (w_0 + w_1 \cdot x_1 + w_2 \cdot x_2 + \cdots + w_6 \cdot x_6) \]
\[ \frac{\partial E}{\partial w_1} = -(t-o) \cdot o \cdot (1-o) \cdot x_1 \]