Facit til forløbet "Cambridge Analytica skandalen - matematik"

\(\textrm{Vm}(\sigma)=]0,1[\)

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 = \(0.0746\)

  • Vægtet sum: \(-2.207\)

  • Prædikteret openness-score: \(0.099\)

  • Sebastians openness-score: \(0.300\)

  • Bettinas openness-score: \(0.420\)

  • Viggas openness-score: \(0.266\)

\[ \frac{\partial}{\partial w_1} (w_0 + w_1 \cdot x_1 + w_2 \cdot x_2 + \cdots + w_6 \cdot x_6) = x_1 \]

\[ \frac{\partial}{\partial w_1} \sigma (w_0 + w_1 \cdot x_1 + w_2 \cdot x_2 + \cdots + w_6 \cdot x_6) = o \cdot (1-o) \cdot x_1 \]

hvor

\[ o = \sigma (w_0 + w_1 \cdot x_1 + w_2 \cdot x_2 + \cdots + w_6 \cdot x_6) \]

\[ \frac{\partial E}{\partial w_1} = -(t-o) \cdot o \cdot (1-o) \cdot x_1 \]