add some certainty stuff

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lukas-heilgenbrunner 2024-04-11 12:39:43 +02:00
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@ -15,9 +15,15 @@ The model with the weights of the current loop iteration predicts pseudo predict
\end{equation} \end{equation}
Those predictions might have any numerical value and have to be squeezed into a proper distribution which sums up to 1. Those predictions might have any numerical value and have to be squeezed into a proper distribution which sums up to 1.
The Softmax function has exactly this effect: $\sum^\mathcal{S}_{i=1}\sigma(z)_i=1$ The Softmax function has exactly this effect: $\sum^\mathcal{S}_{i=1}\sigma(z)_i=1$.
Since we have a two class problem the Softmax results in two result values, the two probabilities of how certain one class is a match.
We want to calculate the distance to the class center and the more far away a prediction is from the center the more certain it is.
Vice versa, the more centered the predictions are the more uncertain the prediction is.
Labels $0$ and $1$ result in a class center of $\frac{0+1}{2}=\frac{1}{2}$.
That means taking the absolute value of the prediction minus the class center results in the certainty of the sample~\eqref{eq:certainty}.
\begin{align} \begin{align}
\label{eq:certainty}
S(z) = | 0.5 - \sigma(\mathbf{z})_0| \; \textit{or} \; \arg\max_j \sigma(\mathbf{z}) S(z) = | 0.5 - \sigma(\mathbf{z})_0| \; \textit{or} \; \arg\max_j \sigma(\mathbf{z})
\end{align} \end{align}