classification

Classification: supervised learning where the target value is class label (discrete attribute, e.g. integer, letter, word)

Training a classifier

We train a classifier $f_{\theta }$ with parameters $\theta$ on a dataset $\mathcal{D}=\{({\mathbf{x}}_i,y_i){\}}_{i=1}^n$ to output the probability of a datapoint belonging to the class $y$ given the feature vector $x$, $P_{\theta }(y|\mathbf{x})$.
The optimal parameters maximize the probability of the true labels:

$$\begin{array}{r}{\theta }^{\ast }=\arg \underset{\theta }{\max }{\mathbb{E}}_{(\mathbf{x},y)\in \mathcal{D}}[P_{\theta }(y|\mathbf{x})])]\end{array}$$

When training with mini-batches $B\subset \mathcal{D}$:

$$\begin{array}{r}{\theta }^{\ast }=\arg \underset{\theta }{\max }{\mathbb{E}}_{B\subset \mathcal{D}}\left[\sum _{(\mathbf{x},y)\in B}{P}_{\theta }(y|\mathbf{x})\right]\end{array}$$

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softmax | cross-entropy loss

Having an “other” class never goes well, because there is no “other” feature the model can map to, same as finding negative examples for contrastive learning.
If you go with uncertainty in distribution, you have the aleatoric vs epistemic uncertainty thing, can’t say whether it’s uncertain or not part of the set.

References

alfcnz NYU