# What is the advantage of having a stochastic classification procedure?

What is the advantage of having a stochastic/probabilistic classification procedure?

The classifiers I have encountered so far are as follows. Suppose we have two outcomes $$A = \{0,1\}$$. Given a feature vector $$x$$, we have calculated a probability for each outcome and return the outcome $$a \in A$$ for which the probability is highest.

Now, I encountered a classification procedure as follows: first, map each $$x$$ to a probability distribution on $$A$$ by a mapping $$H$$. To classify $$x$$, choose an outcome $$a$$ according to the distribution $$H(x)$$.

Why not use the deterministic classification? Suppose $$H(x)$$ is 1 with probability $$0.75$$. Then, the obvious choice for an outcome would be $$1$$ and not $$0$$.

– nbro
Jun 24 '20 at 23:52