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Conditional Probability
If we can learn p(x,y)p(x, y)p(x,y), we can recover p(y∣x)p(y \mid x)p(y∣x) from the definition of Conditional Probability.
The Conditional Probability distribution over labels is represented as p(x∣y)p(x \mid y)p(x∣y).
p(y∣x)=p(x,y)p(x)\displaystyle p(y \mid x)=\frac{p(x, y)}{p(x)}p(y∣x)=p(x)p(x,y)​ by the definition of Conditional Probability.