InfoNCE

\[I(X ; Y) \geq \mathbb{E} [ \frac{1}{K} \sum_{i=1}^K \log \frac{\exp f(x_i, y_i)}{\frac{1}{K} \sum_{j=1}^K exp f(x_i, y_j)} ]\]

where expectation is over \(K\) independent samples \(\{(x_i, y_i)\}_{i=1}^K\) from the joint distribution \(p(x, y)\).