  Since its inception, the neural estimation of mutual information (MI) has
demonstrated the empirical success of modeling expected dependency between
high-dimensional random variables. However, MI is an aggregate statistic and
cannot be used to measure point-wise dependency between different events. In
this work, instead of estimating the expected dependency, we focus on
estimating point-wise dependency (PD), which quantitatively measures how likely
two outcomes co-occur. We show that we can naturally obtain PD when we are
optimizing MI neural variational bounds. However, optimizing these bounds is
challenging due to its large variance in practice. To address this issue, we
develop two methods (free of optimizing MI variational bounds): Probabilistic
Classifier and Density-Ratio Fitting. We demonstrate the effectiveness of our
approaches in 1) MI estimation, 2) self-supervised representation learning, and
3) cross-modal retrieval task.
