Reviews: On Fenchel Mini-Max Learning

Summary of main contribution (in my view): It is easy to obtain a Monte Carlo estimate of the partition function - while such an estimate is unbiased, the log of the estimate is an underestimate of log-partition function. This means that an estimate for the log-likelihood constructed using this estimate *overestimates* the log-likelihood, which causes many issues in practice because it is not good to think the model is doing better than it actually is. Prior work (notably, RAISE [a]) has developed a way of overestimating the log-partition function and therefore underestimating the log-likelihood. But to my knowledge, there does not exist a way of estimating the log-partition function and the log-likelihood in an unbiased fashion. It works by applying a simple transformation, namely the Fenchel conjugate of -log(t).