In the last decades, energy-based models (EBMs) have become an important class of probabilistic models in which a component of the likelihood is intractable and therefore cannot be evaluated explicitly. Consequently, parameter estimation in EBMs is challenging for conventional inference methods. In this work, we provide a unified framework that connects noise contrastive estimation (NCE), reverse logistic regression (RLR), multiple importance sampling (MIS), and bridge sampling within the context of EBMs. We further show that these methods are equivalent under specific conditions. This unified perspective clarifies relationships among existing methods and enables the development of new estimators, with the potential to improve statistical and computational efficiency. Furthermore, this study helps elucidate the success of NCE in terms of its flexibility and robustness, while also identifying scenarios in which its performance can be further improved. Hence, rather than being a purely descriptive review, this work offers a unifying perspective and additional methodological contributions. The MATLAB code used in the numerical experiments is also made freely available to support the reproducibility of the results.

Joulani et al. (2013) have studied multi-armed bandits with delayed feedback under the assumption that the rewards are stochastic and the delays are sampled from a fixed distribution.

However, some recent studies haverecognized that most ofthese approaches failtoimprovethe performance over empirical risk minimization especially when applied to overparameterized neural networks.

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Althoughintuitive,sucha nativelabelassignment strategycannot revealtheunderlying semantic similarity between aquery anditspositivesandnegatives,andimpairs performance, since some negatives are semantically similar to the query or even share the same semantic class as the query.