Optimal and computationally tractable lower bounds for logistic log-likelihoods

The article titled 'Optimal and computationally tractable lower bounds for logistic log-likelihoods' discusses the ongoing research in computational statistics, particularly the optimization of objective functions involving the logit transform, a key component in regression models for binary data. The study emphasizes the development of effective minorize-maximize (MM) algorithms for point estimation and variational schemes for approximate Bayesian inference. While previous efforts have largely concentrated on tangent quadratic minorizers, this research introduces a novel piece-wise quadratic lower bound that uniformly enhances any existing tangent quadratic minorizer. This advancement is crucial as it addresses the uncertainty surrounding the derivation of sharper tangent lower bounds without compromising tractability. The implications of this work extend to the generalized lasso problem, showcasing its relevance in contemporary statistical methodologies.