September 3rd, 2025   

The Department of Statistics is pleased to announce that Professor Victor H. de la Pena’s 2004 paper “Self-normalized processes: exponential inequalities, moment bounds and iterated logarithm laws” (co-authored with Michael J. Klass and Tze Leung Lai) has been featured as being most-read article in “The Annals of Probability”, as reported by Project Euclid on September 3 (https://projecteuclid.org/journals/annals-of-applied-probability). 

This achievement represents the culmination of Professor de la Pena’s pioneering work in self-normalization theory, which he introduced in his 1999 Annals of Probabilitay paper, establishing a sharp extension of Martingale exponential inequalities to the case of Martingales over their quadratic variation. 

Self-normalization is a revolutionary technique that allows valid statistical inference in complex settings where data dependencies make traditional methods fail—from analyzing financial markets to optimizing sequential decision-making—and provides tighter, more adaptive bounds that improve as more data is collected. 

The 1999 and 2004 papers’ methods, decoupling and pseudo-maximization, solved a fundamental challenge that Joseph L. Doob, one of the founders of modern probability, had identified as essential, yet unresolved. 

The results of the papers have enabled breakthrough performance improvements in online learning algorithms that are now fundamental to recommendation systems, clinical trials, and adaptive experimentation. The transformative impact of this theoretical framework on machine learning is especially exemplified by the seminal work of Abbasi-Yadkori et al. (2011) on linear stochastic bandits. In their highly influential paper—now a cornerstone of modern reinforcement learning with thousands of citations—the authors’ key innovation, a novel tail inequality for vector-valued martingales, builds on the techniques introduced by de la Pena, et al. 

“The journey from solving Doob’s theoretical challenge to seeing these methods become essential infrastructure for modern AI applications demonstrating the enduring value of rigorous mathematical foundations,” notes Professor de la Pena.