William Rae Thompson

William Rae Thompson was an American mathematician and statistician best known for inventing Thompson sampling, a foundational heuristic in machine learning and

William Rae Thompson
This article is about the American mathematician. For the Canadian entomologist, see William Robin Thompson.
William Rae Thompson
Born(1896-07-29)July 29, 1896
DiedMay 30, 1993(1993-05-30) (aged 96)
Resting place
Cortland Rural Cemetery, Cortland, New York
EducationColumbia University
Yale University
Known forThompson sampling
SpouseMary E. Dalton Thompson (1903–1992)
Scientific career
InstitutionsYale Department of Pathology
New York State Department of Health

William Rae Thompson was an American mathematician and statistician best known for inventing Thompson sampling, a foundational heuristic in machine learning and reinforcement learning for the multi-armed bandit problem. First published in 1933, his algorithm saw a significant resurgence in the 21st century and has since become a standard technique in artificial intelligence and online decision-making.[1][2] Beyond his work in pure mathematics, Thompson spent decades applying statistical analysis to the medical sciences, with extensive contributions to pathology and immunology.

Early life and education

Thompson earned his Bachelor of Arts from Columbia University in 1923[3]. He then attended Yale University, where he received his Ph.D. in mathematics in 1930.[4] His doctoral dissertation was titled On The Possible Forms Of Discriminants Of Algebraic Fields.[5]

Academic career

Thompson was affiliated with Yale University from 1924 to 1936. Following his graduate studies, he applied his mathematical background to the medical sciences. He worked in the Yale Department of Pathology under Dr. Milton Winternitz, serving as a Research Assistant with the rank of Instructor from 1928 to 1934, and subsequently with the rank of Assistant Professor from 1934 to 1936.[6]

During this time, he contributed to multiple scientific articles published by the Department of Pathology.[7] He later moved to the Division of Laboratories and Research at the New York State Department of Health in Albany, where he continued to publish statistical analyses related to medical testing and immunology through the 1940s and 1950s.[8][9]

In 1953, Thompson was elected as a Fellow of the American Statistical Association in recognition of his contributions to the field of biostatistics.[10]

Publications and Thompson sampling

In 1933, while at Yale, Thompson published the scientific paper "On the likelihood that one unknown probability exceeds another in view of the evidence of two samples" in the journal Biometrika.[11]

The paper introduced what is now known as Thompson sampling. The algorithm proposes a Bayesian approach to the exploration-exploitation dilemma: it allocates a proportion of trials to an action matching the posterior probability that the action is optimal. Thompson originally framed this problem in the context of clinical trials, aiming to minimize patient exposure to inferior treatments.[11]

Legacy and modern resurgence

For several decades after its publication, Thompson's 1933 algorithm was largely overlooked by the broader statistical and computer science communities. As researchers later noted, the algorithm "was largely ignored in the academic literature until recently, although it was independently rediscovered several times in the interim as an effective heuristic."[2] However, in the early 2010s, empirical studies demonstrated its state-of-the-art performance in complex, multi-armed bandit scenarios. As researchers at the time observed, the "Thompson Sampling algorithm has experimentally been shown to be close to optimal,"[12] sparking rapid adoption in online advertising and reinforcement learning.[13]

Today, his 1933 paper has garnered over 5,000 academic citations. The algorithm he invented is recognized as a foundational concept in the field of artificial intelligence, with modern scholars noting that it "addresses a broad range of problems in a computationally efficient manner and is therefore enjoying wide use."[2] It has also been the subject of dedicated modern textbooks and extensive theoretical analysis proving its optimal regret bounds.[1][12]

Because of their similar names and overlapping active periods, the algorithm has frequently been misattributed to the Canadian entomologist William Robin Thompson. Archival records from Yale University definitively separate the mathematician from his contemporary, confirming William Rae Thompson as the true inventor.[14]

Selected publications

  • Hussey, R. G.; Thompson, William R.; Calhoun, E. T. (1927). "The Influence of X-Rays on the Development of Drosophila Larvae". Science. 66 (1698): 65–66. doi:10.1126/science.66.1698.65.
  • Thompson, William R. (1930). On The Possible Forms Of Discriminants Of Algebraic Fields (Ph.D. thesis). Yale University.
  • Thompson, William R. (1933). "On the likelihood that one unknown probability exceeds another in view of the evidence of two samples". Biometrika. 25 (3/4): 285–294. doi:10.1093/biomet/25.3-4.285.
  • Thompson, William R. (1933). "Frequency-Distribution of Volume of Islands of Langerhans in the Pancreas of Man, Monkey and Dog". Science. 78 (2021): 270. doi:10.1126/science.78.2021.270.

References

  1. ^ a b Lattimore, Tor; Szepesvári, Csaba (2020). Bandit Algorithms. Cambridge University Press. doi:10.1017/9781108571401.
  2. ^ a b c Russo, Daniel; Van Roy, Benjamin; Kazerouni, Abbas; Osband, Ian; Wen, Zheng (2018). "A Tutorial on Thompson Sampling". Foundations and Trends in Machine Learning. 11 (1): 1–96. doi:10.1561/2200000070.
  3. ^ Columbia University. Committee on General Catalogue (1932). Columbia University Alumni Register, 1754-1931. New York: Columbia University Press – via HathiTrust.
  4. ^ Historical Register of Yale University, 1701-1937. Yale University. 1939 [1937].
  5. ^ "On The Possible Forms Of Discriminants Of Algebraic Fields". Yale University Library Catalog. Retrieved July 2, 2026.
  6. ^ Historical Register of Yale University, 1701-1937. Yale University. 1939 [1937].
  7. ^ "Department of Pathology, Yale University, records (1891-1981)". Yale University Archives. Retrieved July 2, 2026. Historical records for the Department of Pathology, compiled beginning in 1933, listing multiple articles authored and co-authored by Thompson.
  8. ^ Thompson, William R. (1947). "Use of Moving Averages and Interpolation to Estimate Median-Effective Dose". Bacteriological Reviews. 11 (2): 115–145. PMC 440915.
  9. ^ Thompson, William R.; Rice, Christine E.; Maltaner, Elizabeth; Maltaner, Frank (1949). "Some Fundamental Notions in Estimation of Complement Fixation: I. General Relations and a Proposed Uniform Notation". The Journal of Immunology. 62 (4): 353–361.
  10. ^ "ASA Fellows". American Statistical Association. Retrieved July 6, 2026.
  11. ^ a b Thompson, William R. (1933). "On the likelihood that one unknown probability exceeds another in view of the evidence of two samples". Biometrika. 25 (3/4): 285–294. doi:10.1093/biomet/25.3-4.285.
  12. ^ a b Agrawal, Shipra; Goyal, Navin (2012). "Analysis of Thompson Sampling for the Multi-armed Bandit Problem". Conference on Learning Theory (COLT).
  13. ^ Chapelle, Olivier; Li, Lihong (2011). "An Empirical Evaluation of Thompson Sampling". Advances in Neural Information Processing Systems (NIPS). Vol. 24. pp. 2249–2257.
  14. ^ "Department of Pathology, Yale University, records (1891-1981)". Yale University Archives. Retrieved July 2, 2026.

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