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SUMMARY:Virtual Seminar: 'Statistical Inference with M-Estimators on Bandi
 t Data’ - Kelly Zhang\, Harvard University
DTSTART:20210429T130000Z
DTEND:20210429T140000Z
UID:TALK158950@talks.cam.ac.uk
CONTACT:Alison Quenault
DESCRIPTION:Bandit algorithms are increasingly used in real world sequenti
 al decision making problems\, from online advertising to mobile health. As
  a result\, there are more datasets collected using bandit algorithms and 
 with that an increased desire to be able to use these datasets to answer s
 cientific questions like: Did one type of ad increase the click-through ra
 te more or lead to more purchases? In which contexts is a mobile health in
 tervention effective? However\, it has been shown that classical statistic
 al estimators\, like the ordinary least squares estimator\, fail to provid
 e reliable confidence intervals when used with bandit data. Recently metho
 ds have been developed to conduct statistical inference using simple model
 s fit to data collected with multi-arm bandits. However there is a lack of
  general methods for conducting statistical inference using more complex m
 odels. In this work\, we develop theory justifying the use of M-estimation
  (Van der Vaart\, 2000)\, traditionally used with i.i.d data\, to provide 
 inferential methods for a large class of estimators—including least squa
 res and maximum likelihood estimators—but now with data collected with (
 contextual) bandit algorithms. To do this we generalize the use of adaptiv
 e weights pioneered by Hadad et al. (2019) and Deshpande et al. (2018). Sp
 ecifically\, in settings in which the data is collected via a (contextual)
  bandit algorithm\, we prove that adaptively weighted M-estimators are uni
 formly asymptotically normal and demonstrate empirically that we can use t
 heir asymptotic distribution to construct reliable confidence regions for 
 a variety of inferential targets.
LOCATION:Virtual Seminar 
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