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SUMMARY:Counterfactual inference in sequential experimental design - Raaz 
 Dwivedi (Harvard and MIT)
DTSTART:20220624T123000Z
DTEND:20220624T140000Z
UID:TALK175277@talks.cam.ac.uk
CONTACT:Qingyuan Zhao
DESCRIPTION:We consider the problem of counterfactual inference in sequent
 ially designed experiments wherein a collection of N units each undergo a 
 sequence of interventions for T time periods\, based on policies that sequ
 entially adapt over time. Our goal is counterfactual inference\, i.e.\, es
 timate what would have happened if alternate policies were used\, a proble
 m that is inherently challenging due to the heterogeneity in the outcomes 
 across units and time. To tackle this task\, we introduce a suitable laten
 t factor model where the potential outcomes are determined by exogenous un
 it and time level latent factors. Under suitable conditions\, we show that
  it is possible to estimate the missing (potential) outcomes using a simpl
 e variant of nearest neighbors. First\, assuming a bilinear latent factor 
 model and allowing for an arbitrary adaptive sampling policy\, we establis
 h a distribution-free non-asymptotic guarantee for estimating the missing 
 outcome of any unit at any time\; under suitable regularity conditions\, t
 his guarantee implies that our estimator is consistent. Second\, for a gen
 eric non-parametric latent factor model\, we establish that the estimate f
 or the missing outcome of any unit at time T satisfies a central limit the
 orem as T goes to infinity\, under suitable regularity conditions. Finally
 \, en route to establishing this central limit theorem\, we prove a non-as
 ymptotic mean-squared-error bound for the estimate of the missing outcome 
 of any unit at time T. Our work extends the recently growing literature on
  inference with adaptively collected data by allowing for policies that po
 ol across units and also compliment the matrix completion literature when 
 the entries are revealed sequentially in an arbitrarily dependent manner b
 ased on prior observed data.\n\nhttps://arxiv.org/abs/2202.06891 \n(Joint 
 work with Susan Murphy and Devavrat Shah)
LOCATION:MR3\,  Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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