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CATEGORIES:Causal Inference Reading Group
SUMMARY:Counterfactual inference in sequential experimenta
l design - Raaz Dwivedi (Harvard and MIT)
DTSTART;TZID=Europe/London:20220624T133000
DTEND;TZID=Europe/London:20220624T150000
UID:TALK175277AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/175277
DESCRIPTION:We consider the problem of counterfactual inferenc
e in sequentially designed experiments wherein a c
ollection of N units each undergo a sequence of in
terventions for T time periods\, based on policies
that sequentially adapt over time. Our goal is co
unterfactual inference\, i.e.\, estimate what woul
d have happened if alternate policies were used\,
a problem that is inherently challenging due to th
e heterogeneity in the outcomes across units and t
ime. To tackle this task\, we introduce a suitable
latent factor model where the potential outcomes
are determined by exogenous unit and time level la
tent factors. Under suitable conditions\, we show
that it is possible to estimate the missing (poten
tial) outcomes using a simple variant of nearest n
eighbors. First\, assuming a bilinear latent facto
r model and allowing for an arbitrary adaptive sam
pling policy\, we establish a distribution-free no
n-asymptotic guarantee for estimating the missing
outcome of any unit at any time\; under suitable r
egularity conditions\, this guarantee implies that
our estimator is consistent. Second\, for a gener
ic non-parametric latent factor model\, we establi
sh that the estimate for the missing outcome of an
y unit at time T satisfies a central limit theorem
as T goes to infinity\, under suitable regularity
conditions. Finally\, en route to establishing th
is central limit theorem\, we prove a non-asymptot
ic mean-squared-error bound for the estimate of th
e missing outcome of any unit at time T. Our work
extends the recently growing literature on inferen
ce with adaptively collected data by allowing for
policies that pool across units and also complimen
t the matrix completion literature when the entrie
s are revealed sequentially in an arbitrarily depe
ndent manner based on prior observed data.\n\nhttp
s://arxiv.org/abs/2202.06891 \n(Joint work with Su
san Murphy and Devavrat Shah)
LOCATION:MR3\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge
CONTACT:Qingyuan Zhao
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