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Book Sections Year : 2018

Online targeted learning for time series


We consider the case that we observe a time series where at each time we observe, in chronological order, a covariate vector, a treatment, and an outcome.We assume that the conditional probability distribution of this time-specific data-structure, given the past, depends on it through a fixed (in time) dimensional summary measure, and that this conditional distribution is described by a fixed (in time) mechanism that is known to be an element of some model space (e.g., unspecified). We propose a causal model that is compatible with this statistical model and define a family of causal effects in terms of stochastic interventions on a subset of the treatment nodes on a future outcome, and establish identifiability of these causal effects from the observed data-distribution. A key feature of the estimation problem addressed in this chapter is that the data is ordered and that statistical inference is based on asymptotics in time. A key feature of our proposed "one-step" and targeted minimum loss estimators is that they are online, ie, they can be updated continuously in time and still be computationally feasible, analogue to stochastic gradient descent algorithms for fitting parametric models in the computer science literature.
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hal-01487574 , version 1 (12-03-2017)



Mark J van Der Laan, Antoine Chambaz, Sam Lendle. Online targeted learning for time series. Targeted Learning in Data Science, Springer International Publishing, pp.317-346, 2018, Springer Series in Statistics, ⟨10.1007/978-3-319-65304-4_19⟩. ⟨hal-01487574⟩
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