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474 Targeted learninglihood estimators (van der Laan and Rubin, 2006). In this manner, we canmap any candidate estimator into a targeted estimator and we can use thesuper-learner based on the library of candidate targeted estimators. Alternatively,one computes this targeted fit of a super-learner based on a library ofnon-targeted candidate estimators.40.5 Targeted learningThe real message is that one needs to make the learning process targetedtowards its goal. The goal is to construct a good estimator of Ψ(Q 0 ), andthat is not the same goal as constructing a good estimator of the much moreambitious infinite-dimensional object Q 0 .Forexample,estimatorsofΨ(Q 0 )will have a variance that behaves as 1/n, whileaconsistentestimatorofQ 0at a point will generally only use local data so that its variance converges at asignificant slower rate than 1/n. ThebiasofanestimatorofQ 0 is a function,while the bias of an estimator of ψ 0 is just a finite dimensional vector of realnumbers. For parametric maximum likelihood estimators one fits the unknownparameters by solving the score equations. An MLE in a semi-parametricmodel would aim to solve all (infinite) score equations, but due to the curse ofdimensionality such an MLE simply does not exist for finite samples. However,if we know what score equation really matters for fitting ψ 0 , then we can makesure that our estimator will solve that ψ 0 -specific score equation. The efficientinfluence curve of the target parameter mapping Ψ : M→IR d represents thisscore.40.5.1 Targeted minimum loss based estimation (TMLE)The above mentioned insights evolved into the following explicit procedurecalled Targeted Minimum Loss Based Estimation (TMLE); see, e.g., van derLaan and Rubin (2006), van der Laan (2008) and van der Laan and Rose(2012). Firstly, one constructs an initial estimator of Q 0 such as a loss-basedsuper-learner based on a library of candidate estimators of Q 0 .Onenowdefinesa loss function L(Q) so that Q 0 = arg min Q P 0 L(Q), and a least-favorablesubmodel {Q(ɛ) :ɛ} ⊂Mso that the generalized score d dɛ L{Q(ɛ)}∣ ∣ɛ=0equalsor spans the efficient influence curve D ∗ (Q, g). Here we used the notationP 0 f = ∫ f(o)dP 0 (o). This least-favorable submodel might depend on an unknownnuisance parameter g = g(P ). One is now ready to target the fit Q nin such a way that its targeted version solves the efficient score equationP n D ∗ (Q ∗ n,g 0 ) = 0. That is, one defines ɛ n = arg min ɛ P n L{Q n (ɛ)}, and theresulting update Q 1 n = Q n (ɛ n ). This updating process can be iterated till convergenceat which point ɛ n =0sothatthefinalupdateQ ∗ n solves the scoreequation at ɛ n = 0, and thus P n D ∗ (Q ∗ n,g 0 )=0.Theefficientinfluencecurve