In latent-variable LiNGAM, causal effects are generically identifiable and estimable from higher-order cumulants using a single proxy, even with a proxy-to-treatment edge, or a single instrument for several treatments.
The existence of such a polynomial is guaranteed as long asL 1 is non-Gaussian; see, for example, Kivva et al
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Causal Effect Identification in lvLiNGAM from Higher-Order Cumulants
In latent-variable LiNGAM, causal effects are generically identifiable and estimable from higher-order cumulants using a single proxy, even with a proxy-to-treatment edge, or a single instrument for several treatments.