  Causal effect estimation has been studied by many researchers when only
observational data is available. Sound and complete algorithms have been
developed for pointwise estimation of identifiable causal queries. For
non-identifiable causal queries, researchers developed polynomial programs to
estimate tight bounds on causal effect. However, these are computationally
difficult to optimize for variables with large support sizes. In this paper, we
analyze the effect of "weak confounding" on causal estimands. More
specifically, under the assumption that the unobserved confounders that render
a query non-identifiable have small entropy, we propose an efficient linear
program to derive the upper and lower bounds of the causal effect. We show that
our bounds are consistent in the sense that as the entropy of unobserved
confounders goes to zero, the gap between the upper and lower bound vanishes.
Finally, we conduct synthetic and real data simulations to compare our bounds
with the bounds obtained by the existing work that cannot incorporate such
entropy constraints and show that our bounds are tighter for the setting with
weak confounders.
