How do we know treatment effects vary by person from incomplete data?

Estimating how treatments affect different people requires filling in gaps in panel data (observations of many units over time). Prior matrix completion theory only guaranteed accurate average treatment effects, not individual-level estimates. This work provides an efficient algorithm achieving $\tilde{O}(\sqrt{1/n + n/m^2})$ error per unit, with the first tight row-wise perturbation bounds for low-rank approximation—a technical result useful beyond causal inference.