Fig. 1: Schematic and simulation of effectome inference using IVs.

a, Example of a single fly experiment. Some sets of neurons in the fly are observed (black circles within the field of view of the microscope), and a subset of these express opsin and are being stimulated (neurons under red light) with a white noise pattern (red trace). Another set of neurons may be unobserved. All neurons can have directed interactions via synapses (arrows), and only the effects of stimulated neurons can be estimated (black arrows connecting stimulated neurons to observed neurons). b, In this setup, the laser can be cast as an instrumental variable (IV) that directly affects only the opsin-expressing neurons (arrow labelled α from L to X). Stimulated neurons in turn have a direct effect on downstream observed neurons (arrow β from X to Y), but common unobserved inputs (Z) may corrupt attempts to estimate the direct relationship. The IV approach uses the joint relationship between the laser and downstream neurons to determine the direct effect of the stimulated neurons on postsynaptic neurons. c, Top, a simulated example of confounding effect Z, which is given by a slow drifting signal (smooth green trace). Raw, uncorrupted responses of neurons X and Y are independent (pink and brown traces, middle), meaning that there is no connection from X to Y. Bottom, observations X and Y after adding the confounding signal Z, resulting in substantial correlation. d, The least-squares estimate of the weight from X to Y (blue line; mean ± s.d.; n = 100 simulations) exhibits large bias regardless of sample size, whereas the IV estimate (orange line) converges to the true effectome weight of zero (black dashed line).