Figure 1. A spiking network can exactly solve a high-dimensional causal inference problem.

(a,b) Generative model. A potentially very large number N of hidden causes generate an observation (a). Each cause i is represented as an entry of the N dimensional vector r, and it is characterized by a non-negative number, r_i ≥ 0, called cause coefficient. The cause coefficient r_i indicates both presence of cause i, if non-zero, and its strength, such as contrast or concentration. Associated to each cause i there is a feature vector u_i of dimension M. The observation μ is a linear combination of the feature vectors –causes– weighted by non-negative cause coefficients r_i and corrupted by noise (b). (c) A network of integrate-and-fire neurons with tuned inhibition implements dynamic, spike-based explaining away and solves a causal inference problem corresponding to quadratic programming with non-negativity constraints. Global inhibition (α term) and renormalized reset voltages (β term) implement L1 and L2 regularization, respectively.