Figure 1

The Choice of Model. Three prior distribution candidates over network matrix coefficients: Gaussian, Laplace, and "very sparse" distribution (P(a _ij ) ∝ exp(- τ|a _ij |^0.4)). We show contour plots of density functions over two entries, coloured areas contain the same probability mass for each of the distributions. Upper row: prior distributions (unit variance), and likelihood for single measurement (linear constraint with Gaussian uncertainty). Lower row: corresponding posterior distributions. The Gaussian is spherically distributed, the others shift probability mass towards the axes, giving more mass to sparse tuples (≥ 1 entry close to 0). This effect is clearly visible in the posterior distributions. For the Gaussian prior, the area close to the axes has rather low mass. The Laplace-posterior is skewed: more mass is concentrated close to the vertical axis. Both posteriors are log-concave (and unimodal). The "very sparse"-posterior is shrunk towards the axes more strongly, sparsity is enforced stronger than for the Laplace prior. But it is bimodal, giving two different interpretations for the single observation. This multimodality increases exponentially with the number of dimensions, rendering accurate inference very difficult. The Laplace prior therefore is a good compromise between computational tractability and suitability of the model.