DISCO Nets: DISsimilarity COefficient Networks Supplementary material

In this section, we provide details on the toy example presented in Section 1. We used the following simple experimental setting. All covariances for the bidimensional distributions are diagonal, therefore all bidimensional Gaussian distributions are parametrised by 4 parameters (μ1, μ2, σ1, σ2) where μ, σ is a mean-variance pair on each dimension. We consider a data distribution that is a mixture of 2 bidimensional Gaussian distributions, referred as GMM. The first Gaussian of the mixture, G1, is parametrised by (1, 1.5, 2, 0.8) and the second Gaussian G2 is parametrised by (0,−0.5, 0.7, 0.6). The mixture weights are 0.7 and 0.3, such that GMM = 0.7 × G1 + 0.3 × G2. We consider two models to capture the true data distribution GMM. Each model is able to represent a bidimensional Gaussian distribution parametrised by (μ1, μ2, σ1, σ2). The sets in which to search for the parameters are the same in both dimensions and both models. The set to search the means ranges from −3 to 3 by 1, and the set to search the variances ranges 0.1 to 2 by 0.5. The training dataset is composed of N = 10000 examples drawn randomly from GMM, denoted as (x1, ...,xN ). The testing dataset is composed of 1000 examples drawn randomly from GMM. During training, we draw K = 2 samples from the model and estimate the probabilistic loss defined as: