The cluster sizes are unbalanced with|G 1|/|G 2| = 2, where we randomly choose200 number "0" and100 number of "5" for each repetition. Here we choose three clusters:G1 containing the "T-shirt/top",G2 containing the "Trouser" andG3 containing the "Dress", so that the number of clusters isK = 3 in the algorithms.

We adopt gradient-based method such as Adam [5] to update the model parameters. We use a two-hidden-layer neural network, where each "layer" is a combination of linear, batch norm [4], ReLU, and dropout (p = 0.2) layers with dimension200. SO-EBM draws512samples from the proposal distribution to estimate the gradient of the model parameters. The proposal distribution is a mixture of Gaussians with 3 components where the variancesare {0.02,0.05,0.1}. We use a two-layer gated recurrent unit (GRU) with hidden-size128 as the forecasting model.