IMPLEMENTING A HIERARCHICAL DEEP LEARNING APPROACH FOR SIMULATING MULTILEVEL AUCTION

(2) The ELBO consists of two terms: the reconstruction term, Eqϕ(z|x)[log pθ(x|z)], which measures the ability of the model to reconstruct the data given the latent variable, and the regularization term, DKL(qϕ(z|x)||pθ(z)), which measures the divergence between the approximate posterior and the prior distribution over the latent space. [...] Consequently, it is necessary to approximate both the conditional distribution of the random variable representing the number of bids and the conditional distribution of the bids themselves. [...] We recall that in the context of wasserstein GANs, the critic replaces the discriminator of the original framework, and predicts the distance between a given point and the decision boundary separating real and fake samples (instead of predicting the probability that the input is real). [...] In addition, the decision tree and the k-NN both assigned all instances of the real test-bed to the same class (class 0 for the decision tree and class 1 for the k-NN). [...] To ensure the reliability of the generated data, we evaluated the performances of the synthesizers by employing inception scores and assessing the faithfulness of the synthetic auction features.