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Uncertainty quantification in neural networks gained a lot of attention in the past years. The most popular approaches, Bayesian neural networks (BNNs), Monte Carlo dropout, and deep ensembles have one thing in common: they are all based on some kind of mixture model. While the BNNs build infinite mixture models and are derived via variational inference, the latter two build finite mixtures trained with the maximum likelihood method. In this work we investigate the effect of training an infinite mixture distribution with the maximum likelihood method instead of variational inference. We find that the proposed objective leads to stochastic networks with an increased predictive variance, which improves uncertainty based identification of miss-classification and robustness against adversarial attacks in comparison to a standard BNN with equivalent network structure. The new model also displays higher entropy on out-of-distribution data.
Although deep learning models have driven state-of-the-art performance on a wide array of tasks, they are prone to learning spurious correlations that should not be learned as predictive clues. To mitigate this problem, we propose a causality-based t
We train a generator by maximum likelihood and we also train the same generator architecture by Wasserstein GAN. We then compare the generated samples, exact log-probability densities and approximate Wasserstein distances. We show that an independent
A common assumption in causal modeling posits that the data is generated by a set of independent mechanisms, and algorithms should aim to recover this structure. Standard unsupervised learning, however, is often concerned with training a single model
Given a mixture between two populations of coins, positive coins that each have -- unknown and potentially different -- bias $geqfrac{1}{2}+Delta$ and negative coins with bias $leqfrac{1}{2}-Delta$, we consider the task of estimating the fraction $rh
While deep neural networks provide good performance for a range of challenging tasks, calibration and uncertainty estimation remain major challenges, especially under distribution shift. In this paper, we propose the amortized conditional normalized