Deterministic neural nets have been shown to learn effective predictors on a wide range of machine learning problems. However, as the standard approach is to train the network to minimize a prediction loss, the resultant model remains ignorant to its prediction confidence. Orthogonally to Bayesian neural nets that indirectly infer prediction uncertainty through weight uncertainties, we propose explicit modeling of the same using the theory of subjective logic. By placing a Dirichlet distribution on the class probabilities, we treat predictions of a neural net as subjective opinions and learn the function that collects the evidence leading to these opinions by a deterministic neural net from data. The resultant predictor for a multi-class classification problem is another Dirichlet distribution whose parameters are set by the continuous output of a neural net. We provide a preliminary analysis on how the peculiarities of our new loss function drive improved uncertainty estimation. We observe that our method achieves unprecedented success on detection of out-of-distribution queries and endurance against adversarial perturbations.

Neural networks are the cornerstone of modern machine learning, yet can be difficult to interpret, give overconfident predictions and are vulnerable to adversarial attacks. Bayesian neural networks (BNNs) provide some alleviation of these limitations, but have problems of their own. The key step of specifying prior distributions in BNNs is no trivial task, yet is often skipped out of convenience. In this work, we propose a new class of prior distributions for BNNs, the Dirichlet scale mixture (DSM) prior, that addresses current limitations in Bayesian neural networks through structured, sparsity-inducing shrinkage. Theoretically, we derive general dependence structures and shrinkage results for DSM priors and show how they manifest under the geometry induced by neural networks. In experiments on simulated and real world data we find that the DSM priors encourages sparse networks through implicit feature selection, show robustness under adversarial attacks and deliver competitive predictive performance with substantially fewer effective parameters. In particular, their advantages appear most pronounced in correlated, moderately small data regimes, and are more amenable to weight pruning. Moreover, by adopting heavy-tailed shrinkage mechanisms, our approach aligns with recent findings that such priors can mitigate the cold posterior effect, offering a principled alternative to the commonly used Gaussian priors.

GPN applies a personalized page rank (PPR) module to diffuse the evidence among neighboring nodes.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Ensemble approaches for uncertainty estimation have recently been applied to the tasks of misclassification detection, out-of-distribution input detection and adversarial attack detection. Prior Networks have been proposed as an approach to efficiently emulate an ensemble of models for classification by parameteris-ing a Dirichlet prior distribution over output distributions.

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Pi 1, which is clearly not possible. The possibility form 1 prior-data conflicts is witnessed in the followingexample. Assume a conflict at the upper boundPi. Then kiN > Pi Pi, which is a prior-data agreementwithPi bydefinition. Next, we consider the case for a prior-data conflict, that is, the bounds from Equation 5. We consider a larger version of the chain problem Araya-López et al. [2011] with30-states.

We expand Eq. 10 as: q There are three KL divergence terms in our training objective ELBO (Eq. Medium and Y elp Large datasets, we follow (Guu et al., 2018) to use a three-layer attentional LSTM Skip connections are also used between adjacent LSTM layers. We apply annealing and free-bits techniques following (Li et al., 2019) to the KL term on prototype variable, As in Section 4.3, here we show more generated examples through interpolation on MSCOCO dataset. Table 6: Qualitative examples from the MSCOCO dataset on interpolated sentence generation given the prototype.