arXiv subjects

Lorenzo Noci

Publications and source records attributed to Lorenzo Noci.

21 records · Page 2Linked to original sources

arXiv2021

Disentangling the Roles of Curation, Data-Augmentation and the Prior in the Cold Posterior Effect

The "cold posterior effect" (CPE) in Bayesian deep learning describes the uncomforting observation that the predictive performance of Bayesian neural networks can be significantly improved if the Bayes posterior is artificially sharpened using a temperature parameter T<1. The CPE is problematic in theory and practice and since the effect was identified many researchers have proposed hypotheses to explain the phenomenon. However, despite this intensive research effort the effect remains poorly understood. In this work we provide novel and nuanced evidence relevant to existing explanations for the cold posterior effect, disentangling three hypotheses: 1. The dataset curation hypothesis of Aitchison (2020): we show empirically that the CPE does not arise in a real curated data set but can be produced in a controlled experiment with varying curation strength. 2. The data augmentation hypothesis of Izmailov et al. (2021) and Fortuin et al. (2021): we show empirically that data augmentation is sufficient but not necessary for the CPE to be present. 3. The bad prior hypothesis of Wenzel et al. (2020): we use a simple experiment evaluating the relative importance of the prior and the likelihood, strongly linking the CPE to the prior. Our results demonstrate how the CPE can arise in isolation from synthetic curation, data augmentation, and bad priors. Cold posteriors observed "in the wild" are therefore unlikely to arise from a single simple cause; as a result, we do not expect a simple "fix" for cold posteriors.

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arXiv2021

Precise characterization of the prior predictive distribution of deep ReLU networks

Recent works on Bayesian neural networks (BNNs) have highlighted the need to better understand the implications of using Gaussian priors in combination with the compositional structure of the network architecture. Similar in spirit to the kind of analysis that has been developed to devise better initialization schemes for neural networks (cf. He- or Xavier initialization), we derive a precise characterization of the prior predictive distribution of finite-width ReLU networks with Gaussian weights. While theoretical results have been obtained for their heavy-tailedness, the full characterization of the prior predictive distribution (i.e. its density, CDF and moments), remained unknown prior to this work. Our analysis, based on the Meijer-G function, allows us to quantify the influence of architectural choices such as the width or depth of the network on the resulting shape of the prior predictive distribution. We also formally connect our results to previous work in the infinite width setting, demonstrating that the moments of the distribution converge to those of a normal log-normal mixture in the infinite depth limit. Finally, our results provide valuable guidance on prior design: for instance, controlling the predictive variance with depth- and width-informed priors on the weights of the network.

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arXiv2021

Adversarial Learning for Debiasing Knowledge Graph Embeddings

Knowledge Graphs (KG) are gaining increasing attention in both academia and industry. Despite their diverse benefits, recent research have identified social and cultural biases embedded in the representations learned from KGs. Such biases can have detrimental consequences on different population and minority groups as applications of KG begin to intersect and interact with social spheres. This paper aims at identifying and mitigating such biases in Knowledge Graph (KG) embeddings. As a first step, we explore popularity bias -- the relationship between node popularity and link prediction accuracy. In case of node2vec graph embeddings, we find that prediction accuracy of the embedding is negatively correlated with the degree of the node. However, in case of knowledge-graph embeddings (KGE), we observe an opposite trend. As a second step, we explore gender bias in KGE, and a careful examination of popular KGE algorithms suggest that sensitive attribute like the gender of a person can be predicted from the embedding. This implies that such biases in popular KGs is captured by the structural properties of the embedding. As a preliminary solution to debiasing KGs, we introduce a novel framework to filter out the sensitive attribute information from the KG embeddings, which we call FAN (Filtering Adversarial Network). We also suggest the applicability of FAN for debiasing other network embeddings which could be explored in future work.

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