Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userData augmentation in Bayesian neural networks and the cold posterior effect
182
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Data augmentation is a highly effective approach for improving performance in deep neural networks. The standard view is that it creates an enlarged dataset by adding synthetic data, which raises a problem when combining it with Bayesian inference: how much data are we really conditioning on? This question is particularly relevant to recent observations linking data augmentation to the cold posterior effect. We investigate various principled ways of finding a log-likelihood for augmented datasets. Our approach prescribes augmenting the same underlying image multiple times, both at test and train-time, and averaging either the logits or the predictive probabilities. Empirically, we observe the best performance with averaging probabilities. While there are interactions with the cold posterior effect, neither averaging logits or averaging probabilities eliminates it.
rate research
Read More
Recent work has shown that the prior over functions induced by a deep Bayesian neural network (BNN) behaves as a Gaussian process (GP) as the width of all layers becomes large. However, many BNN applications are concerned with the BNN function space posterior. While some empirical evidence of the posterior convergence was provided in the original works of Neal (1996) and Matthews et al. (2018), it is limited to small datasets or architectures due to the notorious difficulty of obtaining and verifying exactness of BNN posterior approximations. We provide the missing theoretical proof that the exact BNN posterior converges (weakly) to the one induced by the GP limit of the prior. For empirical validation, we show how to generate exact samples from a finite BNN on a small dataset via rejection sampling.
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.
During the past five years the Bayesian deep learning community has developed increasingly accurate and efficient approximate inference procedures that allow for Bayesian inference in deep neural networks. However, despite this algorithmic progress and the promise of improved uncertainty quantification and sample efficiency there are---as of early 2020---no publicized deployments of Bayesian neural networks in industrial practice. In this work we cast doubt on the current understanding of Bayes posteriors in popular deep neural networks: we demonstrate through careful MCMC sampling that the posterior predictive induced by the Bayes posterior yields systematically worse predictions compared to simpler methods including point estimates obtained from SGD. Furthermore, we demonstrate that predictive performance is improved significantly through the use of a cold posterior that overcounts evidence. Such cold posteriors sharply deviate from the Bayesian paradigm but are commonly used as heuristic in Bayesian deep learning papers. We put forward several hypotheses that could explain cold posteriors and evaluate the hypotheses through experiments. Our work questions the goal of accurate posterior approximations in Bayesian deep learning: If the true Bayes posterior is poor, what is the use of more accurate approximations? Instead, we argue that it is timely to focus on understanding the origin of the improved performance of cold posteriors.
This work develops rigorous theoretical basis for the fact that deep Bayesian neural network (BNN) is an effective tool for high-dimensional variable selection with rigorous uncertainty quantification. We develop new Bayesian non-parametric theorems to show that a properly configured deep BNN (1) learns the variable importance effectively in high dimensions, and its learning rate can sometimes break the curse of dimensionality. (2) BNNs uncertainty quantification for variable importance is rigorous, in the sense that its 95% credible intervals for variable importance indeed covers the truth 95% of the time (i.e., the Bernstein-von Mises (BvM) phenomenon). The theoretical results suggest a simple variable selection algorithm based on the BNNs credible intervals. Extensive simulation confirms the theoretical findings and shows that the proposed algorithm outperforms existing classic and neural-network-based variable selection methods, particularly in high dimensions.
We conduct a thorough analysis of the relationship between the out-of-sample performance and the Bayesian evidence (marginal likelihood) of Bayesian neural networks (BNNs), as well as looking at the performance of ensembles of BNNs, both using the Boston housing dataset. Using the state-of-the-art in nested sampling, we numerically sample the full (non-Gaussian and multimodal) network posterior and obtain numerical estimates of the Bayesian evidence, considering network models with up to 156 trainable parameters. The networks have between zero and four hidden layers, either $tanh$ or $ReLU$ activation functions, and with and without hierarchical priors. The ensembles of BNNs are obtained by determining the posterior distribution over networks, from the posterior samples of individual BNNs re-weighted by the associated Bayesian evidence values. There is good correlation between out-of-sample performance and evidence, as well as a remarkable symmetry between the evidence versus model size and out-of-sample performance versus model size planes. Networks with $ReLU$ activation functions have consistently higher evidences than those with $tanh$ functions, and this is reflected in their out-of-sample performance. Ensembling over architectures acts to further improve performance relative to the individual BNNs.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
