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Variational Bayesian Bow tie Neural Networks with Shrinkage (2411.11132v3)

Published 17 Nov 2024 in stat.ML, cs.LG, math.ST, stat.ME, and stat.TH

Abstract: Despite the dominant role of deep models in machine learning, limitations persist, including overconfident predictions, susceptibility to adversarial attacks, and underestimation of variability in predictions. The Bayesian paradigm provides a natural framework to overcome such issues and has become the gold standard for uncertainty estimation with deep models, also providing improved accuracy and a framework for tuning critical hyperparameters. However, exact Bayesian inference is challenging, typically involving variational algorithms that impose strong independence and distributional assumptions. Moreover, existing methods are sensitive to the architectural choice of the network. We address these issues by focusing on a stochastic relaxation of the standard feed-forward rectified neural network and using sparsity-promoting priors on the weights of the neural network for increased robustness to architectural design. Thanks to Polya-Gamma data augmentation tricks, which render a conditionally linear and Gaussian model, we derive a fast, approximate variational inference algorithm that avoids distributional assumptions and independence across layers. Suitable strategies to further improve scalability and account for multimodality are considered.

Summary

  • The paper introduces bow tie neural networks that mitigate overconfident predictions and adversarial vulnerabilities using Bayesian shrinkage.
  • It employs Polya-Gamma augmentation and a structured mean-field variational inference approach to efficiently quantify uncertainty.
  • Experimental results demonstrate robust predictive performance and enhanced model interpretability compared to conventional Bayesian methods.

Overview of Variational Bayesian Bow Tie Neural Networks with Shrinkage

The paper "Variational Bayesian Bow Tie Neural Networks with Shrinkage," authored by Alisa Sheinkman and Sara Wade, presents a comprehensive approach to mitigating some of the critical issues associated with modern neural networks (NNs), such as overconfident predictions and vulnerability to adversarial attacks. It proposes a Bayesian framework leveraging the bow tie neural network model, which is augmented with shrinkage priors for its weights and variational inference for efficient posterior approximation.

Core Contributions

The primary contributions of this paper are two-fold: the introduction of the bow tie neural network model and the development of a variational inference algorithm suited for this architecture. Traditional neural networks often suffer from limited uncertainty quantification capabilities, a problem which Bayesian neural networks (BNNs) are naturally suited to address. However, Bayesian inference in NNs is computationally expensive and typically relies on assumptions that may be too restrictive. This work alleviates these constraints through the following innovations:

  1. Bow Tie Neural Networks (BNNs): The authors introduce bow tie networks, which employ a stochastic relaxation of the ReLU activation function. By utilizing Polya-Gamma data augmentation, the model becomes conditionally linear and Gaussian. This formulation enhances the model's ability to quantify uncertainty without imposing the independence assumptions common in variational algorithms.
  2. Shrinkage Priors: The model incorporates global-local normal-generalized inverse Gaussian priors, promoting sparsity and thus improving computational efficiency and model generalization. These sparsity-inducing priors facilitate data-driven design of neural architectures by informing layer width and depth.
  3. Variational Inference: A structured mean-field approximation is employed to derive the variational posterior, allowing the model to avoid explicit assumptions of layer-wise independence. This makes the inference process faster compared to traditional MCMC methods while achieving competitive predictive performance.

Methodology

Polya-Gamma Augmentation: Polya-Gamma augmentation is a key element in transforming the neural network model, making it amenable to efficient Bayesian inference techniques. This trick highlights the authors' strategy in dealing with complex probabilistic models by rendering them conditionally Gaussian.

Node Selection: A post-processing algorithm based on Bayesian false discovery rates identifies and retains critical network nodes, thereby streamlining the model. This approach helps in deducing a leaner and more interpretable network from the over-parameterized initial structure.

Experimental Evaluation

The proposed variational Bayesian framework is evaluated on a mixture of synthetic and real-world datasets, including UCI benchmarks. The results are benchmarked against existing methods such as stochastic variational inference (SVI) and Bayes by Backprop (BBB). The findings demonstrate that the proposed method maintains robust predictive accuracy across different architectures and datasets.

Particularly, the experiments highlight the effective uncertainty quantification in VBNNs, both with original and sparsified models, showcasing consistent empirical coverage even as the neural network's depth increases. Such results affirm the utility of VBNNs in applications necessitating rigorous uncertainty measures.

Implications and Future Directions

This work underscores the importance of probabilistic deep learning models in achieving reliable predictions, particularly in safety-critical domains where uncertainty quantification is paramount. By integrating efficient approximation methods and novel model architectures, it demonstrates how Bayesian approaches can be both computationally feasible and robust.

Future research could explore extending the bow tie architecture to handle varied data types and output structures, such as classification tasks, potentially using other augmentation strategies. Moreover, expanding the variational approach with stochastic gradient methods could further lighten computational demands, making it applicable to even larger datasets.

Overall, this paper offers a promising path forward for enhancing neural networks with Bayesian principles, marrying computational efficiency with robust uncertainty quantification.

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