Enhancing Uncertainty Estimation and Interpretability via Bayesian Non-negative Decision Layer

TL;DR

A Bayesian Non-negative Decision Layer is developed, which reformulates deep neural networks as a conditional Bayesian non-negative factor analysis and provides reliable uncertainty estimation and improved interpretability.

Abstract

Although deep neural networks have demonstrated significant success due to their powerful expressiveness, most models struggle to meet practical requirements for uncertainty estimation. Concurrently, the entangled nature of deep neural networks leads to a multifaceted problem, where various localized explanation techniques reveal that multiple unrelated features influence the decisions, thereby undermining interpretability. To address these challenges, we develop a Bayesian Non-negative Decision Layer (BNDL), which reformulates deep neural networks as a conditional Bayesian non-negative factor analysis. By leveraging stochastic latent variables, the BNDL can model complex dependencies and provide robust uncertainty estimation. Moreover, the sparsity and non-negativity of the latent variables encourage the model to learn disentangled representations and decision layers, thereby improving interpretability. We also offer theoretical guarantees that BNDL can achieve effective disentangled learning. In addition, we developed a corresponding variational inference method utilizing a Weibull variational inference network to approximate the posterior distribution of the latent variables. Our experimental results demonstrate that with enhanced disentanglement capabilities, BNDL not only improves the model's accuracy but also provides reliable uncertainty estimation and improved interpretability.

Figures (12)

• Figure 1: Illustration of the graphical models. 1(a): the predictive process of output $Y$ for the baseline Deep Neural Network; 1(b): the generative model of DNNs with introducing stochastic latent variable $\boldsymbol{\theta}$ ; 1(c): the generation model of the Bayesian non-negative decision layer; and 1(d): corresponding approximate inference for latent variables $\boldsymbol{\theta}$.
• Figure 2: The leftmost line chart illustrates the average uncertainty and accuracy across subsets of the ImageNet test set. The middle and right panels sample images from the subsets with the highest and lowest uncertainty, as defined by the curve. The top row shows the original images with ground truth labels, while the bottom row displays the model's predictions alongside LIME visualizations.
• Figure 3: Sparsity-accuracy trade-offs for BNDL and Debuggable Network wong2021leveraging. Each point on the curve represents a BNDL classifier. Horizontal dashed lines indicate the fully dense accuracy for each network. The x-axis shows the proportion of non-sparse weights, with higher values indicating denser distributions, while the y-axis represents test accuracy on each dataset.
• Figure 4: The LIME visualizations for BNDL and ResNet-50, focusing on the largest $\boldsymbol{\theta}$ for each image, show that BNDL's features align more closely with the semantic meaning of true labels, suggesting more disentangled representations. As we selected the top-10 super-pixels for visualization, the results may include some less significant super-pixels; this issue is alleviated when we reduce the number of top-$k$ super-pixels.
• Figure 5: Uncertainty Vs Test Acc Curve on other datasets and model.

Theorems & Definitions (5)

• Proposition 1: gillis2023partial
• Definition 1
• Definition 2
• Definition 3
• Proposition 2