In this paper, we visualize and quantify the predictive uncertainty of gradient-based post hoc visual explanations for neural networks. Predictive uncertainty refers to the variability in the network predictions under perturbations to the input. Visual post hoc explainability techniques highlight features within an image to justify a network's prediction. We theoretically show that existing evaluation strategies of visual explanatory techniques partially reduce the predictive uncertainty of neural networks. This analysis allows us to construct a plug in approach to visualize and quantify the remaining predictive uncertainty of any gradient-based explanatory technique. We show that every image, network, prediction, and explanatory technique has a unique uncertainty. The proposed uncertainty visualization and quantification yields two key observations. Firstly, oftentimes under incorrect predictions, explanatory techniques are uncertain about the same features that they are attributing the predictions to, thereby reducing the trustworthiness of the explanation. Secondly, objective metrics of an explanation's uncertainty, empirically behave similarly to epistemic uncertainty. We support these observations on two datasets, four explanatory techniques, and six neural network architectures. The code is available at https://github.com/olivesgatech/VOICE-Uncertainty.
In ill-posed inverse problems, it is commonly desirable to obtain insight into the full spectrum of plausible solutions, rather than extracting only a single reconstruction. Information about the plausible solutions and their likelihoods is encoded in the posterior distribution. However, for high-dimensional data, this distribution is challenging to visualize. In this work, we introduce a new approach for estimating and visualizing posteriors by employing energy-based models (EBMs) over low-dimensional subspaces. Specifically, we train a conditional EBM that receives an input measurement and a set of directions that span some low-dimensional subspace of solutions, and outputs the probability density function of the posterior within that space. We demonstrate the effectiveness of our method across a diverse range of datasets and image restoration problems, showcasing its strength in uncertainty quantification and visualization. As we show, our method outperforms a baseline that projects samples from a diffusion-based posterior sampler, while being orders of magnitude faster. Furthermore, it is more accurate than a baseline that assumes a Gaussian posterior.
Denoisers play a central role in many applications, from noise suppression in low-grade imaging sensors, to empowering score-based generative models. The latter category of methods makes use of Tweedie's formula, which links the posterior mean in Gaussian denoising (\ie the minimum MSE denoiser) with the score of the data distribution. Here, we derive a fundamental relation between the higher-order central moments of the posterior distribution, and the higher-order derivatives of the posterior mean. We harness this result for uncertainty quantification of pre-trained denoisers. Particularly, we show how to efficiently compute the principal components of the posterior distribution for any desired region of an image, as well as to approximate the full marginal distribution along those (or any other) one-dimensional directions. Our method is fast and memory-efficient, as it does not explicitly compute or store the high-order moment tensors and it requires no training or fine tuning of the denoiser. Code and examples are available on the project webpage in https://hilamanor.github.io/GaussianDenoisingPosterior/ .
With the advent of sophisticated machine learning (ML) techniques and the promising results they yield, especially in medical applications, where they have been investigated for different tasks to enhance the decision-making process. Since visualization is such an effective tool for human comprehension, memorization, and judgment, we have presented a first-of-its-kind estimation approach we refer to as Visualized Learning for Machine Learning (VL4ML) that not only can serve to assist physicians and clinicians in making reasoned medical decisions, but it also allows to appreciate the uncertainty visualization, which could raise incertitude in making the appropriate classification or prediction. For the proof of concept, and to demonstrate the generalized nature of this visualized estimation approach, five different case studies are examined for different types of tasks including classification, regression, and longitudinal prediction. A survey analysis with more than 100 individuals is also conducted to assess users' feedback on this visualized estimation method. The experiments and the survey demonstrate the practical merits of the VL4ML that include: (1) appreciating visually clinical/medical estimations; (2) getting closer to the patients' preferences; (3) improving doctor-patient communication, and (4) visualizing the uncertainty introduced through the black box effect of the deployed ML algorithm. All the source codes are shared via a GitHub repository.