Deep Evidential Regression (1910.02600v2)

Abstract: Deterministic neural networks (NNs) are increasingly being deployed in safety critical domains, where calibrated, robust, and efficient measures of uncertainty are crucial. In this paper, we propose a novel method for training non-Bayesian NNs to estimate a continuous target as well as its associated evidence in order to learn both aleatoric and epistemic uncertainty. We accomplish this by placing evidential priors over the original Gaussian likelihood function and training the NN to infer the hyperparameters of the evidential distribution. We additionally impose priors during training such that the model is regularized when its predicted evidence is not aligned with the correct output. Our method does not rely on sampling during inference or on out-of-distribution (OOD) examples for training, thus enabling efficient and scalable uncertainty learning. We demonstrate learning well-calibrated measures of uncertainty on various benchmarks, scaling to complex computer vision tasks, as well as robustness to adversarial and OOD test samples.

• The paper presents evidential regression, which estimates both aleatoric and epistemic uncertainties using a Normal Inverse-Gamma distribution.
• It introduces an evidential regularizer that penalizes misaligned evidence to inflate uncertainty when predictions are inaccurate.
• Empirical evaluations demonstrate competitive predictive accuracy and improved uncertainty calibration in applications like OOD detection and monocular depth estimation.

An Overview of Deep Evidential Regression

In the paper titled "Deep Evidential Regression," the authors tackle the challenge of uncertainty estimation in deterministic neural networks applied to regression tasks. The motivation behind their work lies in the crucial need for robust and calibrated uncertainty measures in safety-critical domains such as autonomous driving and medical diagnostics, where understanding predictive confidence is essential.

The authors introduce a novel methodology termed "evidential regression," aiming to infer both aleatoric and epistemic uncertainties without resorting to Bayesian frameworks or requiring sampling during inference. The core innovation lies in the use of evidential priors placed over the Gaussian likelihood function. This approach envisions the learning process as an evidence acquisition mechanism, wherein neural networks are trained to predict the hyperparameters of the evidential distribution, leading to a grounded estimation of uncertainties.

Methodological Framework

Evidential regression is predicated on leveraging a Normal Inverse-Gamma (NIG) distribution to model the distribution of likelihood parameters such as mean and variance. This higher-order distribution allows for the derivation of predictive, aleatoric, and epistemic uncertainties directly from the hyperparameters of the NIG distribution. This modeling choice circumvents the need for sampling-based techniques traditionally employed in Bayesian neural networks and achieves efficient and scalable uncertainty learning.

Notably, the authors introduce a novel evidential regularizer to penalize incorrect evidence, enabling the model to inflate uncertainty when the prediction is erroneous. The regularizer aligns the learned evidence with the ground truth by focusing on instances with substantial prediction errors.

Empirical Evaluation

The paper provides extensive empirical validation of the evidential regression framework across several benchmarks and use cases. It successfully demonstrates competitive performance in predictive accuracy when compared to traditional methods like dropout, ensembling, and Gaussian MLE while excelling in calibration of uncertainty, particularly under out-of-distribution (OOD) scenarios and adversarial contexts.

For instance, in one-dimensional and real-world regression problems, the authors show that their approach not only delivers comparable accuracy but also better-calibrated uncertainty estimates, even in complex computer vision tasks. Their model exhibits robust performance in scaling to high-dimensional tasks such as monocular depth estimation, showcasing the practical potential of this method in real-world applications.

Implications for AI and Future Directions

The implications of this work are far-reaching. Evidential regression offers a scalable and efficient alternative to Bayesian methods for uncertainty estimation without the computational overhead of sampling. This positions it well for applications requiring real-time predictions with uncertainty measures, such as autonomous vehicles and UAVs. Moreover, the demonstrated ability to generalize to OOD inputs without explicit OOD data in training points towards enhanced robustness in practical deployment.

Future research could explore the impact of different prior choices on likelihood parameters and investigate extensions to other distribution families beyond Gaussian, potentially increasing the method's applicability across a broader range of problems. Exploring deeper theoretical insights into the choice of evidential priors and their impact on convergence and learning dynamics would also be valuable.

Overall, the methodological contributions and empirical findings make this paper a noteworthy addition to the literature on uncertainty estimation, with promising avenues for future exploration and application in AI systems where trust and robustness are paramount.