Deep Evidential Regression, Simply Explained

Deep Evidential Regression, Simply Explained

AI, But Simple Issue #103

AI systems are now integrated in high-stakes domains such as healthcare, security, autonomous vehicles, and finance, where incorrect predictions have severe consequences.

However, most machine learning models provide only a single prediction such as a class label or numerical value without conveying how confident the model actually is.

Feed models an input they have never seen before, and they will still output a number, with no indication of a bad answer.

A couple weeks ago, we looked at conformal prediction, an uncertainty quantification technique that creates guaranteed prediction sets based on quantiles.

Today, we’ll look at another helpful method from this field.

Deep Evidential Regression (Amini et al., 2020), published at NeurIPS by researchers at MIT and Harvard, proposes another method to quantify model uncertainty.

It trains a standard neural network to output not just a prediction, but uncertainty descriptors driven by probability.

The result is a model that is genuinely uncertain about doubtful outputs, calibrated enough to use in safety-critical settings, and fast enough to run in real time.

Deep Evidential Regression has the capability to understand two different types of uncertainties, which puts it a step above a method we have seen before: Gaussian Process Regression.

This is considered important because it can provide a higher level of clarity about prediction confidence and, additionally, can also significantly benefit the training process.

What You’ll Learn

1. The two kinds of uncertainty in machine learning

2. The evidential idea (what previous approaches lacked)

3. The crucial regularizer

4. Applications of evidential regression

5. Why evidential regression matters

What’s Helpful to Know

• Bayesian Inference

  • A statistical inference method that uses Bayes’ theorem to update a prior distribution (a model’s beliefs) given new observations.

• Prior, Posterior, Conjugate Distributions

  • Prior Distribution: The model's initial belief about a parameter before observing any new data.

  • Posterior Distribution: The updated distribution after considering new observations.

  • Conjugate Prior: A convenience where the prior and posterior distributions belong to the same probability family.

• Normal-Inverse-Gamma (NIG) Distribution

  • A higher-level, four-parameter probability distribution. Essentially a distribution over distributions.

• Student’s t-Distribution

  • A probability distribution that looks like a standard normal curve with "heavier tails."

The Two Kinds of Uncertainty

Before understanding the method, it helps to be precise about what uncertainty means for a neural network.

The first is called aleatoric uncertainty, which is an irreducible noise in the data itself.

For instance, if you are predicting depth from a photograph of a mirror, the mirror contains ambiguous information about depth.

• No amount of additional training data resolves this. The uncertainty is in the world and not in the model.

The second is called epistemic uncertainty. This is the model's own ignorance, stemming from limited training data or from encountering inputs it has never seen before.

If a depth estimation model trained on indoor scenes is suddenly shown an outdoor driving scene, it should be highly uncertain because it is operating outside its experience.

• This uncertainty can, in principle, be reduced by training on more diverse data.

Most neural networks collapse both uncertainties into a single output and cannot distinguish between them at all.

On the other hand, Deep Evidential Regression learns both from a single forward pass.