Monte Carlo Dropout

Description

Monte Carlo dropout estimates how uncertain a neural network is about each prediction. Dropout randomly switches off some of the network's units and is normally used only in training, but here it stays on at prediction time. Each forward pass (one run of an input through the network) therefore uses a different random pattern of units, and the input is run through typically tens to a hundred times. The average gives the prediction, and the spread across runs is read as epistemic uncertainty, meaning uncertainty from the model's limited knowledge rather than noise in the data. The method approximates Bayesian inference, but the spread is an estimate whose reliability should be checked against held-out errors.

Example Use Cases

Reliability

Quantifying diagnostic uncertainty in medical imaging models by running 50+ Monte Carlo forward passes to detect when a chest X-ray classification is highly uncertain, prompting radiologist review for borderline cases.

An autonomous-driving team replays recorded camera footage through its object detector with dropout left on, and finds the scenes (night rain, unusual vehicles) where detections vary most between passes. It uses them to decide what data to collect and which scenarios to add to simulation testing.

A grid operator's demand-forecasting network, trained with dropout, is run 100 times each morning. Days on which the forecasts spread beyond the planners' tolerance are sent for human review before reserve capacity is booked.

Limitations

The spread across passes reflects uncertainty about the model's parameters, not noise in the data that varies from input to input. An input in a very noisy region can still show a narrow spread, so a narrow spread does not mean the outcome is predictable.
Each prediction needs many forward passes, typically 50 to 100, so inference costs that many times more compute, and too few passes make the spread itself unstable. The passes can run in parallel, which limits added delay but not total compute, so real-time or edge deployments with tight budgets may not afford it.
The network must have been trained with dropout, and the derivation assumes it sits before every weight layer. A model trained without dropout has to be retrained, so the technique is often unavailable for models already built or bought in.
The size of the spread depends on the dropout probability and weight decay, which the developer sets or tunes on validation data rather than learns from the data. The uncertainty scale is partly a design choice and needs checking against held-out errors.
The spread is an approximation, and its behaviour depends on the architecture. In the original paper's regression experiments, uncertainty kept growing away from the training data with ReLU activations but stayed bounded with TanH, so a narrow spread on unfamiliar inputs is not proof of familiarity.

Resources

Research Papers

Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning

Yarin Gal and Zoubin Ghahramani•Jun 6, 2015

Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. In this paper we develop a new theoretical framework casting dropout training in deep neural networks (NNs) as approximate Bayesian inference in deep Gaussian processes. A direct result of this theory gives us tools to model uncertainty with dropout NNs -- extracting information from existing models that has been thrown away so far. This mitigates the problem of representing uncertainty in deep learning without sacrificing either computational complexity or test accuracy. We perform an extensive study of the properties of dropout's uncertainty. Various network architectures and non-linearities are assessed on tasks of regression and classification, using MNIST as an example. We show a considerable improvement in predictive log-likelihood and RMSE compared to existing state-of-the-art methods, and finish by using dropout's uncertainty in deep reinforcement learning.

Software Packages

torch-uncertainty

Open-source framework for uncertainty and deep learning models in PyTorch 🌱 - torch-uncertainty/torch-uncertainty

Tutorials

Training a LeNet with Monte Carlo dropout - TorchUncertainty Docs

Documentations

mc_dropout - TorchUncertainty Docs

Related Techniques

Name	Description	Assurance Goals
Deep Ensembles	Deep ensembles estimate how uncertain a neural network's predictions are by training several copies of the same network independently and comparing what they predict. Each copy starts from different random initial weights, sees the training data in a different random order, and is trained to output a full predictive distribution, such as a probability for each class or a predicted value with its spread, rather than a single answer. The ensemble's prediction is the average of its members. Where members agree the prediction is usually more reliable, though agreement alone is no guarantee, and where they disagree the model is showing uncertainty about which answer is right, known as epistemic or model uncertainty. In the original study, ensembles of about five networks were better calibrated than single networks, meaning their stated confidence matched how often they were right, and expressed higher uncertainty on inputs from classes absent from the training data.	Reliability Transparency
Out-of-Distribution Detector for Neural Networks	ODIN (Out-of-Distribution Detector for Neural Networks) flags inputs that look unlike the data a neural network classifier was trained on, and it works on an already trained network without retraining it. A classifier reports a confidence score, the highest probability it gives to any class, but that score is often high even for unfamiliar inputs. ODIN adjusts the score in two ways so that familiar and unfamiliar inputs separate better. It divides the classifier's raw output scores by a large constant, called the temperature, before turning them into probabilities, and it nudges the input slightly in the direction that raises the score, which lifts familiar inputs more than unfamiliar ones. An input whose adjusted score falls below a chosen threshold is flagged as out-of-distribution, so its prediction can be withheld or referred for review.	Reliability Safety
Bootstrap Ensembles	Bootstrap ensembles estimate how much a model's predictions depend on the particular sample of data it was trained on. The training set is resampled with replacement many times, each resample (a bootstrap replicate) holding as many cases as the original so that some cases are repeated and others left out; one model is trained on each replicate with the same settings, and every new input is passed through all of the models. The spread of the models' predictions for an input, reported as a standard deviation or as a range between percentiles, estimates the uncertainty in the model's prediction for that input, and inputs where the models disagree are those the training data constrain least. The spread covers uncertainty in the fitted model only, not the random variation in individual outcomes, so an interval meant to contain a case's actual outcome must add an estimate of that noise, for example from the models' errors on held-out data. Putting a confidence interval around a measured performance score is a different procedure, which resamples the evaluation set and retrains nothing; see Bootstrap Confidence Intervals for Evaluation Metrics.	Reliability Transparency Fairness