Stacked Negative Correlation Learning for Deep Ensembling

This repository contains the code used for the experiments in the Master thesis "From Generalists to Specialists: Empowering Weak Learners in Deep Ensembles"

Thesis Abstract

Ensemble learning is a machine learning technique that leverages the predictions of multiple diverse predictors to enhance overall predictive performance. In recent years the approach has regained significant research attention due to deep ensembles empirically providing state-of-the-art generalisation accuracy and uncertainty estimates.

This thesis provides a critical empirical analysis of state-of-the-art approaches to deep ensembling, highlighting a critical deficiency: their inability to train specialised models. A limitation that leads to inefficient utilisation of learning capacities due to redundant learnings, resulting in compromised accuracy and diminishing returns for larger ensemble sizes.

In response, we propose Stacked Negative Correlation Learning (SNCL), a novel ensembling method that effectively encourages ensemble members to specialise in distinguishing between class subsets. SNCL incorporates negative correlation learning and stacked generalisation through a novel concurrent training scheme for stacked ensembles, effectively overcoming some of their limitations and leveraging the advantages of both methods.

Through extensive experimentation and analysis, we demonstrate that SNCL effectively reduces redundancies within deep ensembles, yielding improved generalisation accuracy with comparable model complexities. Our proposal further enhances the state-of-the-art performance of deep ensembles for uncertainty quantification by reducing in-domain uncertainty, thereby improving out-of-distribution detection capabilities, which are desirable in safety-critical domains.

Our results demonstrate that SNCL can significantly enhance the performance of deep ensembles in high-dimensional multi-class classification settings, presenting a powerful alternative to state-of-the-art techniques by enabling more efficient deep ensembling. We highlight its potential benefits for practical applications and avenues for future research.

Repository structure

Note: All experimental results are saved in the folder /plots/ as .png and .svg with descriptive naming.

This repository combines code for multiple datasets and two different repositories. It is structured as follows:

• SNCLtraining.py: The main script to train ensembles with SNCL, GNCL or independently. We recommend to use Neptune.ai for detailed tracking of results. Trained models are saved in the folder /models/.
• performTrainingTrials.sh: Bash script to perform all training trials included in the thesis.
• accuracyAndDiversityPlots.py: Plots accuracy and diversity for the tested configurations. Note: This script requires a .csv export from neptune.ai to retrieve the detailed results.
• removalExperiment.py: Performs a pruning experiment to assess the robustness of specific ensembles.
• qualitativeAnalysesForSpecialization.py: Visualizes the weight matrices of meta-learners and class-specific accuracies of submodels and ensembles.
• conformalPredictionWithMAPIE.py: Performs conformal prediction with the library MAPIE to assess the in-domain uncertainty of previously trained ensemble models
• generateAndPlotEntropies.py: Generates the softmax entropies for the predictions of the previously trained ensemble models on the datasets CIFAR-10, CIFAR-10C and SVHN. The entropies are saved as .npz files in /data/ for subsequent ood detection based on thresholding. Plot the entropy densities (estimated via gaussian KDE) per dataset and per model.
• oodDetectionWithSoftmaxEntropies.py: Performs ood detection based on the softmax entropies emitted by the trained ensembles, provides AUROC plots and saves results as .csv in /data/.
• models.py: Contains implementations of the ensemble model and meta-learner.
• utils.py: Contains utilities for dataset retrieval and pre-processing.
• temperatureScaling.py: Temperature scaling for stacked ensembles, adapted from https://github.com/gpleiss/temperature_scaling.

Requirements

The following packages are required to run all of the provided code:

• numpy
• scipy
• PyTorch
• matplotlib
• MAPIE (https://github.com/scikit-learn-contrib/MAPIE/tree/master)
• sklearn
• neptune

Running the experiments

We recommend to use Neptune.ai for detailed tracking of results. Please configure the api key and project name in SNCLtraining.py. We provide the bash script performTrainingTrials.sh to perform all training trials included in the thesis. Individual configurations can be performed through the command-line, e.g.:

python3 'SNCLtraining.py' --ncl_weight 0.5 --ncl_type GNCL --base_models 10 --neptuneai none --silent True

To reproduce the experimental results we suggest the following order of execution:

1. performTrainingTrials.sh
2. accuracyAndDiversityPlots.py

Note: The subsequent scripts must be provided with run-ids of specific models trained in 1).

3. removalExperiment.py
4. qualitativeAnalysesForSpecialization.py
5. conformalPredictionWithMAPIE.py
6. generateAndPlotEntropies.py
7. oodDetectionWithSoftmaxEntropies.py

All experimental results will be saved in the folder /plots/ as .png and .svg with descriptive naming.