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Fabio Cuzzolin

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9 papers

2 author rows

AAAI Conference 2026 Conference Paper

Credal Ensemble Distillation for Uncertainty Quantification

Kaizheng Wang
Fabio Cuzzolin
David Moens
Hans Hallez

Deep ensembles (DE) have emerged as a powerful approach for quantifying predictive uncertainty and distinguishing its aleatoric and epistemic components, thereby enhancing model robustness and reliability. However, their high computational and memory costs during inference pose significant challenges for wide practical deployment. To overcome this issue, we propose credal ensemble distillation (CED), a novel framework that compresses a DE into a single model, CREDIT, for classification tasks. Instead of a single softmax probability distribution, CREDIT predicts class-wise probability intervals that define a credal set, a convex set of probability distributions, for uncertainty quantification. Empirical results on out-of-distribution detection benchmarks demonstrate that CED achieves superior or comparable uncertainty estimation compared to several existing baselines, while substantially reducing inference overhead compared to DE.

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TMLR Journal 2025 Journal Article

ASTRA: A Scene-aware Transformer-based Model for Trajectory Prediction

Izzeddin Teeti
Aniket Thomas
Munish Monga
Sachin Kumar Giroh
Uddeshya Singh
Andrew Bradley
Biplab Banerjee
Fabio Cuzzolin

We present ASTRA (A Scene-aware Transformer-based model for trajectory prediction), a light-weight pedestrian trajectory forecasting model that integrates the scene context, spatial dynamics, social inter-agent interactions and temporal progressions for precise forecasting. We utilised a U-Net-based feature extractor, via its latent vector representation, to capture scene representations and a graph-aware transformer encoder for capturing social interactions. These components are integrated to learn an agent-scene aware embedding, enabling the model to learn spatial dynamics and forecast the future trajectory of pedestrians. The model is designed to produce both deterministic and stochastic outcomes, with the stochastic predictions being generated by incorporating a Conditional Variational Auto-Encoder (CVAE). ASTRA also proposes a simple yet effective weighted penalty loss function, which helps to yield predictions that outperform a wide array of state-of-the-art deterministic and generative models. ASTRA demonstrates an average improvement of 27%/10% in deterministic/stochastic settings on the ETH-UCY dataset, and 26% improvement on the PIE dataset, respectively, along with seven times fewer parameters than the existing state-of-the-art model (see Figure 1). Additionally, the model's versatility allows it to generalize across different perspectives, such as Bird's Eye View (BEV) and Ego-Vehicle View (EVV).

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ICLR Conference 2025 Conference Paper

Credal Wrapper of Model Averaging for Uncertainty Estimation in Classification

Kaizheng Wang
Fabio Cuzzolin
Keivan Shariatmadar
David Moens
Hans Hallez

This paper presents an innovative approach, called credal wrapper, to formulating a credal set representation of model averaging for Bayesian neural networks (BNNs) and deep ensembles (DEs), capable of improving uncertainty estimation in classification tasks. Given a finite collection of single predictive distributions derived from BNNs or DEs, the proposed credal wrapper approach extracts an upper and a lower probability bound per class, acknowledging the epistemic uncertainty due to the availability of a limited amount of distributions. Such probability intervals over classes can be mapped on a convex set of probabilities (a credal set) from which, in turn, a unique prediction can be obtained using a transformation called intersection probability transformation. In this article, we conduct extensive experiments on several out-of-distribution (OOD) detection benchmarks, encompassing various dataset pairs (CIFAR10/100 vs SVHN/Tiny-ImageNet, CIFAR10 vs CIFAR10-C, CIFAR100 vs CIFAR100-C and ImageNet vs ImageNet-O) and using different network architectures (such as VGG16, ResNet-18/50, EfficientNet B2, and ViT Base). Compared to the BNN and DE baselines, the proposed credal wrapper method exhibits superior performance in uncertainty estimation and achieves a lower expected calibration error on corrupted data.

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ICLR Conference 2025 Conference Paper

Random-Set Neural Networks

Shireen Kudukkil Manchingal
Muhammad Mubashar
Kaizheng Wang
Keivan Shariatmadar
Fabio Cuzzolin

Machine learning is increasingly deployed in safety-critical domains where erroneous predictions may lead to potentially catastrophic consequences, highlighting the need for learning systems to be aware of how confident they are in their own predictions: in other words, 'to know when they do not know’. In this paper, we propose a novel Random-Set Neural Network (RS-NN) approach to classification which predicts *belief functions* (rather than classical probability vectors) over the class list using the mathematics of *random sets*, i.e., distributions over the collection of *sets* of classes. RS-NN encodes the 'epistemic' uncertainty induced by training sets that are insufficiently representative or limited in size via the size of the convex set of probability vectors associated with a predicted belief function. Our approach outperforms state-of-the-art Bayesian and Ensemble methods in terms of accuracy, uncertainty estimation and out-of-distribution (OoD) detection on multiple benchmarks (CIFAR-10 vs SVHN/Intel-Image, MNIST vs FMNIST/KMNIST, ImageNet vs ImageNet-O). RS-NN also scales up effectively to large-scale architectures (e.g. WideResNet-28-10, VGG16, Inception V3, EfficientNetB2 and ViT-Base-16), exhibits remarkable robustness to adversarial attacks and can provide statistical guarantees in a conformal learning setting.

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NeurIPS Conference 2024 Conference Paper

Credal Deep Ensembles for Uncertainty Quantification

Kaizheng Wang
Fabio Cuzzolin
Shireen K. Manchingal
Keivan Shariatmadar
David Moens
Hans Hallez

This paper introduces an innovative approach to classification called Credal Deep Ensembles (CreDEs), namely, ensembles of novel Credal-Set Neural Networks (CreNets). CreNets are trained to predict a lower and an upper probability bound for each class, which, in turn, determine a convex set of probabilities (credal set) on the class set. The training employs a loss inspired by distributionally robust optimization which simulates the potential divergence of the test distribution from the training distribution, in such a way that the width of the predicted probability interval reflects the epistemic uncertainty about the future data distribution. Ensembles can be constructed by training multiple CreNets, each associated with a different random seed, and averaging the outputted intervals. Extensive experiments are conducted on various out-of-distributions (OOD) detection benchmarks (CIFAR10/100 vs SVHN/Tiny-ImageNet, CIFAR10 vs CIFAR10-C, ImageNet vs ImageNet-O) and using different network architectures (ResNet50, VGG16, and ViT Base). Compared to Deep Ensemble baselines, CreDEs demonstrate higher test accuracy, lower expected calibration error, and significantly improved epistemic uncertainty estimation.

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NeurIPS Conference 2024 Conference Paper

Credal Learning Theory

Michele Caprio
Maryam Sultana
Eleni G. Elia
Fabio Cuzzolin

Statistical learning theory is the foundation of machine learning, providing theoretical bounds for the risk of models learned from a (single) training set, assumed to issue from an unknown probability distribution. In actual deployment, however, the data distribution may (and often does) vary, causing domain adaptation/generalization issues. In this paper we lay the foundations for a `credal' theory of learning, using convex sets of probabilities (credal sets) to model the variability in the data-generating distribution. Such credal sets, we argue, may be inferred from a finite sample of training sets. Bounds are derived for the case of finite hypotheses spaces (both assuming realizability or not), as well as infinite model spaces, which directly generalize classical results.

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IJCAI Conference 2022 Conference Paper

Vision-based Intention and Trajectory Prediction in Autonomous Vehicles: A Survey

Izzeddin Teeti
Salman Khan
Ajmal Shahbaz
Andrew Bradley
Fabio Cuzzolin

This survey targets intention and trajectory prediction in Autonomous Vehicles (AV), as AV companies compete to create dedicated prediction pipelines to avoid collisions. The survey starts with a formal definition of the prediction problem and highlights its challenges, to then critically compare the models proposed in the last 2-3 years in terms of how they overcome these challenges. Further, it lists the latest methodological and technical trends in the field and comments on the efficacy of different machine learning blocks in modelling various aspects of the prediction problem. It also summarises the popular datasets and metrics used to evaluate prediction models, before concluding with the possible research gaps and future directions.

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UAI Conference 2017 Conference Paper

The Total Belief Theorem

Chunlai Zhou
Fabio Cuzzolin

In this paper, motivated by the treatment of conditional constraints in the data association problem, we state and prove the generalisation of the law of total probability to belief functions, as finite random sets. Our results apply to the case in which Dempster’s conditioning is employed. We show that the solution to the resulting total belief problem is in general not unique, whereas it is unique when the a-priori belief function is Bayesian. Examples and case studies underpin the theoretical contributions. Finally, our results are compared to previous related work on the generalisation of Jeffrey’s rule by Spies and Smets.

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JELIA Conference 2008 Conference Paper

On the Credal Structure of Consistent Probabilities

Fabio Cuzzolin

Abstract In this paper we introduce a novel, simpler form of the polytope of inner Bayesian approximations of a belief function, or “consistent probabilities”. We prove that the set of vertices of this polytope is generated by all possible permutations of elements of the domain, mirroring a similar behavior of outer consonant approximations.

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