Decision Focused Learning has emerged as a critical paradigm for integrating machine learning with downstream optimisation. Despite its promise, existing methodologies predominantly rely on probabilistic models and focus narrowly on task objectives, overlooking the nuanced challenges posed by epistemic uncertainty, non-probabilistic modelling approaches, and the integration of uncertainty into optimisation constraints. This paper bridges these gaps by introducing innovative frameworks: (i) a non-probabilistic lens for epistemic uncertainty representation, leveraging intervals (the least informative uncertainty model), Contamination (hybrid model), and probability boxes (the most informative uncertainty model); (ii) methodologies to incorporate uncertainty into constraints, expanding Decision-Focused Learning's utility in constrained environments; (iii) the adoption of Imprecise Decision Theory for ambiguity-rich decision-making contexts; and (iv) strategies for addressing sparse data challenges. Empirical evaluations on benchmark optimisation problems demonstrate the efficacy of these approaches in improving decision quality and robustness and dealing with said gaps.

X Y the available training set, diverse, ranging from single point estimates N being the number of training instances. In Bayesian (often averaged over prediction samples) to Neural Networks (BNNs) (Buntine and Weigend, 1991; predictive distributions, to set-valued or Neal, 2012; Jospin et al., 2022; Kingma and Welling, credal-set representations. We propose a novel 2013), this uncertainty is explicitly represented through unified evaluation framework for uncertaintyaware posterior predictive distributions over the parameter classifiers, applicable to a wide range space. In Deep Ensembles (DEs) (Lakshminarayanan of model classes, which allows users to tailor et al., 2017), a predictive distribution is formed by the trade-off between accuracy and precision aggregating the individual predictions generated by of predictions via a suitably designed performance multiple independently trained models.

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).

This paper explores the utility of diffusion-based models for anomaly detection, focusing on their efficacy in identifying deviations in both compact and high-resolution datasets. Diffusion-based architectures, including Denoising Diffusion Probabilistic Models (DDPMs) and Diffusion Transformers (DiTs), are evaluated for their performance using reconstruction objectives. By leveraging the strengths of these models, this study benchmarks their performance against traditional anomaly detection methods such as Isolation Forests, One-Class SVMs, and COPOD. The results demonstrate the superior adaptability, scalability, and robustness of diffusion-based methods in handling complex real-world anomaly detection tasks. Key findings highlight the role of reconstruction error in enhancing detection accuracy and underscore the scalability of these models to high-dimensional datasets. Future directions include optimizing encoder-decoder architectures and exploring multi-modal datasets to further advance diffusion-based anomaly detection.

The aim of this paper is to formalise the task of continual semi-supervised anomaly detection (CSAD), with the aim of highlighting the importance of such a problem formulation which assumes as close to real-world conditions as possible. After an overview of the relevant definitions of continual semi-supervised learning, its components, anomaly detection extension, and the training protocols; the paper introduces a baseline model of a variational autoencoder (VAE) to work with semi-supervised data along with a continual learning method of deep generative replay with outlier rejection. The results show that such a use of extreme value theory (EVT) applied to anomaly detection can provide promising results even in comparison to an upper baseline of joint training. The results explore the effects of how much labelled and unlabelled data is present, of which class, and where it is located in the data stream. Outlier rejection shows promising initial results where it often surpasses a baseline method of Elastic Weight Consolidation (EWC). A baseline for CSAD is put forward along with the specific dataset setups used for reproducability and testability for other practitioners. Future research directions include other CSAD settings and further research into efficient continual hyperparameter tuning.

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, capable of improving uncertainty estimation in classification tasks. Given a finite collection of single distributions derived from BNNs or deep ensembles, the proposed approach extracts an upper and a lower probability bound per class, acknowledging the epistemic uncertainty due to the availability of a limited amount of sampled predictive 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 multiple 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, Res18/50, EfficientNet B2, and ViT Base). Compared to BNN and deep ensemble baselines, the proposed credal representation methodology exhibits superior performance in uncertainty estimation and achieves lower expected calibration error on OOD samples.

The purpose of this paper is to look into how central notions in statistical learning theory, such as realisability, generalise under the assumption that train and test distribution are issued from the same credal set, i.e., a convex set of probability distributions. This can be considered as a first step towards a more general treatment of statistical learning under epistemic uncertainty.

Uncertainty estimation is increasingly attractive for improving the reliability of neural networks. In this work, we present novel credal-set interval neural networks (CreINNs) designed for classification tasks. CreINNs preserve the traditional interval neural network structure, capturing weight uncertainty through deterministic intervals, while forecasting credal sets using the mathematical framework of probability intervals. Experimental validations on an out-of-distribution detection benchmark (CIFAR10 vs SVHN) showcase that CreINNs outperform epistemic uncertainty estimation when compared to variational Bayesian neural networks (BNNs) and deep ensembles (DEs). Furthermore, CreINNs exhibit a notable reduction in computational complexity compared to variational BNNs and demonstrate smaller model sizes than DEs.

Statistical learning theory is the foundation of machine learning, providing theoretical bounds for the risk of models learnt 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.

The theory of belief functions [162, 67] is a modelling language for representing and combining elementary items of evidence, which do not necessarily come in the form of sharp statements, with the goal of maintaining a mathematical representation of an agent's beliefs about those aspects of the world which the agent is unable to predict with reasonable certainty. While arguably a more appropriate mathematical description of uncertainty than classical probability theory, for the reasons we have thoroughly explored in [50], the theory of evidence is relatively simple to understand and implement, and does not require one to abandon the notion of an event, as is the case, for instance, for Walley's imprecise probability theory [193]. It is grounded in the beautiful mathematics of random sets, and exhibits strong relationships with many other theories of uncertainty. As mathematical objects, belief functions have fascinating properties in terms of their geometry, algebra [207] and combinatorics. Despite initial concerns about the computational complexity of a naive implementation of the theory of evidence, evidential reasoning can actually be implemented on large sample spaces [156] and in situations involving the combination of numerous pieces of evidence [74]. Elementary items of evidence often induce simple belief functions, which can be combined very efficiently with complexity O(n + 1).