arXiv subjects

Michele Caprio

Publications and source records attributed to Michele Caprio.

At least 37 records · Page 2Linked to original sources

arXiv2026

A Category-Theoretic Analysis of Conformal Prediction

Conformal prediction (CP) produces prediction regions with finite-sample, distribution free coverage guarantees, but its interpretation as a quantitative uncertainty tool is often left implicit. We develop a category-theoretic approach that makes this structure explicit. We show that Full Conformal Prediction can be represented as a morphism in two categories capturing (i) stability of set-valued procedures and (ii) measurability of random regions. Under mild conditions, we prove a commuting diagram result that decomposes the construction of a conformal region into two steps: Extracting a set of predictive distributions from the data, and then deriving a prediction region from this set. This decomposition provides a principled route to numerical uncertainty summaries beyond region size. We further prove an asymptotic compatibility result showing that, for Bayesian predictive scores in regular regimes, conformal regions converge to Bayesian predictive density level sets; We also provide quantitative rates under local empirical process and boundary regularity assumptions. This highlights a bridge between Bayesian, frequentist, and imprecise probabilistic prediction. We additionally identify conditions under which upper posterior constructions are related to e-posteriors, clarifying when e-value-based and conformal-imprecise representations can coincide. Finally, we show that the region extractor is functorial; This yields a modular privacy-compatible perspective in which privacy-preserving outer approximations of shared summary objects lead to conservative global prediction regions.

stat.ML↗

arXiv2026

Epistemic Errors of Imperfect Multitask Learners When Distributions Shift

Uncertainty-aware machine learners, such as Bayesian neural networks, output a quantification of uncertainty instead of a point prediction. We provide uncertainty-aware learners with a principled framework to characterize, and identify ways to eliminate, errors that arise from reducible (epistemic) uncertainty. We introduce a principled definition of epistemic error, and provide a decompositional epistemic error bound which operates in the very general setting of imperfect multitask learning under distribution shift. In this setting, the training (source) data may arise from multiple tasks, the test (target) data may differ systematically from the source data tasks, and/or the learner may not arrive at an accurate characterization of the source data. Our bound separately attributes epistemic errors to each of multiple aspects of the learning procedure and environment. As corollaries of the general result, we provide epistemic error bounds specialized to the settings of Bayesian transfer learning and distribution shift within $ε$-neighborhoods.

cs.LG↗

arXiv2026

CREDO: Epistemic-Aware Conformalized Credal Envelopes for Regression

Conformal prediction delivers prediction intervals with distribution-free coverage, but its intervals can look overconfident in regions where the model is extrapolating, because standard conformal scores do not explicitly represent epistemic uncertainty. Credal methods, by contrast, make epistemic effects visible by working with sets of plausible predictive distributions, but they are typically model-based and lack calibration guarantees. We introduce CREDO, a simple "credal-then-conformalize" recipe that combines both strengths. CREDO first builds an interpretable credal envelope that widens when local evidence is weak, then applies split conformal calibration on top of this envelope to guarantee marginal coverage without further assumptions. This separation of roles yields prediction intervals that are interpretable: their width can be decomposed into aleatoric noise, epistemic inflation, and a distribution-free calibration slack. We provide a fast implementation based on trimming extreme posterior predictive endpoints, prove validity, and show on benchmark regressions that CREDO maintains target coverage while improving sparsity adaptivity at competitive efficiency.

stat.ML↗

arXiv2026

Imprecise Markov Semigroups and their Ergodicity

We introduce the concept of an imprecise Markov semigroup $\mathbf Q$. It is a tool that allows us to represent ambiguity around both the transition probabilities and the invariant measure of a continuous-time Markov process via a collection of Markov semigroups, each associated with a (possibly different) Markov process. We use techniques from topology, geometry, and probability to analyze ergodic limits under model uncertainty encoded by $\mathbf Q$. We establish long-term bounds that are uniform in the initial state and identify regimes in which the imprecision in these bounds collapses asymptotically. Our results are proved in progressively more general settings. We first assume that $\mathbf Q$ is compact and that the state space is Euclidean or a Riemannian manifold, working with a fixed bounded observable. We then allow the state space to be standard Borel, while keeping $\mathbf Q$ compact and the observable fixed. Finally, we drop compactness and work on Polish metric spaces of finite diameter, where we treat arbitrary bounded Lipschitz observables. The importance of our findings for the fields of artificial intelligence and computer vision is also discussed at a high level; In particular, in the study of how the probability of an output evolves over time as we perturb the input of a convolutional autoencoder.

math.PR↗

arXiv2026

When Do Credal Sets Stabilize? Fixed-Point Theorems for Credal Set Updates

Many machine learning algorithms rely on iterative updates of uncertainty representations, ranging from variational inference and expectation-maximization, to reinforcement learning, continual learning, and multi-agent learning. In the presence of imprecision and ambiguity, credal sets -- closed, convex sets of probability distributions -- have emerged as a popular framework for representing imprecise probabilistic beliefs. Under such imprecision, many learning problems in imprecise probabilistic machine learning (IPML) may be viewed as processes involving successive applications of update rules on credal sets. This naturally raises the question of whether this iterative process converges to stable fixed points -- or, more generally, under what conditions on the updating mechanism such fixed points exist, and whether they can be attained. We provide the first analysis of this problem, and illustrate our findings using Credal Bayesian Deep Learning as a concrete example. Our work demonstrates that incorporating imprecision into the learning process not only enriches the representation of uncertainty, but also reveals structural conditions under which stability emerges, thereby offering new insights into the dynamics of iterative learning under imprecision.

cs.LG↗

arXiv2025

Credal and Interval Deep Evidential Classifications

Uncertainty Quantification (UQ) presents a pivotal challenge in the field of Artificial Intelligence (AI), profoundly impacting decision-making, risk assessment and model reliability. In this paper, we introduce Credal and Interval Deep Evidential Classifications (CDEC and IDEC, respectively) as novel approaches to address UQ in classification tasks. CDEC and IDEC leverage a credal set (closed and convex set of probabilities) and an interval of evidential predictive distributions, respectively, allowing us to avoid overfitting to the training data and to systematically assess both epistemic (reducible) and aleatoric (irreducible) uncertainties. When those surpass acceptable thresholds, CDEC and IDEC have the capability to abstain from classification and flag an excess of epistemic or aleatoric uncertainty, as relevant. Conversely, within acceptable uncertainty bounds, CDEC and IDEC provide a collection of labels with robust probabilistic guarantees. CDEC and IDEC are trained using standard backpropagation and a loss function that draws from the theory of evidence. They overcome the shortcomings of previous efforts, and extend the current evidential deep learning literature. Through extensive experiments on MNIST, CIFAR-10 and CIFAR-100, together with their natural OoD shifts (F-MNIST/K-MNIST, SVHN/Intel, TinyImageNet), we show that CDEC and IDEC achieve competitive predictive accuracy, state-of-the-art OoD detection under epistemic and total uncertainty, and tight, well-calibrated prediction regions that expand reliably under distribution shift. An ablation over ensemble size further demonstrates that CDEC attains stable uncertainty estimates with only a small ensemble.

cs.LG↗

arXiv2025

PoseDiff: A Unified Diffusion Model Bridging Robot Pose Estimation and Video-to-Action Control

We present PoseDiff, a conditional diffusion model that unifies robot state estimation and control within a single framework. At its core, PoseDiff maps raw visual observations into structured robot states-such as 3D keypoints or joint angles-from a single RGB image, eliminating the need for multi-stage pipelines or auxiliary modalities. Building upon this foundation, PoseDiff extends naturally to video-to-action inverse dynamics: by conditioning on sparse video keyframes generated by world models, it produces smooth and continuous long-horizon action sequences through an overlap-averaging strategy. This unified design enables scalable and efficient integration of perception and control. On the DREAM dataset, PoseDiff achieves state-of-the-art accuracy and real-time performance for pose estimation. On Libero-Object manipulation tasks, it substantially improves success rates over existing inverse dynamics modules, even under strict offline settings. Together, these results show that PoseDiff provides a scalable, accurate, and efficient bridge between perception, planning, and control in embodied AI. The video visualization results can be found on the project page: https://haozhuo-zhang.github.io/PoseDiff-project-page/.

cs.RO↗

arXiv2025

IBCL: Zero-shot Model Generation under Stability-Plasticity Trade-offs

Algorithms that balance the stability-plasticity trade-off are well studied in the Continual Learning literature. However, only a few focus on obtaining models for specified trade-off preferences. When solving the problem of continual learning under specific trade-offs (CLuST), state-of-the-art techniques leverage rehearsal-based learning, which requires retraining when a model corresponding to a new trade-off preference is requested. This is inefficient, since there potentially exists a significant number of different trade-offs, and a large number of models may be requested. As a response, we propose Imprecise Bayesian Continual Learning (IBCL), an algorithm that tackles CLuST efficiently. IBCL replaces retraining with a constant-time convex combination. Given a new task, IBCL (1) updates the knowledge base as a convex hull of model parameter distributions, and (2) generates one Pareto-optimal model per given trade-off via convex combination without additional training. That is, obtaining models corresponding to specified trade-offs via IBCL is zero-shot. Experiments whose baselines are current CLuST algorithms show that IBCL improves classification by at most 44% on average per task accuracy, and by 45% on peak per task accuracy while maintaining a near-zero to positive backward transfer, with memory overheads converging to constants. In addition, its training overhead, measured by the number of batch updates, remains constant at every task, regardless of the number of preferences requested. IBCL also improves multi-objective reinforcement learning tasks by maintaining the same Pareto front hypervolume, while significantly reducing the training cost. Details can be found at: https://github.com/ibcl-anon/ibcl.

cs.LG↗

arXiv2025

Finite Admixture Models: a Bridge with Stochastic Geometry and Choquet Theory

Given a finite admixture model whose components and weights are unknown, let the number of identifiable components be a function of the amount of data sampled from a known distribution on the unit simplex. We use techniques from stochastic convex geometry to find the growth rate of its expected value. In addition, when the components are known but the weights are not, we provide an application of the classic Glivenko-Cantelli's theorem that allows us to retrieve the Choquet measure supported on the identifiable admixture components. In turn, this gives us the identifiable admixture weights. Finally, we propose a novel algorithm that estimates the model capturing the complexity of the data using only the strictly necessary number of components.

math.ST↗

arXiv2025

TAR: Teacher-Aligned Representations via Contrastive Learning for Quadrupedal Locomotion

Quadrupedal locomotion via Reinforcement Learning (RL) is commonly addressed using the teacher-student paradigm, where a privileged teacher guides a proprioceptive student policy. However, key challenges such as representation misalignment between privileged teacher and proprioceptive-only student, covariate shift due to behavioral cloning, and lack of deployable adaptation; lead to poor generalization in real-world scenarios. We propose Teacher-Aligned Representations via Contrastive Learning (TAR), a framework that leverages privileged information with self-supervised contrastive learning to bridge this gap. By aligning representations to a privileged teacher in simulation via contrastive objectives, our student policy learns structured latent spaces and exhibits robust generalization to Out-of-Distribution (OOD) scenarios, surpassing the fully privileged "Teacher". Results showed accelerated training by 2x compared to state-of-the-art baselines to achieve peak performance. OOD scenarios showed better generalization by 40% on average compared to existing methods. Moreover, TAR transitions seamlessly into learning during deployment without requiring privileged states, setting a new benchmark in sample-efficient, adaptive locomotion and enabling continual fine-tuning in real-world scenarios. Open-source code and videos are available at https://amrmousa.com/TARLoco/.

cs.RO↗

arXiv2025

Optimal Transport for $ε$-Contaminated Credal Sets: To the Memory of Sayan Mukherjee

We present generalized versions of Monge's and Kantorovich's optimal transport problems with the probabilities being transported replaced by lower probabilities. We show that, when the lower probabilities are the lower envelopes of $ε$-contaminated sets, then our version of Monge's, and a restricted version of our Kantorovich's problems, coincide with their respective classical versions. We also give sufficient conditions for the existence of our version of Kantorovich's optimal plan, and for the two problems to be equivalent. As a byproduct, we show that for $ε$-contaminations the lower probability versions of Monge's and Kantorovich's optimal transport problems need not coincide. The applications of our results to Machine Learning and Artificial Intelligence are also discussed.

stat.ML↗

arXiv2025

Conformal Prediction Regions are Imprecise Highest Density Regions

Recently, Cella and Martin proved how, under an assumption called consonance, a credal set (i.e. a closed and convex set of probabilities) can be derived from the conformal transducer associated with transductive conformal prediction. We show that the Imprecise Highest Density Region (IHDR) associated with such a credal set corresponds to the classical Conformal Prediction Region. In proving this result, we establish a new relationship between Conformal Prediction and Imprecise Probability (IP) theories, via the IP concept of a cloud. A byproduct of our presentation is the discovery that consonant plausibility functions are monoid homomorphisms, a new algebraic property of an IP tool.

stat.ML↗

arXiv2025

Distributionally Robust Statistical Verification with Imprecise Neural Networks

A particularly challenging problem in AI safety is providing guarantees on the behavior of high-dimensional autonomous systems. Verification approaches centered around reachability analysis fail to scale, and purely statistical approaches are constrained by the distributional assumptions about the sampling process. Instead, we pose a distributionally robust version of the statistical verification problem for black-box systems, where our performance guarantees hold over a large family of distributions. This paper proposes a novel approach based on uncertainty quantification using concepts from imprecise probabilities. A central piece of our approach is an ensemble technique called Imprecise Neural Networks, which provides the uncertainty quantification. Additionally, we solve the allied problem of exploring the input set using active learning. The active learning uses an exhaustive neural-network verification tool Sherlock to collect samples. An evaluation on multiple physical simulators in the openAI gym Mujoco environments with reinforcement-learned controllers demonstrates that our approach can provide useful and scalable guarantees for high-dimensional systems.

cs.AI↗

arXiv2025

Conformalized Credal Regions for Classification with Ambiguous Ground Truth

An open question in \emph{Imprecise Probabilistic Machine Learning} is how to empirically derive a credal region (i.e., a closed and convex family of probabilities on the output space) from the available data, without any prior knowledge or assumption. In classification problems, credal regions are a tool that is able to provide provable guarantees under realistic assumptions by characterizing the uncertainty about the distribution of the labels. Building on previous work, we show that credal regions can be directly constructed using conformal methods. This allows us to provide a novel extension of classical conformal prediction to problems with ambiguous ground truth, that is, when the exact labels for given inputs are not exactly known. The resulting construction enjoys desirable practical and theoretical properties: (i) conformal coverage guarantees, (ii) smaller prediction sets (compared to classical conformal prediction regions) and (iii) disentanglement of uncertainty sources (epistemic, aleatoric). We empirically verify our findings on both synthetic and real datasets.

stat.ML↗

arXiv2024

Credal Learning Theory

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.

cs.LG↗

arXiv2024

Credal Bayesian Deep Learning

Uncertainty quantification and robustness to distribution shifts are important goals in machine learning and artificial intelligence. Although Bayesian Neural Networks (BNNs) allow for uncertainty in the predictions to be assessed, different sources of predictive uncertainty cannot be distinguished properly. We present Credal Bayesian Deep Learning (CBDL). Heuristically, CBDL allows to train an (uncountably) infinite ensemble of BNNs, using only finitely many elements. This is possible thanks to prior and likelihood finitely generated credal sets (FGCSs), a concept from the imprecise probability literature. Intuitively, convex combinations of a finite collection of prior-likelihood pairs are able to represent infinitely many such pairs. After training, CBDL outputs a set of posteriors on the parameters of the neural network. At inference time, such posterior set is used to derive a set of predictive distributions that is in turn utilized to distinguish between (predictive) aleatoric and epistemic uncertainties, and to quantify them. The predictive set also produces either (i) a collection of outputs enjoying desirable probabilistic guarantees, or (ii) the single output that is deemed the best, that is, the one having the highest predictive lower probability -- another imprecise-probabilistic concept. CBDL is more robust than single BNNs to prior and likelihood misspecification, and to distribution shift. We show that CBDL is better at quantifying and disentangling different types of (predictive) uncertainties than single BNNs and ensemble of BNNs. In addition, we apply CBDL to two case studies to demonstrate its downstream tasks capabilities: one, for motion prediction in autonomous driving scenarios, and two, to model blood glucose and insulin dynamics for artificial pancreas control. We show that CBDL performs better when compared to an ensemble of BNNs baseline.

cs.LG↗

arXiv2024

DC4L: Distribution Shift Recovery via Data-Driven Control for Deep Learning Models

Deep neural networks have repeatedly been shown to be non-robust to the uncertainties of the real world, even to naturally occurring ones. A vast majority of current approaches have focused on data-augmentation methods to expand the range of perturbations that the classifier is exposed to while training. A relatively unexplored avenue that is equally promising involves sanitizing an image as a preprocessing step, depending on the nature of perturbation. In this paper, we propose to use control for learned models to recover from distribution shifts online. Specifically, our method applies a sequence of semantic-preserving transformations to bring the shifted data closer in distribution to the training set, as measured by the Wasserstein distance. Our approach is to 1) formulate the problem of distribution shift recovery as a Markov decision process, which we solve using reinforcement learning, 2) identify a minimum condition on the data for our method to be applied, which we check online using a binary classifier, and 3) employ dimensionality reduction through orthonormal projection to aid in our estimates of the Wasserstein distance. We provide theoretical evidence that orthonormal projection preserves characteristics of the data at the distributional level. We apply our distribution shift recovery approach to the ImageNet-C benchmark for distribution shifts, demonstrating an improvement in average accuracy of up to 14.21% across a variety of state-of-the-art ImageNet classifiers. We further show that our method generalizes to composites of shifts from the ImageNet-C benchmark, achieving improvements in average accuracy of up to 9.81%. Finally, we test our method on CIFAR-100-C and report improvements of up to 8.25%.

cs.LG↗

arXiv2023

Second-Order Uncertainty Quantification: A Distance-Based Approach

In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order probability distributions, i.e., predictions in the form of distributions on probability distributions. A completely conclusive solution has not yet been found, however, as shown by recent criticisms of commonly used uncertainty measures associated with second-order distributions, identifying undesirable theoretical properties of these measures. In light of these criticisms, we propose a set of formal criteria that meaningful uncertainty measures for predictive uncertainty based on second-order distributions should obey. Moreover, we provide a general framework for developing uncertainty measures to account for these criteria, and offer an instantiation based on the Wasserstein distance, for which we prove that all criteria are satisfied.

cs.LG↗