Traditional machine learning models provide a single-class prediction for a given input instance. This may be inadequate in some scenarios, especially when the cost of erroneous predictions is high. Cautious random forests are cautious classification models that may output sets of possible classes as predictions when uncertainty is high, thus reducing the risk of making incorrect decisions. However, making such indeterminate predictions carries a cost, as resolving indeterminacy typically necessitates further analysis and manual intervention. This work focuses on explaining why an indeterminate prediction has been made and how indeterminacy can be resolved. To this end, we use counterfactual examples associated with determinate predictions. We propose a branch-and-bound algorithm that can efficiently generate proximal, plausible, and actionable counterfactual examples. Several experimental results are presented to demonstrate the advantages of our proposed method.

Self-learning is a widely used semi-supervised learning strategy that leverages model predictions to label unlabeled data. However, conventional approaches often ignore the uncertainty inherent in these predictions, leading to confirmation bias and overconfident models. In this work, we propose a cautious self-learning framework that integrates label-wise uncertainty quantification through credal sets. By distinguishing between aleatoric and epistemic uncertainty, our method adjusts pseudo-labels to reflect both the inherent ambiguity of the data and the model’s limited knowledge. We employ a variance-based decomposition and a label-wise Beta distribution estimation to construct credal sets that mitigate class imbalance and reduce overconfidence during iterative training. Experiments across six benchmark datasets demonstrate that our approach consistently improves classification accuracy compared to hard and soft pseudo-labeling strategies, achieving superior performance. These results highlight the importance of uncertainty-aware self-learning and show that cautious pseudo-labeling can enhance robustness and generalization in semi-supervised learning.

To generate accurate and reliable predictions, modern AI systems need to combine data from multiple modalities, such as text, images, audio, spreadsheets, and time series. However, collecting training and test data for many modalities is challenging and time-consuming, creating a need for cost-efficient multi-modal data acquisition. In this paper we advocate that this can be realized by disentangling epistemic and aleatoric uncertainty. It is commonly assumed in the machine learning community that epistemic uncertainty can be reduced by collecting more data, while aleatoric uncertainty is irreducible. We claim that this assumption can be challenged in modern multi-modal AI systems, and we introduces an innovative data acquisition framework where uncertainty disentanglement leads to actionable decisions, allowing cost-efficient sampling in two directions: sample size and data modality. The main hypothesis is that aleatoric uncertainty decreases as the number of modalities increases, while epistemic uncertainty decreases by collecting more observations. We provide a theoretical analysis and proof-of-concept implementations on various multi-modal datasets to prove the usefulness of our framework, which combines ideas from active learning, active feature acquisition and uncertainty quantification.

Probabilistic Circuits (PCs) are prominent tractable probabilistic models, allowing for a wide range of exact inferences. This paper focuses on a main algorithm for training PCs, LearnSPN, arguably a gold standard due to its efficiency, performance, and ease of use, in particular for tabular data. We show that LearnSPN is a greedy likelihood maximizer under mild assumptions. While inferences in PCs may use the entire circuit structure for processing queries, LearnSPN applies a hard method for learning PCs, propagating at each sum node a data point through one and only one of the children/edges as in a hard clustering process. We propose a new learning procedure named SoftLearn, that induces a PC using a soft clustering process. We investigate the effect of this learning-inference compatibility in PCs. Our experiments show that SoftLearn outperforms LearnSPN in many situations, yielding better likelihoods and arguably better samples. We also analyze comparable tractable models to highlight the differences between soft/hard learning and model querying.

Processing geospatial data requires to manage many sources of uncertainties; some appear in classical inference problems, some others are specific to this setting. The goal of this paper is to study the management of these uncertainties via standard intervals and sets when the inference model considered relies on inverse distance weighting. We provide a general discussion with examples, together with a study of the associated optimisation problems induced by different sources of uncertainty. We conclude the paper by an illustration on a semi-synthetic use case, generated according to data recorded via real studies.

Probabilistic Circuits (PCs) are a class of tractable models that allow a range of efficient and exact computations while achieving state-of-the-art performance in some domains. In this work, we propose a sample-based procedure to let the distribution encoded by a PC satisfy probabilistic propositional logic constraints. This sample-based method is proposed as a direct competitor to a mathematical approach previously introduced, which is based on optimizing a convex upper bound of the KL divergence. In our empirical study, we compare both methods in two different scenarios, where constraints are utilized to: i) apply fairness to a distribution; and ii) improve the performance of a PC model under scarce data. Our results indicate that although both methods are competitive to one another in the case of fairness, sample-based method has an advantage in scenarios with scarce data.

This paper presents a novel extension of the discrete Bayesian classifier (DBC) into a set-valued classification framework grounded in imprecise probability theory. The standard DBC framework, which relies on partitioning the input space into profiles and estimating class-conditional probabilities, may not be very robust to distribution changes or imperfections in observed data. In the hope to mitigate such issues, we introduce the Credal Discrete Classifier (CDC), an imprecise-probabilistic extension of the traditional Bayesian approach. By representing uncertainties in the estimated probabilities through belief functions, CDC offers interval-valued risks and set-valued decisions, thereby enhancing robustness. Experimental results on several benchmark datasets demonstrate that CDC effectively balances accuracy and determinacy by allowing for set-valued predictions in uncertain contexts, often outperforming or matching traditional precise classifiers.

Classifiers now demonstrate impressive performances in many domains. However, in some applications where the cost of an erroneous decision is high, set-valued predictions may be preferable to classical crisp decisions, being less informative but more reliable. Cautious classifiers aim at producing such imprecise predictions so as to reduce the risk of making wrong decisions. In this paper, we describe two cautious classification approaches rooted in the ensemble learning paradigm, which consist in combining probability intervals. These intervals are aggregated within the framework of belief functions, using two proposed strategies that can be regarded as generalizations of classical averaging and voting. Our strategies aim at maximizing the lower expected discounted utility to achieve a good compromise between model accuracy and determinacy. The efficiency and performance of the proposed procedure are illustrated using imprecise decision trees, thus giving birth to cautious variants of the random forest classifier. The performance and properties of these variants are illustrated using 15 datasets.

The contribution of this paper consists of a deep reinforcement learning (DRL) based method for autonomous train collision avoidance. While DRL applied to autonomous vehicles’ collision avoidance has shown interesting results compared to traditional methods, train-like vehicles are not currently covered. In addition, DRL applied to collision avoidance suffers from sparse rewards, which can lead to poor convergence and long training time. To overcome these limitations, this paper proposes a method for training a reinforcement learning (RL) agent for collision avoidance using local obstacle information mapped into occupancy grids. This method also integrates a network architecture containing a predictive auxiliary task consisting in future state prediction and encouraging the intermediate representation to be predictive of obstacle trajectories. A comparison study conducted on multiple simulated scenarios demonstrates that the trained policy outperforms other deep-learning-based policies as well as human driving in terms of both safety and efficiency. As a first step toward the certification of a DRL based method, this paper proposes to approximate the policy learned by the RL agent with an interpretable decision tree. Although this approximation results in a loss of performance, it enables a safety analysis of the learned function and thus paves the way to use the strengths of RL in certifiable algorithms. As this work is pioneering the use of RL for collision avoidance of rail-guided vehicles, and to facilitate future work by other engineers and researchers, a RL-ready simulator is provided with this paper.

This work addresses integrating probabilistic propositional logic constraints into the distribution encoded by a probabilistic circuit (PC). PCs are a class of tractable models that allow efficient computations (such as conditional and marginal probabilities) while achieving state-of-the-art performance in some domains. The proposed approach takes both a PC and constraints as inputs, and outputs a new PC that satisfies the constraints. This is done efficiently via convex optimization without the need to retrain the entire model. Empirical evaluations indicate that the combination of constraints and PCs can have multiple use cases, including the improvement of model performance under scarce or incomplete data, as well as the enforcement of machine learning fairness measures into the model without compromising model fitness. We believe that these ideas will open possibilities for multiple other applications involving the combination of logics and deep probabilistic models.

In this paper, we focus on the Discrete Bayesian Classifier (DBC), which discretizes the input space into regions where class probabilities are estimated. We investigate fuzzy partitioning as an alternative to the hard partitioning classically used to discretize the space. We show that our approach not only boosts the DBC's performance and resilience to noise, but also mitigates the loss of information due to discretization. The benefits of soft partitioning are demonstrated experimentally on several synthetic and real datasets.

In supervised learning problems, it is common to have a lot of unlabeled data, but little labeled data. It is then desirable to leverage the unlabeled data to improve the learning procedure. One way to do this is to have a model predict "pseudolabels" for the unlabeled data, so as to use them for learning. In self-learning, the pseudo-labels are provided by the very same model to which they are fed. As these pseudo-labels are by nature uncertain and only partially reliable, it is then natural to model this uncertainty and take it into account in the learning process, if only to robustify the self-learning procedure. This paper describes such an approach, where we use Venn-Abers Predictors to produce calibrated credal labels so as to quantify the pseudo-labeling uncertainty. These labels are then included in the learning process by optimizing an adapted loss. Experiments show that taking into account pseudo-label uncertainty both robustifies the self-learning procedure and allows it to converge faster in general.

A plug-in hybrid electric vehicle (PHEV) satisfies the driver's power demand with two types of energy potentials: fuel and electrical energy provided by a battery. Classically, the battery consumption is planned over a trip to minimize the expected fuel consumption. A cautious driver will save battery potential to cross restricted areas (with desired low or even zero fuel consumption) without the fuel engine. This paper proposes an approach to minimize energy consumption while controlling the risk of a PHEV falling short of battery potential when crossing a restricted area. We use a nonlinear Gaussian process, trained on real vehicle data, for predicting the vehicle consumption. We take into account prediction uncertainty by ensuring that the driver's highest power demand will be satisfied with a high probability. The interest of the approach is demonstrated by a simulated trip around Paris.

Cautious classifiers are designed to make indeterminate decisions when the uncertainty on the input data or the model output is too high, so as to reduce the risk of making wrong decisions. In this paper, we propose two cautious decision-making procedures, by aggregating trees providing probability intervals constructed via the imprecise Dirichlet model. The trees are aggregated in the belief functions framework, by maximizing the lower expected discounted utility, so as to achieve a good compromise between model accuracy and determinacy. They can be regarded as generalizations of the two classical aggregation strategies for tree ensembles, i.e., averaging and voting. The efficiency and performance of the proposed procedures are tested on random forests and illustrated on three UCI datasets.

We consider the problem of supervised classification. We focus on the problem of calibrating the classifier's outputs. We show that the p-values provided by Inductive Conformal Prediction (ICP) can be interpreted as a possibility distribution over the set of classes. This allows us to use ICP to compute a predictive belief function which is calibrated by construction. We also propose a learning method which provides p-values in a simpler and faster way, by making use of a multi-output regression model. Results obtained on the Cifar10 and Digits data sets show that our approach is comparable to standard ICP in terms of accuracy and calibration, while offering a reduced complexity and avoiding the use of a calibration set.

Random forest is an efficient and accurate classification model, which makes decisions by aggregating a set of trees, either by voting or by averaging class posterior probability estimates. However, tree outputs may be unreliable in presence of scarce data. The imprecise Dirichlet model (IDM) provides workaround, by replacing point probability estimates with interval-valued ones. This paper investigates a new tree aggregation method based on the theory of belief functions to combine such probability intervals, resulting in a cautious random forest classifier. In particular, we propose a strategy for computing tree weights based on the minimization of a convex cost function, which takes both determinacy and accuracy into account and makes it possible to adjust the level of cautiousness of the model. The proposed model is evaluated on 25 UCI datasets and is demonstrated to be more adaptive to the noise in training data and to achieve a better compromise between informativeness and cautiousness.