arXiv subjects

Jeremie Houssineau

Publications and source records attributed to Jeremie Houssineau.

At least 19 recordsLinked to original sources

arXiv2026

From Bayes' Rule to Bayes Rules: Optimal Information Processing and Axiomatic Foundations Beyond Probability

This paper develops principled updating rules for possibilistic inference, where uncertainty about a fixed parameter is represented by a possibility function, the maxitive analogue of a probability distribution, and comparisons are made pointwise via a partial order. From two complementary foundations, an information-conservation viewpoint and an axiomatic viewpoint, we derive the same canonical update: the posterior is the prior-likelihood product followed by supremum normalisation. The two derivations agree for an arbitrary loss, differing only in where the learning-rate parameter enters. This parameter controls epistemic strength and is not identifiable from the normalising evidence alone, clarifying the role of analogous learning-rate parameters in generalised Bayesian updating.

math.ST↗

arXiv2026

Possibilistic Predictive Uncertainty for Deep Learning

Deep neural networks achieve impressive results across diverse applications, yet their overconfidence on unseen inputs necessitates reliable epistemic uncertainty modeling. Existing methods for uncertainty modeling face a fundamental dilemma: Bayesian approaches provide principled estimates but remain computationally prohibitive, while efficient second-order predictors lack rigorous connections between their specific objectives and epistemic uncertainty quantification. To resolve this dilemma, we introduce Dirichlet-approximated possibilistic posterior predictions (DAPPr), a principled framework grounded in possibility theory. We define a possibilistic posterior over parameters, project it to the prediction space via supremum operators, and approximate the projected posterior using learnable Dirichlet possibility functions. This projection-and-approximation strategy yields a simple training objective with closed-form solutions. Despite its simplicity, extensive experiments across diverse benchmarks show that DAPPr achieves competitive or superior uncertainty quantification performance over state-of-the-art second-order predictors while maintaining both principled derivation and computational efficiency. Code is available at https://github.com/MaxwellYaoNi/DAPPr.

cs.LG↗

arXiv2026

Action-Free Offline-to-Online RL via Discretised State Policies

Most existing offline RL methods presume the availability of action labels within the dataset, but in many practical scenarios, actions may be missing due to privacy, storage, or sensor limitations. We formalise the setting of action-free offline-to-online RL, where agents must learn from datasets consisting solely of $(s,r,s')$ tuples and later leverage this knowledge during online interaction. To address this challenge, we propose learning state policies that recommend desirable next-state transitions rather than actions. Our contributions are twofold. First, we introduce a simple yet novel state discretisation transformation and propose Offline State-Only DecQN (\algo), a value-based algorithm designed to pre-train state policies from action-free data. \algo{} integrates the transformation to scale efficiently to high-dimensional problems while avoiding instability and overfitting associated with continuous state prediction. Second, we propose a novel mechanism for guided online learning that leverages these pre-trained state policies to accelerate the learning of online agents. Together, these components establish a scalable and practical framework for leveraging action-free datasets to accelerate online RL. Empirical results across diverse benchmarks demonstrate that our approach improves convergence speed and asymptotic performance, while analyses reveal that discretisation and regularisation are critical to its effectiveness.

stat.ML↗

arXiv2025

Maxitive Donsker-Varadhan Formulation for Possibilistic Variational Inference

Variational inference (VI) is a cornerstone of modern Bayesian learning, enabling approximate inference in complex models. However, its formulation depends on expectations and divergences defined through high-dimensional integrals, often rendering analytical treatment impossible and necessitating heavy reliance on approximations. Possibility theory, an imprecise probability framework, allows us to directly model epistemic uncertainty instead of relying on a subjective interpretation of probabilities. While this framework provides robustness and interpretability under sparse or imprecise information, adapting VI to the possibilistic setting requires rethinking core concepts such as divergences, which presuppose additivity. In this work, we develop a principled formulation for performing possibilistic VI by establishing a maxitive analogue of the classical Donsker-Varadhan formulation. The resulting framework enables us to derive a learning rule for possibilistic VI with exponential-family candidates and practical update rules for neural-network training, giving rise to a family of optimizers termed CBOpt. Finally, we demonstrate that CBOpt achieves competitive performance on both in-domain and out-of-domain image classification tasks.

stat.ML↗

arXiv2025

Possibilistic Instrumental Variable Regression with Potentially Invalid Instruments

Instrumental variable regression is a common approach for causal inference in the presence of unobserved confounding. However, identifying valid instruments is often difficult in practice. In this paper, we propose a novel method based on possibility theory that performs posterior inference on the treatment effect, conditional on a user-specified set of potential violations of the instrument exogeneity assumption. Our method can provide valid results even when only a single, potentially invalid, instrument is available. Crucially, and in contrast with existing methods, we prove a finite-sample coverage guarantee for the exactly calibrated (validified) uncertainty intervals when the violation set contains the true value, and we provide practical MC/$\chi^2$ approximations. Simulation experiments and real-data applications indicate strong performance of the proposed approach.

stat.ME↗

arXiv2025

Evaluation-Time Policy Switching for Offline Reinforcement Learning

Offline reinforcement learning (RL) looks at learning how to optimally solve tasks using a fixed dataset of interactions from the environment. Many off-policy algorithms developed for online learning struggle in the offline setting as they tend to over-estimate the behaviour of out of distributions actions. Existing offline RL algorithms adapt off-policy algorithms, employing techniques such as constraining the policy or modifying the value function to achieve good performance on individual datasets but struggle to adapt to different tasks or datasets of different qualities without tuning hyper-parameters. We introduce a policy switching technique that dynamically combines the behaviour of a pure off-policy RL agent, for improving behaviour, and a behavioural cloning (BC) agent, for staying close to the data. We achieve this by using a combination of epistemic uncertainty, quantified by our RL model, and a metric for aleatoric uncertainty extracted from the dataset. We show empirically that our policy switching technique can outperform not only the individual algorithms used in the switching process but also compete with state-of-the-art methods on numerous benchmarks. Our use of epistemic uncertainty for policy switching also allows us to naturally extend our method to the domain of offline to online fine-tuning allowing our model to adapt quickly and safely from online data, either matching or exceeding the performance of current methods that typically require additional modification or hyper-parameter fine-tuning.

cs.LG↗

arXiv2024

Investigating Relational State Abstraction in Collaborative MARL

This paper explores the impact of relational state abstraction on sample efficiency and performance in collaborative Multi-Agent Reinforcement Learning. The proposed abstraction is based on spatial relationships in environments where direct communication between agents is not allowed, leveraging the ubiquity of spatial reasoning in real-world multi-agent scenarios. We introduce MARC (Multi-Agent Relational Critic), a simple yet effective critic architecture incorporating spatial relational inductive biases by transforming the state into a spatial graph and processing it through a relational graph neural network. The performance of MARC is evaluated across six collaborative tasks, including a novel environment with heterogeneous agents. We conduct a comprehensive empirical analysis, comparing MARC against state-of-the-art MARL baselines, demonstrating improvements in both sample efficiency and asymptotic performance, as well as its potential for generalization. Our findings suggest that a minimal integration of spatial relational inductive biases as abstraction can yield substantial benefits without requiring complex designs or task-specific engineering. This work provides insights into the potential of relational state abstraction to address sample efficiency, a key challenge in MARL, offering a promising direction for developing more efficient algorithms in spatially complex environments.

cs.AI↗

arXiv2024

Improving Active Learning with a Bayesian Representation of Epistemic Uncertainty

A popular strategy for active learning is to specifically target a reduction in epistemic uncertainty, since aleatoric uncertainty is often considered as being intrinsic to the system of interest and therefore not reducible. Yet, distinguishing these two types of uncertainty remains challenging and there is no single strategy that consistently outperforms the others. We propose to use a particular combination of probability and possibility theories, with the aim of using the latter to specifically represent epistemic uncertainty, and we show how this combination leads to new active learning strategies that have desirable properties. In order to demonstrate the efficiency of these strategies in non-trivial settings, we introduce the notion of a possibilistic Gaussian process (GP) and consider GP-based multiclass and binary classification problems, for which the proposed methods display a strong performance for both simulated and real datasets.

stat.ME↗

arXiv2024

Redesigning the ensemble Kalman filter with a dedicated model of epistemic uncertainty

The problem of incorporating information from observations received serially in time is widespread in the field of uncertainty quantification. Within a probabilistic framework, such problems can be addressed using standard filtering techniques. However, in many real-world problems, some (or all) of the uncertainty is epistemic, arising from a lack of knowledge, and is difficult to model probabilistically. This paper introduces a possibilistic ensemble Kalman filter designed for this setting and characterizes some of its properties. Using possibility theory to describe epistemic uncertainty is appealing from a philosophical perspective, and it is easy to justify certain heuristics often employed in standard ensemble Kalman filters as principled approaches to capturing uncertainty within it. The possibilistic approach motivates a robust mechanism for characterizing uncertainty which shows good performance with small sample sizes, and can outperform standard ensemble Kalman filters at given sample size, even when dealing with genuinely aleatoric uncertainty.

stat.ME↗

arXiv2024

Mitigating Relative Over-Generalization in Multi-Agent Reinforcement Learning

In decentralized multi-agent reinforcement learning, agents learning in isolation can lead to relative over-generalization (RO), where optimal joint actions are undervalued in favor of suboptimal ones. This hinders effective coordination in cooperative tasks, as agents tend to choose actions that are individually rational but collectively suboptimal. To address this issue, we introduce MaxMax Q-Learning (MMQ), which employs an iterative process of sampling and evaluating potential next states, selecting those with maximal Q-values for learning. This approach refines approximations of ideal state transitions, aligning more closely with the optimal joint policy of collaborating agents. We provide theoretical analysis supporting MMQ's potential and present empirical evaluations across various environments susceptible to RO. Our results demonstrate that MMQ frequently outperforms existing baselines, exhibiting enhanced convergence and sample efficiency.

cs.LG↗

arXiv2024

Robust Multi-Sensor Multi-Target Tracking Using Possibility Labeled Multi-Bernoulli Filter

With the increasing complexity of multiple target tracking scenes, a single sensor may not be able to effectively monitor a large number of targets. Therefore, it is imperative to extend the single-sensor technique to Multi-Sensor Multi-Target Tracking (MSMTT) for enhanced functionality. Typical MSMTT methods presume complete randomness of all uncertain components, and therefore effective solutions such as the random finite set filter and covariance intersection method have been derived to conduct the MSMTT task. However, the presence of epistemic uncertainty, arising from incomplete information, is often disregarded within the context of MSMTT. This paper develops an innovative possibility Labeled Multi-Bernoulli (LMB) Filter based on the labeled Uncertain Finite Set (UFS) theory. The LMB filter inherits the high robustness of the possibility generalized labeled multi-Bernoulli filter with simplified computational complexity. The fusion of LMB UFSs is derived and adapted to develop a robust MSMTT scheme. Simulation results corroborate the superior performance exhibited by the proposed approach in comparison to typical probabilistic methods.

cs.IT↗

arXiv2022

Decentralised possibilistic inference with applications to target tracking

Fusing and sharing information from multiple sensors over a network is a challenging task, partly due to the absence of a foundational rule for fusing probability distributions that preserves the independence of sources. To address this, we propose a decentralised inference framework based on possibility theory. Unlike probabilistic approaches that rely on ad-hoc averaging, we derive a principled fusion rule that is proven to be asymptotically exact, meaning it recovers the posterior of the optimal centralised possibilistic approach. We apply this rule to the possibilistic Bernoulli filter, leveraging its hierarchical nature to jointly infer data association and state estimation, distinct from standard decentralised Kalman filtering. We demonstrate that the proposed approach maintains the independence of local posteriors during fusion and, even under necessary approximations to handle Gaussian mixtures, significantly outperforms probabilistic geometric and arithmetic average fusion baselines in terms of cardinality and localisation error.

eess.SP↗

arXiv2022

Robust Bayesian inference in complex models with possibility theory

We propose a general solution to the problem of robust Bayesian inference in complex settings where outliers may be present. In practice, the automation of robust Bayesian analyses is important in the many applications involving large and complex datasets. The proposed solution relies on a reformulation of Bayesian inference based on possibility theory, and leverages the observation that, in this context, the marginal likelihood of the data assesses the consistency between prior and likelihood rather than model fitness. Our approach does not require additional parameters in its simplest form and has a limited impact on the computational complexity when compared to non-robust solutions. The generality of our solution is demonstrated via applications on simulated and real data including matrix estimation and change-point detection.

stat.ME↗

arXiv2021

On Unbiased Score Estimation for Partially Observed Diffusions

We consider the problem of statistical inference for a class of partially-observed diffusion processes, with discretely-observed data and finite-dimensional parameters. We construct unbiased estimators of the score function, i.e. the gradient of the log-likelihood function with respect to parameters, with no time-discretization bias. These estimators can be straightforwardly employed within stochastic gradient methods to perform maximum likelihood estimation or Bayesian inference. As our proposed methodology only requires access to a time-discretization scheme such as the Euler-Maruyama method, it is applicable to a wide class of diffusion processes and observation models. Our approach is based on a representation of the score as a smoothing expectation using Girsanov theorem, and a novel adaptation of the randomization schemes developed in Mcleish [2011], Rhee and Glynn [2015], Jacob et al. [2020a]. This allows one to remove the time-discretization bias and burn-in bias when computing smoothing expectations using the conditional particle filter of Andrieu et al. [2010]. Central to our approach is the development of new couplings of multiple conditional particle filters. We prove under assumptions that our estimators are unbiased and have finite variance. The methodology is illustrated on several challenging applications from population ecology and neuroscience.

stat.ME↗

arXiv2021

A linear algorithm for multi-target tracking in the context of possibility theory

We present a modelling framework for multi-target tracking based on possibility theory and illustrate its ability to account for the general lack of knowledge that the target-tracking practitioner must deal with when working with real data. We also introduce and study variants of the notions of point process and intensity function, which lead to the derivation of an analogue of the probability hypothesis density (PHD) filter. The gains provided by the considered modelling framework in terms of flexibility lead to the loss of some of the abilities that the PHD filter possesses; in particular the estimation of the number of targets by integration of the intensity function. Yet, the proposed recursion displays a number of advantages such as facilitating the introduction of observation-driven birth schemes and the modelling the absence of information on the initial number of targets in the scene. The performance of the proposed approach is demonstrated on simulated data.

stat.ME↗

arXiv2020

Uncertainty modelling and computational aspects of data association

A novel solution to the smoothing problem for multi-object dynamical systems is proposed and evaluated. The systems of interest contain an unknown and varying number of dynamical objects that are partially observed under noisy and corrupted observations. An alternative representation of uncertainty is considered in order to account for the lack of information about the different aspects of this type of complex system. The corresponding statistical model can be formulated as a hierarchical model consisting of conditionally-independent hidden Markov models. This particular structure is leveraged to propose an efficient method in the context of Markov chain Monte Carlo (MCMC) by relying on an approximate solution to the corresponding filtering problem, in a similar fashion to particle MCMC. This approach is shown to outperform existing algorithms in a range of scenarios.

stat.CO↗

arXiv2020

Elements of asymptotic theory with outer probability measures

Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis testing need to be analysed in order to understand their behaviour, and motivate their use. In this article, we consider a class of outer measures based on the supremum of particular functions that we refer to as possibility functions. We then characterise the asymptotic behaviour of the corresponding Bayesian posterior uncertainties, from which the properties of the corresponding maximum a posteriori estimators can be deduced. These results are largely based on versions of both the law of large numbers and the central limit theorem that are adapted to possibility functions. Our motivation with outer measures is through the notion of uncertainty quantification, where verification of these procedures is of crucial importance. These introduced concepts shed a new light on some standard concepts such as the Fisher information and sufficient statistics and naturally strengthen the link between the frequentist and Bayesian approaches.

math.ST↗

arXiv2020

Parameter estimation with a class of outer probability measures

We explore the interplay between random and deterministic phenomena using a representation of uncertainty based on the measure-theoretic concept of outer measure. The meaning of the analogues of different probabilistic concepts is investigated and examples of application are given. The novelty of this article lies mainly in the suitability of the tools introduced for jointly representing random and deterministic uncertainty. These tools are shown to yield intuitive results in simple situations and to generalise easily to more complex cases. Connections with Dempster-Shafer theory, the empirical Bayes methods and generalised Bayesian inference are also highlighted.

stat.ME↗