Nikita Kotelevskii

Nikita Kotelevskii, Maxime Vono, Eric Moulines et al.

Personalised federated learning (FL) aims at collaboratively learning a machine learning model taylored for each client. Albeit promising advances have been made in this direction, most of existing approaches works do not allow for uncertainty quantification which is crucial in many applications. In addition, personalisation in the cross-device setting still involves important issues, especially for new clients or those having small number of observations. This paper aims at filling these gaps. To this end, we propose a novel methodology coined FedPop by recasting personalised FL into the population modeling paradigm where clients' models involve fixed common population parameters and random effects, aiming at explaining data heterogeneity. To derive convergence guarantees for our scheme, we introduce a new class of federated stochastic optimisation algorithms which relies on Markov chain Monte Carlo methods. Compared to existing personalised FL methods, the proposed methodology has important benefits: it is robust to client drift, practical for inference on new clients, and above all, enables uncertainty quantification under mild computational and memory overheads. We provide non-asymptotic convergence guarantees for the proposed algorithms and illustrate their performances on various personalised federated learning tasks.

Asma Ahmed Hashmi, Aigerim Zhumabayeva, Nikita Kotelevskii et al.

The success of Deep Neural Network (DNN) models significantly depends on the quality of provided annotations. In medical image segmentation, for example, having multiple expert annotations for each data point is common to minimize subjective annotation bias. Then, the goal of estimation is to filter out the label noise and recover the ground-truth masks, which are not explicitly given. This paper proposes a probabilistic model for noisy observations that allows us to build a confident classification and segmentation models. To accomplish it, we explicitly model label noise and introduce a new information-based regularization that pushes the network to recover the ground-truth labels. In addition, for segmentation task we adjust the loss function by prioritizing learning in high-confidence regions where all the annotators agree on labeling. We evaluate the proposed method on a series of classification tasks such as noisy versions of MNIST, CIFAR-10, Fashion-MNIST datasets as well as CIFAR-10N, which is real-world dataset with noisy human annotations. Additionally, for segmentation task, we consider several medical imaging datasets, such as, LIDC and RIGA that reflect real-world inter-variability among multiple annotators. Our experiments show that our algorithm outperforms state-of-the-art solutions for the considered classification and segmentation problems.

Nikita Kotelevskii, Maiya Goloburda, Vladimir Kondratyev et al.

Most uncertainty quantification (UQ) approaches provide a single scalar value as a measure of model reliability. However, different uncertainty measures could provide complementary information on the prediction confidence. Even measures targeting the same type of uncertainty (e.g., ensemble-based and density-based measures of epistemic uncertainty) may capture different failure modes. We take a multidimensional view on UQ by stacking complementary UQ measures into a vector. Such vectors are assigned with Monge-Kantorovich ranks produced by an optimal-transport-based ordering method. The prediction is then deemed more uncertain than the other if it has a higher rank. The resulting VecUQ-OT algorithm uses entropy-regularized optimal transport. The transport map is learned on vectors of scores from in-distribution data and, by design, applies to unseen inputs, including out-of-distribution cases, without retraining. Our framework supports flexible non-additive uncertainty fusion (including aleatoric and epistemic components). It yields a robust ordering for downstream tasks such as selective prediction, misclassification detection, out-of-distribution detection, and selective generation. Across synthetic, image, and text data, VecUQ-OT shows high efficiency even when individual measures fail. The code for the method is available at: https://github.com/stat-ml/multidimensional_uncertainty.

Theodore Papamarkou, Pierre Alquier, Matthias Bauer et al.

LLMs excel at predictive tasks and complex reasoning tasks, but many high-value deployments rely on decisions under uncertainty, for example, which tool to call, which expert to consult, or how many resources to invest. While the usefulness and feasibility of Bayesian approaches remain unclear for LLM inference, this position paper argues that the control layer of an agentic AI system (that orchestrates LLMs and tools) is a clear case where Bayesian principles should shine. Bayesian decision theory provides a framework for agentic systems that can help to maintain beliefs over task-relevant latent quantities, to update these beliefs from observed agentic and human-AI interactions, and to choose actions. Making LLMs themselves explicitly Bayesian belief-updating engines remains computationally intensive and conceptually nontrivial as a general modeling target. In contrast, this paper argues that coherent decision-making requires Bayesian principles at the orchestration level of the agentic system, not necessarily the LLM agent parameters. This paper articulates practical properties for Bayesian control that fit modern agentic AI systems and human-AI collaboration, and provides concrete examples and design patterns to illustrate how calibrated beliefs and utility-aware policies can improve agentic AI orchestration.

Nikita Kotelevskii, Vladimir Kondratyev, Martin Takáč et al.

There are various measures of predictive uncertainty in the literature, but their relationships to each other remain unclear. This paper uses a decomposition of statistical pointwise risk into components, associated with different sources of predictive uncertainty, namely aleatoric uncertainty (inherent data variability) and epistemic uncertainty (model-related uncertainty). Together with Bayesian methods, applied as an approximation, we build a framework that allows one to generate different predictive uncertainty measures. We validate our method on image datasets by evaluating its performance in detecting out-of-distribution and misclassified instances using the AUROC metric. The experimental results confirm that the measures derived from our framework are useful for the considered downstream tasks.

Nikita Kotelevskii, Samuel Horváth, Karthik Nandakumar et al.

In modern federated learning, one of the main challenges is to account for inherent heterogeneity and the diverse nature of data distributions for different clients. This problem is often addressed by introducing personalization of the models towards the data distribution of the particular client. However, a personalized model might be unreliable when applied to the data that is not typical for this client. Eventually, it may perform worse for these data than the non-personalized global model trained in a federated way on the data from all the clients. This paper presents a new approach to federated learning that allows selecting a model from global and personalized ones that would perform better for a particular input point. It is achieved through a careful modeling of predictive uncertainties that helps to detect local and global in- and out-of-distribution data and use this information to select the model that is confident in a prediction. The comprehensive experimental evaluation on the popular real-world image datasets shows the superior performance of the model in the presence of out-of-distribution data while performing on par with state-of-the-art personalized federated learning algorithms in the standard scenarios.

Vincent Plassier, Nikita Kotelevskii, Aleksandr Rubashevskii et al.

Conformal Prediction (CP) stands out as a robust framework for uncertainty quantification, which is crucial for ensuring the reliability of predictions. However, common CP methods heavily rely on data exchangeability, a condition often violated in practice. Existing approaches for tackling non-exchangeability lead to methods that are not computable beyond the simplest examples. This work introduces a new efficient approach to CP that produces provably valid confidence sets for fairly general non-exchangeable data distributions. We illustrate the general theory with applications to the challenging setting of federated learning under data heterogeneity between agents. Our method allows constructing provably valid personalized prediction sets for agents in a fully federated way. The effectiveness of the proposed method is demonstrated in a series of experiments on real-world datasets.

Dzianis Piatrashyn, Nikita Kotelevskii, Kirill Grishchenkov et al.

Recently, LLM-based agents have become increasingly popular across many applications, including complex sequential decision-making problems. However, they inherit the tendency of LLMs to hallucinate, leading to incorrect decisions. In sequential settings, even a single mistake can irreversibly degrade the trajectory, making hallucinations an even bigger problem. Although larger LLMs hallucinate less, they incur a significantly higher per-token cost. In this paper, we address this tradeoff by proposing ReDAct (Reason-Defer-Act). In ReDAct, an agent is equipped with two LLMs: a small, cheap model used by default, and a large, more reliable but expensive model. When the predictive uncertainty of the small model exceeds a calibrated threshold, the decision is deferred to the large model. We evaluate our approach in text-based embodied environments such as ALFWorld and MiniGrid and show that deferring only about 15% of decisions to the large model can match the quality of using it exclusively, while significantly reducing inference costs.

Alexander Fishkov, Kajetan Schweighofer, Mykyta Ielanskyi et al.

Quantifying uncertainty of machine learning model predictions is essential for reliable decision-making, especially in safety-critical applications. Recently, uncertainty quantification (UQ) theory has advanced significantly, building on a firm basis of learning with proper scoring rules. However, these advances were focused on classification, while extending these ideas to regression remains challenging. In this work, we introduce a unified UQ framework for regression based on proper scoring rules, such as CRPS, logarithmic, squared error, and quadratic scores. We derive closed-form expressions for the resulting uncertainty measures under practical parametric assumptions and show how to estimate them using ensembles of models. In particular, the derived uncertainty measures naturally decompose into aleatoric and epistemic components. The framework recovers popular regression UQ measures based on predictive variance and differential entropy. Our broad evaluation on synthetic and real-world regression datasets provides guidance for selecting reliable UQ measures.

Daniil Kazantsev, Mohsen Guizani, Eric Moulines et al.

Reliable probabilities are critical in high-risk applications, yet common calibration criteria (confidence, class-wise) are only necessary for full distributional calibration, and post-hoc methods often lack distribution-free guarantees. We propose a set-based notion of calibration, cumulative mass calibration, and a corresponding empirical error measure: the Cumulative Mass Calibration Error (CMCE). We develop a new calibration procedure that starts with conformal prediction to obtain a set of labels that gives the desired coverage. We then instantiate two simple post-hoc calibrators: a mass normalization and a temperature scaling-based rule, tuned to the conformal constraint. On multi-class image benchmarks, especially with a large number of classes, our methods consistently improve CMCE and standard metrics (ECE, cw-ECE, MCE) over baselines, delivering a practical, scalable framework with theoretical guarantees.

Vladimir Kondratyev, Alexander Fishkov, Nikita Kotelevskii et al.

We propose a framework for conditional vector quantile regression (CVQR) that combines neural optimal transport with amortized optimization, and apply it to multivariate conformal prediction. Classical quantile regression does not extend naturally to multivariate responses, while existing approaches often ignore the geometry of joint distributions. Our method parametrizes the conditional vector quantile function as the gradient of a convex potential implemented by an input-convex neural network, ensuring monotonicity and uniform ranks. To reduce the cost of solving high-dimensional variational problems, we introduced amortized optimization of the dual potentials, yielding efficient training and faster inference. We then exploit the induced multivariate ranks for conformal prediction, constructing distribution-free predictive regions with finite-sample validity. Unlike coordinatewise methods, our approach adapts to the geometry of the conditional distribution, producing tighter and more informative regions. Experiments on benchmark datasets show improved coverage-efficiency trade-offs compared to baselines, highlighting the benefits of integrating neural optimal transport with conformal prediction.

Viktor Kovalchuk, Nikita Kotelevskii, Maxim Panov et al.

Federated learning (FL) usually shares model weights or gradients, which is costly for large models. Logit-based FL reduces this cost by sharing only logits computed on a public proxy dataset. However, aggregating information from heterogeneous clients is still challenging. This paper studies this problem, introduces and compares three logit aggregation methods: simple averaging, uncertainty-weighted averaging, and a learned meta-aggregator. Evaluated on MNIST and CIFAR-10, these methods reduce communication overhead, improve robustness under non-IID data, and achieve accuracy competitive with centralized training.

Nikita Kotelevskii, Aleksandr Artemenkov, Kirill Fedyanin et al.

This paper proposes a fast and scalable method for uncertainty quantification of machine learning models' predictions. First, we show the principled way to measure the uncertainty of predictions for a classifier based on Nadaraya-Watson's nonparametric estimate of the conditional label distribution. Importantly, the proposed approach allows to disentangle explicitly aleatoric and epistemic uncertainties. The resulting method works directly in the feature space. However, one can apply it to any neural network by considering an embedding of the data induced by the network. We demonstrate the strong performance of the method in uncertainty estimation tasks on text classification problems and a variety of real-world image datasets, such as MNIST, SVHN, CIFAR-100 and several versions of ImageNet.

Achille Thin, Nikita Kotelevskii, Arnaud Doucet et al.

Variational auto-encoders (VAE) are popular deep latent variable models which are trained by maximizing an Evidence Lower Bound (ELBO). To obtain tighter ELBO and hence better variational approximations, it has been proposed to use importance sampling to get a lower variance estimate of the evidence. However, importance sampling is known to perform poorly in high dimensions. While it has been suggested many times in the literature to use more sophisticated algorithms such as Annealed Importance Sampling (AIS) and its Sequential Importance Sampling (SIS) extensions, the potential benefits brought by these advanced techniques have never been realized for VAE: the AIS estimate cannot be easily differentiated, while SIS requires the specification of carefully chosen backward Markov kernels. In this paper, we address both issues and demonstrate the performance of the resulting Monte Carlo VAEs on a variety of applications.

Achille Thin, Nikita Kotelevskii, Christophe Andrieu et al.

Markov Chain Monte Carlo (MCMC) is a class of algorithms to sample complex and high-dimensional probability distributions. The Metropolis-Hastings (MH) algorithm, the workhorse of MCMC, provides a simple recipe to construct reversible Markov kernels. Reversibility is a tractable property that implies a less tractable but essential property here, invariance. Reversibility is however not necessarily desirable when considering performance. This has prompted recent interest in designing kernels breaking this property. At the same time, an active stream of research has focused on the design of novel versions of the MH kernel, some nonreversible, relying on the use of complex invertible deterministic transforms. While standard implementations of the MH kernel are well understood, the aforementioned developments have not received the same systematic treatment to ensure their validity. This paper fills the gap by developing general tools to ensure that a class of nonreversible Markov kernels, possibly relying on complex transforms, has the desired invariance property and leads to convergent algorithms. This leads to a set of simple and practically verifiable conditions.

Achille Thin, Nikita Kotelevskii, Jean-Stanislas Denain et al.

In this contribution, we propose a new computationally efficient method to combine Variational Inference (VI) with Markov Chain Monte Carlo (MCMC). This approach can be used with generic MCMC kernels, but is especially well suited to \textit{MetFlow}, a novel family of MCMC algorithms we introduce, in which proposals are obtained using Normalizing Flows. The marginal distribution produced by such MCMC algorithms is a mixture of flow-based distributions, thus drastically increasing the expressivity of the variational family. Unlike previous methods following this direction, our approach is amenable to the reparametrization trick and does not rely on computationally expensive reverse kernels. Extensive numerical experiments show clear computational and performance improvements over state-of-the-art methods.