The authors study sequential decision processes without reward function. The goal is to learn the transition dynamics such that various reward functions could be optimised efficiently in the future. The authors extend recent work to the linear function approximation case. They provide an analysis of the sample complexity, and show that while for linear MDPs complexity is polynomial, this is not true for MDPs with a linear optimal value functions, providing insight on the hardness of this second class of problems. The strengths of the paper are the theoretical development of the algorithm and the lower bound for MDPs with linear optimal Q functions.

Probabilistic model checking traditionally verifies properties on the expected value of a measure of interest. This restriction may fail to capture the quality of service of a significant proportion of a system's runs, especially when the probability distribution of the measure of interest is poorly represented by its expected value due to heavy-tail behaviors or multiple modalities. Recent works inspired by distributional reinforcement learning use discrete histograms to approximate integer reward distribution, but they struggle with continuous reward space and present challenges in balancing accuracy and scalability. We propose a novel method for handling both continuous and discrete reward distributions in Discrete Time Markov Chains using moment matching with Erlang mixtures. By analytically deriving higher-order moments through Moment Generating Functions, our method approximates the reward distribution with theoretically bounded error while preserving the statistical properties of the true distribution. This detailed distributional insight enables the formulation and robust model checking of quality properties based on the entire reward distribution function, rather than restricting to its expected value. We include a theoretical foundation ensuring bounded approximation errors, along with an experimental evaluation demonstrating our method's accuracy and scalability in practical model-checking problems.

The asymptotic properties of Bayesian Neural Networks (BNNs) have been extensively studied, particularly regarding their approximations by Gaussian processes in the infinite-width limit. We extend these results by showing that posterior BNNs can be approximated by Student-t processes, which offer greater flexibility in modeling uncertainty. Specifically, we show that, if the parameters of a BNN follow a Gaussian prior distribution, and the variance of both the last hidden layer and the Gaussian likelihood function follows an Inverse-Gamma prior distribution, then the resulting posterior BNN converges to a Student-t process in the infinite-width limit. Our proof leverages the Wasserstein metric to establish control over the convergence rate of the Student-t process approximation.

Synthetic data generation for tabular datasets must balance fidelity, efficiency, and versatility to meet the demands of real-world applications. We introduce the Tabular Auto-Regressive Generative Network (TabularARGN), a flexible framework designed to handle mixed-type, multivariate, and sequential datasets. By training on all possible conditional probabilities, TabularARGN supports advanced features such as fairness-aware generation, imputation, and conditional generation on any subset of columns. The framework achieves state-of-the-art synthetic data quality while significantly reducing training and inference times, making it ideal for large-scale datasets with diverse structures. Evaluated across established benchmarks, including realistic datasets with complex relationships, TabularARGN demonstrates its capability to synthesize high-quality data efficiently. By unifying flexibility and performance, this framework paves the way for practical synthetic data generation across industries.

This paper tackles the problem of jointly estimating the noise covariance matrix alongside primary parameters (such as poses and points) from measurements corrupted by Gaussian noise. In such settings, the noise covariance matrix determines the weights assigned to individual measurements in the least squares problem. We show that the joint problem exhibits a convex structure and provide a full characterization of the optimal noise covariance estimate (with analytical solutions) within joint maximum a posteriori and likelihood frameworks and several variants. Leveraging this theoretical result, we propose two novel algorithms that jointly estimate the primary parameters and the noise covariance matrix. To validate our approach, we conduct extensive experiments across diverse scenarios and offer practical insights into their application in robotics and computer vision estimation problems with a particular focus on SLAM.

Transformers have demonstrated remarkable in-context learning (ICL) capabilities, adapting to new tasks by simply conditioning on demonstrations without parameter updates. Compelling empirical and theoretical evidence suggests that ICL, as a general-purpose learner, could outperform task-specific models. However, it remains unclear to what extent the transformers optimally learn in-context compared to principled learning algorithms. To bridge this gap, we introduce a new framework for quantifying optimality of ICL as a learning algorithm in stylized settings. Our findings reveal a striking dichotomy: while ICL initially matches the efficiency of a Bayes optimal estimator, its efficiency significantly deteriorates in long context. Through an information-theoretic analysis, we show that the diminishing efficiency is inherent to ICL. These results clarify the trade-offs in adopting ICL as a universal problem solver, motivating a new generation of on-the-fly adaptive methods without the diminishing efficiency.

To evaluate the fidelity of synthetic tabular data, numerous metrics have been proposed to assess accuracy and diversity, including both low-order statistics (e.g., Density Estimation and Correlation Score (Zhang et al., 2023), Average Coverage Scores (Zein & Urvoy, 2022)) and high-order statistics (e.g., α-Precision and β-Recall (Alaa et al., 2022)). However, these metrics operate at a high level and fail to evaluate whether synthetic data preserves logical relationships, such as hierarchical or semantic dependencies between features. This highlights the need for a more fine-grained, context-aware evaluation of multivariate dependencies. To address this, we propose three evaluation metrics: Hierarchical Consistency Score (HCS), Multivariate Dependency Index (MDI), and Distributional Similarity Index (DSI). To assess the effectiveness of these metrics in quantifying inter-column relationships, we select five representative tabular data generation methods from different categories for evaluation. Their performance is measured using both existing and our proposed metrics on a real-world dataset rich in logical consistency and dependency constraints. Experimental results validate the effectiveness of our proposed metrics and reveal the limitations of existing approaches in preserving logical relationships in synthetic tabular data. Additionally, we discuss potential pathways to better capture logical constraints within joint distributions, paying the way for future advancements in synthetic tabular data generation.

Availability of datasets is a strong driver for research on 3D semantic understanding, and whilst obtaining unlabeled 3D point cloud data is straightforward, manually annotating this data with semantic labels is time-consuming and costly. Recently, Vision Foundation Models (VFMs) enable open-set semantic segmentation on camera images, potentially aiding automatic labeling. However,VFMs for 3D data have been limited to adaptations of 2D models, which can introduce inconsistencies to 3D labels. This work introduces Label Any Pointcloud (LeAP), leveraging 2D VFMs to automatically label 3D data with any set of classes in any kind of application whilst ensuring label consistency. Using a Bayesian update, point labels are combined into voxels to improve spatio-temporal consistency. A novel 3D Consistency Network (3D-CN) exploits 3D information to further improve label quality. Through various experiments, we show that our method can generate high-quality 3D semantic labels across diverse fields without any manual labeling. Further, models adapted to new domains using our labels show up to a 34.2 mIoU increase in semantic segmentation tasks.

Neural ordinary differential equations (ODEs) provide expressive representations of invertible transport maps that can be used to approximate complex probability distributions, e.g., for generative modeling, density estimation, and Bayesian inference. We show that for a large class of transport maps $T$, there exists a time-dependent ODE velocity field realizing a straight-line interpolation $(1-t)x + tT(x)$, $t \in [0,1]$, of the displacement induced by the map. Moreover, we show that such velocity fields are minimizers of a training objective containing a specific minimum-energy regularization. We then derive explicit upper bounds for the $C^k$ norm of the velocity field that are polynomial in the $C^k$ norm of the corresponding transport map $T$; in the case of triangular (Knothe--Rosenblatt) maps, we also show that these bounds are polynomial in the $C^k$ norms of the associated source and target densities. Combining these results with stability arguments for distribution approximation via ODEs, we show that Wasserstein or Kullback--Leibler approximation of the target distribution to any desired accuracy $\epsilon > 0$ can be achieved by a deep neural network representation of the velocity field whose size is bounded explicitly in terms of $\epsilon$, the dimension, and the smoothness of the source and target densities. The same neural network ansatz yields guarantees on the value of the regularized training objective.

Concerns about the use of data and algorithms for decision-making have risen in concert with the ascendancy of data-driven methods. Prior research has investigated problems ranging from privacy violations to explainability and accountability [10] [12]. Here, we focus on fairness, which addresses discrimination and disparate treatment in data and algorithms [1]. Recently, fairness research has focused significantly on algorithmic fairness, which aims to investigate algorithms for unfairness and intervene on algorithms to prevent unfair outcomes. Prior work has developed metrics for fairness, methods for fair variable selection, and mechanisms to correct unfair models [14] [11]. Algorithmic fairness evolved out of concerns about the use of algorithms in high-stakes contexts, particularly those that have a history of disparity and discrimination. When training an algorithm on data from a discriminatory process, it is common for the algorithm to learn to replicate that discrimination, or'garbage in, garbage out'. Much work in algorithmic fairness focuses on detecting, evaluating, and correcting unfair algorithms under a garbage-in-garbage-out regime. However, little work focuses on assessing the extent to which the data-generating process itself is'garbage',