Generative modeling of non-negative, discrete data, such as symbolic music, remains challenging due to two persistent limitations in existing methods. Firstly, many approaches rely on modeling continuous embeddings, which is suboptimal for inherently discrete data distributions. Secondly, most models optimize variational bounds rather than exact data likelihood, resulting in inaccurate likelihood estimates and degraded sampling quality. While recent diffusion-based models have addressed these issues separately, we tackle them jointly. In this work, we introduce the Information-Theoretic Discrete Poisson Diffusion Model (ItDPDM), inspired by photon arrival process, which combines exact likelihood estimation with fully discrete-state modeling. Central to our approach is an information-theoretic Poisson Reconstruction Loss (PRL) that has a provable exact relationship with the true data likelihood. ItDPDM achieves improved likelihood and sampling performance over prior discrete and continuous diffusion models on a variety of synthetic discrete datasets. Furthermore, on real-world datasets such as symbolic music and images, ItDPDM attains superior likelihood estimates and competitive generation quality-demonstrating a proof of concept for distribution-robust discrete generative modeling.

Predicting the trajectories of vehicles is crucial for the development of autonomous driving (AD) systems, particularly in complex and dynamic traffic environments. In this study, we introduce HiT (Human-like Trajectory Prediction), a novel model designed to enhance trajectory prediction by incorporating behavior-aware modules and dynamic centrality measures. Unlike traditional methods that primarily rely on static graph structures, HiT leverages a dynamic framework that accounts for both direct and indirect interactions among traffic participants. This allows the model to capture the subtle yet significant influences of surrounding vehicles, enabling more accurate and human-like predictions. To evaluate HiT's performance, we conducted extensive experiments using diverse and challenging real-world datasets, including NGSIM, HighD, RounD, ApolloScape, and MoCAD++. The results demonstrate that HiT consistently outperforms other top models across multiple metrics, particularly excelling in scenarios involving aggressive driving behaviors. This research presents a significant step forward in trajectory prediction, offering a more reliable and interpretable approach for enhancing the safety and efficiency of fully autonomous driving systems.

Instrumental variables (IV) analysis is an important applied tool for areas such as healthcare and consumer economics. For IV analysis in high-dimensional settings, the Generalized Method of Moments (GMM) using deep neural networks offers an efficient approach. With non-i.i.d. data sourced from scattered decentralized clients, federated learning is a popular paradigm for training the models while promising data privacy. However, to our knowledge, no federated algorithm for either GMM or IV analysis exists to date. In this work, we introduce federated instrumental variables analysis (FedIV) via federated generalized method of moments (FedGMM). We formulate FedGMM as a federated zero-sum game defined by a federated non-convex non-concave minimax optimization problem, which is solved using federated gradient descent ascent (FedGDA) algorithm. One key challenge arises in theoretically characterizing the federated local optimality. To address this, we present properties and existence results of clients' local equilibria via FedGDA limit points. Thereby, we show that the federated solution consistently estimates the local moment conditions of every participating client. The proposed algorithm is backed by extensive experiments to demonstrate the efficacy of our approach.

Hollmann et al. ( Nature 637 (2025) 319-326) recently introduced TabPFN, a transformer-based deep learning model for regression and classification on tabular data, which they claim "outperforms all previous methods on datasets with up to 10,000 samples by a wide margin, using substantially less training time. " Furthermore, they have called TabPFN a "foundation model" for tabular data, as it can support "data generation, density estimation, learning reusable embeddings and fine-tuning" . If these statements are well-supported, TabPFN may have the potential to supersede existing modeling approaches on a wide range of statistical tasks, mirroring a similar revolution in other areas of artificial intelligence that began with the advent of large language models. In this paper, we provide a tailored explanation of how TabPFN works for a statistics audience, by emphasizing its interpretation as approximate Bayesian inference. We also provide more evidence of TabPFN's "foundation model" capabilities: We show that an out-of-the-box application of TabPFN vastly outperforms specialized state-of-the-art methods for semi-supervised parameter estimation, prediction under covariate shift, and heterogeneous treatment effect estimation. We further show that TabPFN can outperform LASSO at sparse regression and can break a robustness-efficiency trade-off in classification.

We present Causal Posterior Estimation (CPE), a novel method for Bayesian inference in simulator models, i.e., models where the evaluation of the likelihood function is intractable or too computationally expensive, but where one can simulate model outputs given parameter values. CPE utilizes a normalizing flow-based (NF) approximation to the posterior distribution which carefully incorporates the conditional dependence structure induced by the graphical representation of the model into the neural network. Thereby it is possible to improve the accuracy of the approximation. We introduce both discrete and continuous NF architectures for CPE and propose a constant-time sampling procedure for the continuous case which reduces the computational complexity of drawing samples to O(1) as for discrete NFs. We show, through an extensive experimental evaluation, that by incorporating the conditional dependencies induced by the graphical model directly into the neural network, rather than learning them from data, CPE is able to conduct highly accurate posterior inference either outperforming or matching the state of the art in the field.

Quantifying differences between probability distributions is fundamental to statistics and machine learning, primarily for comparing statistical uncertainty. In contrast, epistemic uncertainty (EU) -- due to incomplete knowledge -- requires richer representations than those offered by classical probability. Imprecise probability (IP) theory offers such models, capturing ambiguity and partial belief. This has driven growing interest in imprecise probabilistic machine learning (IPML), where inference and decision-making rely on broader uncertainty models -- highlighting the need for metrics beyond classical probability. This work introduces the Integral Imprecise Probability Metric (IIPM) framework, a Choquet integral-based generalisation of classical Integral Probability Metric (IPM) to the setting of capacities -- a broad class of IP models encompassing many existing ones, including lower probabilities, probability intervals, belief functions, and more. Theoretically, we establish conditions under which IIPM serves as a valid metric and metrises a form of weak convergence of capacities. Practically, IIPM not only enables comparison across different IP models but also supports the quantification of epistemic uncertainty within a single IP model. In particular, by comparing an IP model with its conjugate, IIPM gives rise to a new class of EU measures -- Maximum Mean Imprecision -- which satisfy key axiomatic properties proposed in the Uncertainty Quantification literature. We validate MMI through selective classification experiments, demonstrating strong empirical performance against established EU measures, and outperforming them when classical methods struggle to scale to a large number of classes. Our work advances both theory and practice in IPML, offering a principled framework for comparing and quantifying epistemic uncertainty under imprecision.

A classifier is considered interpretable if each of its decisions has an explanation which is small enough to be easily understood by a human user. A DNF formula can be seen as a binary classifier $κ$ over boolean domains. The size of an explanation of a positive decision taken by a DNF $κ$ is bounded by the size of the terms in $κ$, since we can explain a positive decision by giving a term of $κ$ that evaluates to true. Since both positive and negative decisions must be explained, we consider that interpretable DNFs are those $κ$ for which both $κ$ and $\overlineκ$ can be expressed as DNFs composed of terms of bounded size. In this paper, we study the family of $k$-DNFs whose complements can also be expressed as $k$-DNFs. We compare two such families, namely depth-$k$ decision trees and nested $k$-DNFs, a novel family of models. Experiments indicate that nested $k$-DNFs are an interesting alternative to decision trees in terms of interpretability and accuracy.

Electronic Health Records (EHR) offer rich real-world data for personalized medicine, providing insights into disease progression, treatment responses, and patient outcomes. However, their sparsity, heterogeneity, and high dimensionality make them difficult to model, while the lack of standardized ground truth further complicates predictive modeling. To address these challenges, we propose SCORE, a semi-supervised representation learning framework that captures multi-domain disease profiles through patient embeddings. SCORE employs a Poisson-Adapted Latent factor Mixture (PALM) Model with pre-trained code embeddings to characterize codified features and extract meaningful patient phenotypes and embeddings. To handle the computational challenges of large-scale data, it introduces a hybrid Expectation-Maximization (EM) and Gaussian Variational Approximation (GVA) algorithm, leveraging limited labeled data to refine estimates on a vast pool of unlabeled samples. We theoretically establish the convergence of this hybrid approach, quantify GVA errors, and derive SCORE's error rate under diverging embedding dimensions. Our analysis shows that incorporating unlabeled data enhances accuracy and reduces sensitivity to label scarcity. Extensive simulations confirm SCORE's superior finite-sample performance over existing methods. Finally, we apply SCORE to predict disability status for patients with multiple sclerosis (MS) using partially labeled EHR data, demonstrating that it produces more informative and predictive patient embeddings for multiple MS-related conditions compared to existing approaches.

This paper presents a new approach for jointly calibrating magnetometers and inertial measurement units, focusing on improving calibration accuracy and computational efficiency. The proposed method formulates the calibration problem as a maximum a posteriori estimation problem, treating both the calibration parameters and orientation trajectory of the sensors as unknowns. This formulation enables efficient optimization with closed-form derivatives. The method is compared against two state-of-the-art approaches in terms of computational complexity and estimation accuracy. Simulation results demonstrate that the proposed method achieves lower root mean square error in calibration parameters while maintaining competitive computational efficiency. Further validation through real-world experiments confirms the practical benefits of our approach: it effectively reduces position drift in a magnetic field-aided inertial navigation system by more than a factor of two on most datasets. Moreover, the proposed method calibrated 30 magnetometers in less than 2 minutes. The contributions include a new calibration method, an analysis of existing methods, and a comprehensive empirical evaluation. Datasets and algorithms are made publicly available to promote reproducible research.

We consider 1-dimensional location estimation, where we estimate a parameter \lambda from n samples \lambda \eta_i, with each \eta_i drawn i.i.d. For fixed f the maximum-likelihood estimate (MLE) is well-known to be optimal in the limit as n \to \infty: it is asymptotically normal with variance matching the Cramer-Rao lower bound of \frac{1}{n\mathcal{I}}, where \mathcal{I} is the Fisher information of f . However, this bound does not hold for finite n, or when f varies with n . We show for arbitrary f and n that one can recover a similar theory based on the Fisher information of a smoothed version of f, where the smoothing radius decays with n .