Bayesian experimental design (BED) provides a principled framework for optimizing data collection, but existing approaches do not apply to crucial real-world settings such as dynamical systems with partial observability, where only noisy and incomplete observations are available. These systems are naturally modeled as state-space models (SSMs), where latent states mediate the link between parameters and data, making the likelihood -- and thus information-theoretic objectives like the expected information gain (EIG) -- intractable. In addition, the dynamical nature of the system requires online algorithms that update posterior distributions and select designs sequentially in a computationally efficient manner. We address these challenges by deriving new estimators of the EIG and its gradient that explicitly marginalize latent states, enabling scalable stochastic optimization in nonlinear SSMs. Our approach leverages nested particle filters (NPFs) for efficient online inference with convergence guarantees. Applications to realistic models, such as the susceptible-infected-recovered (SIR) and a moving source location task, show that our framework successfully handles both partial observability and online computation.

Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, although theoretical results supporting the validity of these methods are scant. The rectified flow can be regarded as an approximation to optimal transport, but in contrast to other transport methods that require optimization over a function space, computing the rectified flow only requires standard statistical tools such as regression or density estimation. Because of this, one can leverage standard data analysis tools for regression and density estimation to develop empirical versions of transport maps. We study some structural properties of the rectified flow, including existence, uniqueness, and regularity, as well as the related statistical properties, such as rates of convergence and central limit theorems, for some selected estimators. To do so, we analyze separately the bounded and unbounded cases as each presents unique challenges. In both cases, we are able to establish convergence at faster rates than the ones for the usual nonparametric regression and density estimation.

A common challenge for decision makers is selecting actions whose rewards are unknown and evolve over time based on prior policies. For instance, repeated use may reduce an action's effectiveness (habituation), while inactivity may restore it (recovery). These nonstationarities are captured by the Reducing or Gaining Unknown Efficacy (ROGUE) bandit framework, which models real-world settings such as behavioral health interventions. While existing algorithms can compute sublinear regret policies to optimize these settings, they may not provide sufficient exploration due to overemphasis on exploitation, limiting the ability to estimate population-level effects. This is a challenge of particular interest in micro-randomized trials (MRTs) that aid researchers in developing just-in-time adaptive interventions that have population-level effects while still providing personalized recommendations to individuals. In this paper, we first develop ROGUE-TS, a Thompson Sampling algorithm tailored to the ROGUE framework, and provide theoretical guarantees of sublinear regret. We then introduce a probability clipping procedure to balance personalization and population-level learning, with quantified trade-off that balances regret and minimum exploration probability. Validation on two MRT datasets concerning physical activity promotion and bipolar disorder treatment shows that our methods both achieve lower regret than existing approaches and maintain high statistical power through the clipping procedure without significantly increasing regret. This enables reliable detection of treatment effects while accounting for individual behavioral dynamics. For researchers designing MRTs, our framework offers practical guidance on balancing personalization with statistical validity.

Artificial intelligence seems to be taking over the world with systems that model pixels, words, and phonemes. The world is arguably made up, not of pixels, words, and phonemes but of entities (objects, things, including events) with properties and relations among them. Surely we should model these, not the perception or description of them. You might suspect that concentrating on modeling words and pixels is because all of the (valuable) data in the world is in terms of text and images. If you look into almost any company you will find their most valuable data is in spreadsheets, databases and other relational formats. These are not the form that are studied in introductory machine learning, but are full of product numbers, student numbers, transaction numbers and other identifiers that can't be interpreted naively as numbers. The field that studies this sort of data has various names including relational learning, statistical relational AI, and many others. This paper explains why relational learning is not taking over the world -- except in a few cases with restricted relations -- and what needs to be done to bring it to it's rightful prominence.

CLAX is a JAX-based library that implements classic click models using modern gradient-based optimization. While neural click models have emerged over the past decade, complex click models based on probabilistic graphical models (PGMs) have not systematically adopted gradient-based optimization, preventing practitioners from leveraging modern deep learning frameworks while preserving the interpretability of classic models. CLAX addresses this gap by replacing EM-based optimization with direct gradient-based optimization in a numerically stable manner. The framework's modular design enables the integration of any component, from embeddings and deep networks to custom modules, into classic click models for end-to-end optimization. We demonstrate CLAX's efficiency by running experiments on the full Baidu-ULTR dataset comprising over a billion user sessions in $\approx$ 2 hours on a single GPU, orders of magnitude faster than traditional EM approaches. CLAX implements ten classic click models, serving both industry practitioners seeking to understand user behavior and improve ranking performance at scale and researchers developing new click models. CLAX is available at: https://github.com/philipphager/clax

In the era of AI-driven science and engineering, we often want to design discrete objects in silico according to user-specified properties. For example, we may wish to design a protein to bind its target, arrange components within a circuit to minimize latency, or find materials with certain properties. Given a property predictive model, in silico design typically involves training a generative model over the design space (e.g., protein sequence space) to concentrate on designs with the desired properties. Distributional optimization -- which can be formalized as an estimation of distribution algorithm or as reinforcement learning policy optimization -- finds the generative model that maximizes an objective function in expectation. Optimizing a distribution over discrete-valued designs is in general challenging because of the combinatorial nature of the design space. However, many property predictors in scientific applications are decomposable in the sense that they can be factorized over design variables in a way that could in principle enable more effective optimization. For example, amino acids at a catalytic site of a protein may only loosely interact with amino acids of the rest of the protein to achieve maximal catalytic activity. Current distributional optimization algorithms are unable to make use of such decomposability structure. Herein, we propose and demonstrate use of a new distributional optimization algorithm, Decomposition-Aware Distributional Optimization (DADO), that can leverage any decomposability defined by a junction tree on the design variables, to make optimization more efficient. At its core, DADO employs a soft-factorized "search distribution" -- a learned generative model -- for efficient navigation of the search space, invoking graph message-passing to coordinate optimization across linked factors.

The analysis and control of stochastic dynamical systems rely on probabilistic models such as (continuous-space) Markov decision processes, but large or continuous state spaces make exact analysis intractable and call for principled quantitative abstraction. This work develops a unified theory of such abstraction by integrating category theory, coalgebra, quantitative logic, and optimal transport, centred on a canonical $\varepsilon$-quotient of the behavioral pseudo-metric with a universal property: among all abstractions that collapse behavioral differences below $\varepsilon$, it is the most detailed, and every other abstraction achieving the same discounted value-loss guarantee factors uniquely through it. Categorically, a quotient functor $Q_\varepsilon$ from a category of probabilistic systems to a category of metric specifications admits, via the Special Adjoint Functor Theorem, a right adjoint $R_\varepsilon$, yielding an adjunction $Q_\varepsilon \dashv R_\varepsilon$ that formalizes a duality between abstraction and realization; logically, a quantitative modal $μ$-calculus with separate reward and transition modalities is shown, for a broad class of systems, to be expressively complete for the behavioral pseudo-metric, with a countable fully abstract fragment suitable for computation. The theory is developed coalgebraically over Polish spaces and the Giry monad and validated on finite-state models using optimal-transport solvers, with experiments corroborating the predicted contraction properties and structural stability and aligning with the theoretical value-loss bounds, thereby providing a rigorous foundation for quantitative state abstraction and representation learning in probabilistic domains.

Despite rapid advances in AI, safety remains the main bottleneck to deploying machine-learning systems. A critical safety component is out-of-distribution detection: given an input, decide whether it comes from the same distribution as the training data. In generative models, the most natural OOD score is the data likelihood. Actually, under the assumption of uniformly distributed OOD data, the likelihood is even the optimal OOD detector, as we show in this work. However, earlier work reported that likelihood often fails in practice, raising doubts about its usefulness. We explore whether, in practice, the representation space also suffers from the inability to learn good density estimation for OOD detection, or if it is merely a problem of the pixel space typically used in generative models. To test this, we trained a Variational Diffusion Model not on images, but on the representation space of a pre-trained ResNet-18 to assess the performance of our likelihood-based detector in comparison to state-of-the-art methods from the OpenOOD suite.

Complex inference tasks, such as those encountered in Pulsar Timing Array (PTA) data analysis, rely on Bayesian frameworks. The high-dimensional parameter space and the strong interdependencies among astrophysical, pulsar noise, and nuisance parameters introduce significant challenges for efficient learning and robust inference. These challenges are emblematic of broader issues in decision science, where model over-parameterization and prior sensitivity can compromise both computational tractability and the reliability of the results. We address these issues in the framework of hierarchical Bayesian modeling by introducing a reparameterization strategy. Our approach employs Normalizing Flows (NFs) to decorrelate the parameters governing hierarchical priors from those of astrophysical interest. The use of NF-based mappings provides both the flexibility to realize the reparametrization and the tractability to preserve proper probability densities. We further adopt i-nessai, a flow-guided nested sampler, to accelerate exploration of complex posteriors. This unified use of NFs improves statistical robustness and computational efficiency, providing a principled methodology for addressing hierarchical Bayesian inference in PTA analysis.

Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical method for parameter inference. While MLE performs well in canonical GLMs, it can become computationally inefficient near the true parameter value. In more general settings with non-canonical or fully general link functions, the resulting optimization landscape is often non-convex, non-smooth, and numerically unstable. To address these challenges, we investigate an alternative estimator based on solving the variational inequality (VI) formulation of the GLM likelihood equations, originally proposed by Juditsky and Nemirovski as an alternative for solving nonlinear least-squares problems. Unlike their focus on algorithmic convergence in monotone settings, we analyze the VI approach from a statistical perspective, comparing it systematically with the MLE. We also extend the theory of VI estimators to a broader class of link functions, including non-monotone cases satisfying a strong Minty condition, and show that it admits weaker smoothness requirements than MLE, enabling faster, more stable, and less locally trapped optimization. Theoretically, we establish both non-asymptotic estimation error bounds and asymptotic normality for the VI estimator, and further provide convergence guarantees for fixed-point and stochastic approximation algorithms. Numerical experiments show that the VI framework preserves the statistical efficiency of MLE while substantially extending its applicability to more challenging GLM settings.