We propose geodesic-based optimization methods on dually flat spaces, where the geometric structure of the parameter manifold is closely related to the form of the objective function. A primary application is maximum likelihood estimation in statistical models, especially exponential families, whose model manifolds are dually flat. We show that an m-geodesic update, which directly optimizes the log-likelihood, can theoretically reach the maximum likelihood estimator in a single step. In contrast, an e-geodesic update has a practical advantage in cases where the parameter space is geodesically complete, allowing optimization without explicitly handling parameter constraints. We establish the theoretical properties of the proposed methods and validate their effectiveness through numerical experiments.

Applied researchers now routinely work with regression models that feature a large number of covariates. A primary inferential goal in econometrics is to estimate the ceteris paribus effect of a specific variable while controlling for other variables (Belloni et al., 2013a, 2018). The prevailing practice interprets the coefficient on a regressor as a causal effect, conditional on the included controls. As the plausibility of conditional unconfoundedness is often argued using a large set of covariates, practitioners have increasingly embraced high-dimensional regression models. This setting has been extensively studied, predominantly using frequentist methods. Bayesian inference, on the other hand, has long been valued for its coherent framework for handling uncertainty in statistical analysis. As highlighted by Rubin (1984), Bayesian methods provide direct answers to many empirical questions by quantifying uncertainty about unknown parameters conditional on the observed data.

The Weibull distribution is a commonly adopted choice for modeling the survival of systems subject to maintenance over time. When only proxy indicators and censored observations are available, it becomes necessary to express the distribution's parameters as functions of time-dependent covariates. Deep neural networks provide the flexibility needed to learn complex relationships between these covariates and operational lifetime, thereby extending the capabilities of traditional regression-based models. Motivated by the analysis of a fleet of military vehicles operating in highly variable and demanding environments, as well as by the limitations observed in existing methodologies, this paper introduces WTNN, a new neural network-based modeling framework specifically designed for Weibull survival studies. The proposed architecture is specifically designed to incorporate qualitative prior knowledge regarding the most influential covariates, in a manner consistent with the shape and structure of the Weibull distribution. Through numerical experiments, we show that this approach can be reliably trained on proxy and right-censored data, and is capable of producing robust and interpretable survival predictions that can improve existing approaches.

Accurate and efficient surrogate modeling is essential for modern computational science, and there are a staggering number of emulation methods to choose from. With new methods being developed all the time, comparing the relative strengths and weaknesses of different methods remains a challenge due to inconsistent benchmarking practices and (sometimes) limited reproducibility and transparency. In this work, we present a large-scale, fully reproducible comparison of $29$ distinct emulators across $60$ canonical test functions and $40$ real emulation datasets. To facilitate rigorous, apples-to-apples comparisons, we introduce the R package \texttt{duqling}, which streamlines reproducible simulation studies using a consistent, simple syntax, and automatic internal scaling of inputs. This framework allows researchers to compare emulators in a unified environment and makes it possible to replicate or extend previous studies with minimal effort, even across different publications. Our results provide detailed empirical insight into the strengths and weaknesses of state-of-the-art emulators and offer guidance for both method developers and practitioners selecting a surrogate for new data. We discuss best practices for emulator comparison and highlight how \texttt{duqling} can accelerate research in emulator design and application.

Reinforcement learning in mobile health (mHealth) interventions requires balancing intervention efficacy with user burden, particularly when state measurements (for example, user surveys or feedback) are costly yet essential. The Act-Then-Measure (ATM) heuristic addresses this challenge by decoupling control and measurement actions within the Action-Contingent Noiselessly Observable Markov Decision Process (ACNO-MDP) framework. However, the standard ATM algorithm relies on a temporal-difference-inspired Q-learning method, which is prone to instability in sparse and noisy environments. In this work, we propose a Bayesian extension to ATM that replaces standard Q-learning with a Kalman filter-style Bayesian update, maintaining uncertainty-aware estimates of Q-values and enabling more stable and sample-efficient learning. We evaluate our method in both toy environments and clinically motivated testbeds. In small, tabular environments, Bayesian ATM achieves comparable or improved scalarized returns with substantially lower variance and more stable policy behavior. In contrast, in larger and more complex mHealth settings, both the standard and Bayesian ATM variants perform poorly, suggesting a mismatch between ATM's modeling assumptions and the structural challenges of real-world mHealth domains. These findings highlight the value of uncertainty-aware methods in low-data settings while underscoring the need for new RL algorithms that explicitly model causal structure, continuous states, and delayed feedback under observation cost constraints.

Moralisation and Triangulation are transformations allowing to switch between different ways of factoring a probability distribution into a graphical model. Moralisation allows to view a Bayesian network (a directed model) as a Markov network (an undirected model), whereas triangulation addresses the opposite direction. We present a categorical framework where these transformations are modelled as functors between a category of Bayesian networks and one of Markov networks. The two kinds of network (the objects of these categories) are themselves represented as functors from a `syntax' domain to a `semantics' codomain. Notably, moralisation and triangulation can be defined inductively on such syntax via functor pre-composition. Moreover, while moralisation is fully syntactic, triangulation relies on semantics. This leads to a discussion of the variable elimination algorithm, reinterpreted here as a functor in its own right, that splits the triangulation procedure in two: one purely syntactic, the other purely semantic. This approach introduces a functorial perspective into the theory of probabilistic graphical models, which highlights the distinctions between syntactic and semantic modifications.

Collaborative pursuit-evasion in cluttered environments presents significant challenges due to sparse rewards and constrained Fields of View (FOV). Standard Multi-Agent Reinforcement Learning (MARL) often suffers from inefficient exploration and fails to scale to large scenarios. We propose PGF-MAPPO (Path-Guided Frontier MAPPO), a hierarchical framework bridging topological planning with reactive control. To resolve local minima and sparse rewards, we integrate an A*-based potential field for dense reward shaping. Furthermore, we introduce Directional Frontier Allocation, combining Farthest Point Sampling (FPS) with geometric angle suppression to enforce spatial dispersion and accelerate coverage. The architecture employs a parameter-shared decentralized critic, maintaining O(1) model complexity suitable for robotic swarms. Experiments demonstrate that PGF-MAPPO achieves superior capture efficiency against faster evaders. Policies trained on 10x10 maps exhibit robust zero-shot generalization to unseen 20x20 environments, significantly outperforming rule-based and learning-based baselines.

Inferring the eventual goal of a mobile agent from noisy observations of its trajectory is a fundamental estimation problem. We initiate the study of such intent inference using a variant of a Rao-Blackwellized Particle Filter (RBPF), subject to the assumption that the agent's intent manifests through closed-loop behavior with a state-of-the-art provable practical stability property. Leveraging the assumed closed-form agent dynamics, the RBPF analytically marginalizes the linear-Gaussian substructure and updates particle weights only, improving sample efficiency over a standard particle filter. Two difference estimators are introduced: a Gaussian mixture model using the RBPF weights and a reduced version confining the mixture to the effective sample. We quantify how well the adversary can recover the agent's intent using information-theoretic leakage metrics and provide computable lower bounds on the Kullback-Leibler (KL) divergence between the true intent distribution and RBPF estimates via Gaussian-mixture KL bounds. We also provide a bound on the difference in performance between the two estimators, highlighting the fact that the reduced estimator performs almost as well as the complete one. Experiments illustrate fast and accurate intent recovery for compliant agents, motivating future work on designing intent-obfuscating controllers.

Energy-based models trained on evolutionary data can now generate novel protein sequences with custom functions [38]. A crucial, yet poorly understood, step in these successes is the use of an artificially low sampling "temperature" to produce functional sequences from the trained model. This adjustment is often the deciding factor between generating functional enzymes and inert polypeptides. A fundamental question arises as to what necessitates temperature tuning and what it reveals about the space of functional proteins and the limits of the models trained on finite data. Temperature tuning is a broadly used heuristic across machine learning contexts, used to improve training [16, 33, 34], generalization/generative performance [14, 45, 47, 48], and energy-landscape dynamics for memory retrieval [35]. It follows the basic intuition that one can navigate the trade-off between fidelity (producing believable, high-probability outputs at low temperature) and diversity (exploring a wide range of novel outputs at high temperature). Despite its widespread use, this practice lacks a principled, quantitative explanation and has not been systematically connected to known issues of the fitting procedure--particularly how it connects to fundamental limits in the learning process, such as biases introduced by training on finite data [5, 9, 10, 21, 22, 41].

Scalable multi-agent driving simulation requires behavior models that are both realistic and computationally efficient. We address this by optimizing the behavior model that controls individual traffic participants. To improve efficiency, we adopt an instance-centric scene representation, where each traffic participant and map element is modeled in its own local coordinate frame. This design enables efficient, viewpoint-invariant scene encoding and allows static map tokens to be reused across simulation steps. To model interactions, we employ a query-centric symmetric context encoder with relative positional encodings between local frames. We use Adversarial Inverse Reinforcement Learning to learn the behavior model and propose an adaptive reward transformation that automatically balances robustness and realism during training. Experiments demonstrate that our approach scales efficiently with the number of tokens, significantly reducing training and inference times, while outperforming several agent-centric baselines in terms of positional accuracy and robustness.