Inference in dynamic probabilistic models is a complex task involving expensive operations. In particular, for Hidden Markov Models, the whole state space has to be enumerated for advancing in time. Even states with negligible probabilities are considered, resulting in computational inefficiency and increased noise due to the propagation of unlikely probability mass. We propose to denoise the future and speed up inference by using only the top-p states, i.e., the most probable states with accumulated probability p. We show that the error introduced by using only the top-p states is bound by p and the so-called minimal mixing rate of the underlying model. Moreover, in our empirical evaluation, we show that we can expect speedups of at least an order of magnitude, while the error in terms of total variation distance is below 0.09.

While Variational Inference (VI) is central to modern generative models like Variational Autoencoders (VAEs) and Denoising Diffusion Models (DDMs), its pedagogical treatment is split across disciplines. In statistics, VI is typically framed as a Bayesian method for posterior approximation. In machine learning, however, VAEs and DDMs are developed from a Frequentist viewpoint, where VI is used to approximate a maximum likelihood estimator. This creates a barrier for statisticians, as the principles behind VAEs and DDMs are hard to contextualize without a corresponding Frequentist introduction to VI. This paper provides that introduction: we explain the theory for VI, VAEs, and DDMs from a purely Frequentist perspective, starting with the classical Expectation-Maximization (EM) algorithm. We show how VI arises as a scalable solution for intractable E-steps and how VAEs and DDMs are natural, deep-learning-based extensions of this framework, thereby bridging the gap between classical statistical inference and modern generative AI.

Modeling dynamical systems and unraveling their underlying causal relationships is central to many domains in the natural sciences. Various physical systems, such as those arising in cell biology, are inherently high-dimensional and stochastic in nature, and admit only partial, noisy state measurements. This poses a significant challenge for addressing the problems of modeling the underlying dynamics and inferring the network structure of these systems. Existing methods are typically tailored either for structure learning or modeling dynamics at the population level, but are limited in their ability to address both problems together. In this work, we address both problems simultaneously: we present StructureFlow, a novel and principled simulation-free approach for jointly learning the structure and stochastic population dynamics of physical systems. We showcase the utility of StructureFlow for the tasks of structure learning from interventions and dynamical (trajectory) inference of conditional population dynamics. We empirically evaluate our approach on high-dimensional synthetic systems, a set of biologically plausible simulated systems, and an experimental single-cell dataset. We show that StructureFlow can learn the structure of underlying systems while simultaneously modeling their conditional population dynamics -- a key step toward the mechanistic understanding of systems behavior.

The intricate dynamics of stock markets have led to extensive research on models that are able to effectively explain their inherent complexities. This study leverages the econometrics literature to explore the dynamic factor model as an interpretable model with sufficient predictive capabilities for capturing essential market phenomena. Although the model has been extensively applied for predictive purposes, this study focuses on analyzing the extracted loadings and common factors as an alternative framework for understanding stock price dynamics. The results reveal novel insights into traditional market theories when applied to the Philippine Stock Exchange using the Kalman method and maximum likelihood estimation, with subsequent validation against the capital asset pricing model. Notably, a one-factor model extracts a common factor representing systematic or market dynamics similar to the composite index, whereas a two-factor model extracts common factors representing market trends and volatility. Furthermore, an application of the model for nowcasting the growth rates of the Philippine gross domestic product highlights the potential of the extracted common factors as viable real-time market indicators, yielding over a 34% decrease in the out-of-sample prediction error. Overall, the results underscore the value of dynamic factor analysis in gaining a deeper understanding of market price movement dynamics.

Detecting symmetry from data is a fundamental problem in signal analysis, providing insight into underlying structure and constraints. When data emerge as trajectories of dynamical systems, symmetries encode structural properties of the dynamics that enable model reduction, principled comparison across conditions, and detection of regime changes. While recent optimal transport methods provide practical tools for data-driven symmetry detection in this setting, they rely on deterministic thresholds and lack uncertainty quantification, limiting robustness to noise and ability to resolve hierarchical symmetry structures. We present a Bayesian framework that formulates symmetry detection as probabilistic model selection over a lattice of candidate subgroups, using a Gibbs posterior constructed from Wasserstein distances between observed data and group-transformed copies. We establish three theoretical guarantees: $(i)$ a Bayesian Occam's razor favoring minimal symmetry consistent with data, $(ii)$ conjugation equivariance ensuring frame-independence, and $(iii)$ stability bounds under perturbations for robustness to noise. Posterior inference is performed via Metropolis-Hastings sampling and numerical experiments on equivariant dynamical systems and synthetic point clouds demonstrate accurate symmetry recovery under high noise and small sample sizes. An application to human gait dynamics reveals symmetry changes induced by mechanical constraints, demonstrating the framework's utility for statistical inference in biomechanical and dynamical systems.

Timely and reliable decision-making is vital for flood emergency response, yet it remains severely hindered by limited and imprecise situational awareness due to various budget and data accessibility constraints. Traditional flood management systems often rely on in-situ sensors to calibrate remote sensing-based large-scale flood depth forecasting models, and further take flood depth estimates to optimize flood response decisions. However, these approaches often take fixed, decision task-agnostic strategies to decide where to put in-situ sensors (e.g., maximize overall information gain) and train flood forecasting models (e.g., minimize average forecasting errors), but overlook that systems with the same sensing gain and average forecasting errors may lead to distinct decisions. To address this, we introduce a novel decision-focused framework that strategically selects locations for in-situ sensor placement and optimize spatio-temporal flood forecasting models to optimize downstream flood response decision regrets. Our end-to-end pipeline integrates four components: a contextual scoring network, a differentiable sensor selection module under hard budget constraints, a spatio-temporal flood reconstruction and forecasting model, and a differentiable decision layer tailored to task-specific objectives. Central to our approach is the incorporation of Implicit Maximum Likelihood Estimation (I-MLE) to enable gradient-based learning over discrete sensor configurations, and probabilistic decision heads to enable differentiable approximation to various constrained disaster response tasks.

Sampling multiple responses is a common way to improve LLM output quality, but it comes at the cost of additional computation. The key challenge is deciding when to stop generating new samples to balance accuracy gains against efficiency. To address this, we introduce BEACON (Bayesian Efficient Adaptive Criterion for Optimal N-stopping), a principled adaptive sampling framework grounded in Sequential Search with Bayesian Learning. BEACON sequentially generates responses from the policy LLM, updates posterior belief over reward distributions in real time without further training, and determines when to stop by weighing expected gains against computational cost. Sampling terminates once the marginal utility of further exploration no longer justifies the expense. We establish both theoretical optimality guarantees and practical tractability, and show empirically that BEACON reduces average sampling by up to 80% while maintaining response quality. We further demonstrate BEACON's utility for cost-efficient preference data generation and outline practical extensions, offering actionable insights for future researchers.

Reinforcement Learning with V erifiable Reward (RL VR) has significantly advanced the complex reasoning abilities of Large Language Models (LLMs). However, it struggles to break through the inherent capability boundaries of the base LLM, due to its essentially on-policy strategy coupled with LLM's immense action space and sparse reward. Critically, RL VR can lead to the capability boundary collapse, narrowing the LLM's problem-solving scope. To address this problem, we propose RL-PLUS, a novel hybrid-policy optimization approach for LLMs that synergizes internal exploitation with external data to achieve stronger reasoning capabilities and surpass the boundaries of base models. RL-PLUS integrates two core components, i.e., Multiple Importance Sampling to address distributional mismatch from external data, and Exploration-Based Advantage Function to guide the model towards high-value, unexplored reasoning paths. We provide both theoretical analysis and extensive experiments to demonstrate the superiority and gen-eralizability of our approach. Compared with existing RL VR methods, RL-PLUS achieves 1) state-of-the-art performance on six math reasoning benchmarks; 2) superior performance on six out-of-distribution reasoning tasks; 3) consistent and significant gains across diverse model families, with average relative improvements up to 69.2%. Moreover, the analysis of Pass@k curves indicates that RL-PLUS effectively resolves the capability boundary collapse problem.

The integration of vision-language models (VLMs) is driving a new generation of embodied agents capable of operating in human-centered environments. However, as deployment expands, these systems face growing safety risks, particularly when executing hazardous instructions. Current safety evaluation benchmarks remain limited: they cover only narrow scopes of hazards and focus primarily on final outcomes, neglecting the agent's full perception-planning-execution process and thereby obscuring critical failure modes. Therefore, we present SAFE, a benchmark for systematically assessing the safety of embodied VLM agents on hazardous instructions. SAFE comprises three components: SAFE-THOR, an extensible adversarial simulation sandbox with a universal adapter that maps high-level VLM outputs to low-level embodied controls, supporting diverse agent workflow integration; SAFE-VERSE, a risk-aware task suite inspired by Asimov's Three Laws of Robotics, comprising 45 adversarial scenarios, 1,350 hazardous tasks, and 9,900 instructions that span risks to humans, environments, and agents; and SAFE-DIAGNOSE, a multi-level and fine-grained evaluation protocol measuring agent performance across perception, planning, and execution. Applying SAFE to nine state-of-the-art VLMs and two embodied agent workflows, we uncover systematic failures in translating hazard recognition into safe planning and execution. Our findings reveal fundamental limitations in current safety alignment and demonstrate the necessity of a comprehensive, multi-stage evaluation for developing safer embodied intelligence.

N-agent ad hoc teamwork (NAHT) is a newly introduced challenge in multi-agent reinforcement learning, where controlled subteams of varying sizes must dynamically collaborate with varying numbers and types of unknown teammates without pre-coordination. The existing learning algorithm (POAM) considers only independent learning for its flexibility in dealing with a changing number of agents. However, independent learning fails to fully capture the inter-agent dynamics essential for effective collaboration. Based on our observation that transformers deal effectively with sequences with varying lengths and have been shown to be highly effective for a variety of machine learning problems, this work introduces a centralized, transformer-based method for N-agent ad hoc teamwork. Our proposed approach incorporates historical observations and actions of all controlled agents, enabling optimal responses to diverse and unseen teammates in partially observable environments. Empirical evaluation on a StarCraft II task demonstrates that MAT-NAHT outperforms POAM, achieving superior sample efficiency and generalization, without auxiliary agent-modeling objectives. Keywords: multi-agent reinforcement learning, ad hoc teamwork, transformers, agent modeling Acknowledgements This work has taken place in the Learning Agents Research Group (LARG) at UT Austin.