Multi-agent reinforcement learning (MARL), as a thriving field, explores how multiple agents independently make decisions in a shared dynamic environment. Due to environmental uncertainties, policies in MARL must remain robust to tackle the sim-to-real gap. We focus on robust two-player zero-sum Markov games (TZMGs) in offline settings, specifically on tabular robust TZMGs (RTZMGs). We propose a model-based algorithm (\textit{RTZ-VI-LCB}) for offline RTZMGs, which is optimistic robust value iteration combined with a data-driven Bernstein-style penalty term for robust value estimation. By accounting for distribution shifts in the historical dataset, the proposed algorithm establishes near-optimal sample complexity guarantees under partial coverage and environmental uncertainty. An information-theoretic lower bound is developed to confirm the tightness of our algorithm's sample complexity, which is optimal regarding both state and action spaces. To the best of our knowledge, RTZ-VI-LCB is the first to attain this optimality, sets a new benchmark for offline RTZMGs, and is validated experimentally.

The thriving field of multi-agent reinforcement learning (MARL) studies how a group of interacting agents make decisions autonomously in a shared dynamic environment. Existing theoretical studies in this area suffer from at least two of the following obstacles: memory inefficiency, the heavy dependence of sample complexity on the long horizon and the large state space, the high computational complexity, non-Markov policy, non-Nash policy, and high burn-in cost. In this work, we take a step towards settling this problem by designing a model-free self-play algorithm \emph{Memory-Efficient Nash Q-Learning (ME-Nash-QL)} for two-player zero-sum Markov games, which is a specific setting of MARL. ME-Nash-QL is proven to enjoy the following merits. First, it can output an $\varepsilon$-approximate Nash policy with space complexity $O(SABH)$ and sample complexity $\widetilde{O}(H^4SAB/\varepsilon^2)$, where $S$ is the number of states, $\{A, B\}$ is the number of actions for two players, and $H$ is the horizon length. It outperforms existing algorithms in terms of space complexity for tabular cases, and in terms of sample complexity for long horizons, i.e., when $\min\{A, B\}\ll H^2$. Second, ME-Nash-QL achieves the lowest computational complexity $O(T\mathrm{poly}(AB))$ while preserving Markov policies, where $T$ is the number of samples. Third, ME-Nash-QL also achieves the best burn-in cost $O(SAB\,\mathrm{poly}(H))$, whereas previous algorithms have a burn-in cost of at least $O(S^3 AB\,\mathrm{poly}(H))$ to attain the same level of sample complexity with ours.

Data assimilation (DA) is a cornerstone of scientific and engineering applications, combining model forecasts with sparse and noisy observations to estimate latent system states. Classical DA methods, such as the ensemble Kalman filter, rely on Gaussian approximations and heuristic tuning (e.g., inflation and localization) to scale to high dimensions. While often successful, these approximations can make the methods unstable or inaccurate when the underlying distributions of states and observations depart significantly from Gaussianity. To address this limitation, we introduce DAISI, a scalable filtering algorithm built on flow-based generative models that enables flexible probabilistic inference using data-driven priors. The core idea is to use a stationary, pre-trained generative prior to assimilate observations via guidance-based conditional sampling while incorporating forecast information through a novel inverse-sampling step. This step maps the forecast ensemble into a latent space to provide initial conditions for the conditional sampling, allowing us to encode model dynamics into the DA pipeline without having to retrain or fine-tune the generative prior at each assimilation step. Experiments on challenging nonlinear systems show that DAISI achieves accurate filtering results in regimes with sparse, noisy, and nonlinear observations where traditional methods struggle.

The effectiveness of self-supervised learning (SSL) for physiological time series depends on the ability of a pretraining objective to preserve information about the underlying physiological state while filtering out unrelated noise. However, existing strategies are limited due to reliance on heuristic principles or poorly constrained generative tasks. To address this limitation, we propose a pretraining framework that exploits the information structure of a dynamical systems generative model across multiple time-series. This framework reveals our key insight that class identity can be efficiently captured by extracting information about the generative variables related to the system parameters shared across similar time series samples, while noise unique to individual samples should be discarded. Building on this insight, we propose PULSE, a cross-reconstruction-based pretraining objective for physiological time series datasets that explicitly extracts system information while discarding non-transferrable sample-specific ones. We establish theory that provides sufficient conditions for the system information to be recovered, and empirically validate it using a synthetic dynamical systems experiment. Furthermore, we apply our method to diverse real-world datasets, demonstrating that PULSE learns representations that can broadly distinguish semantic classes, increase label efficiency, and improve transfer learning.

Deep neural networks often struggle to recognize when an input lies outside their training experience, leading to unreliable and overconfident predictions. Building dependable machine learning systems therefore requires methods that can both estimate predictive \textit{uncertainty} and detect \textit{out-of-distribution (OOD)} samples in a unified manner. In this paper, we propose \textbf{TIE: a Training--Inversion--Exclusion} framework for visually interpretable and uncertainty-guided anomaly detection that jointly addresses these challenges through iterative refinement. TIE extends a standard $n$-class classifier to an $(n+1)$-class model by introducing a garbage class initialized with Gaussian noise to represent outlier inputs. Within each epoch, TIE performs a closed-loop process of \textit{training, inversion, and exclusion}, where highly uncertain inverted samples reconstructed from the just-trained classifier are excluded into the garbage class. Over successive iterations, the inverted samples transition from noisy artifacts into visually coherent class prototypes, providing transparent insight into how the model organizes its learned manifolds. During inference, TIE rejects OOD inputs by either directly mapping them to the garbage class or producing low-confidence, uncertain misclassifications within the in-distribution classes that are easily separable, all without relying on external OOD datasets. A comprehensive threshold-based evaluation using multiple OOD metrics and performance measures such as \textit{AUROC}, \textit{AUPR}, and \textit{FPR@95\%TPR} demonstrates that TIE offers a unified and interpretable framework for robust anomaly detection and calibrated uncertainty estimation (UE) achieving near-perfect OOD detection with \textbf{\(\!\approx\!\) 0 FPR@95\%TPR} when trained on MNIST or FashionMNIST and tested against diverse unseen datasets.

Modern artificial intelligence systems make critical decisions yet often fail silently when uncertain -- even well-calibrated models provide no mechanism to identify \textit{which specific predictions} are unreliable. We develop a geometric framework addressing both calibration and instance-level uncertainty quantification for neural network probability outputs. Treating probability vectors as points on the $(c-1)$-dimensional probability simplex equipped with the Fisher--Rao metric, we construct: (i) Additive Log-Ratio (ALR) calibration maps that reduce exactly to Platt scaling for binary problems while extending naturally to multi-class settings, and (ii) geometric reliability scores that translate calibrated probabilities into actionable uncertainty measures, enabling principled deferral of ambiguous predictions to human review. Theoretical contributions include: consistency of the calibration estimator at rate $O_p(n^{-1/2})$ via M-estimation theory (Theorem~1), and tight concentration bounds for reliability scores with explicit sub-Gaussian parameters enabling sample size calculations for validation set design (Theorem~2). We conjecture Neyman--Pearson optimality of our neutral zone construction based on connections to Bhattacharyya coefficients. Empirical validation on Adeno-Associated Virus classification demonstrates that the two-stage framework captures 72.5\% of errors while deferring 34.5\% of samples, reducing automated decision error rates from 16.8\% to 6.9\%. Notably, calibration alone yields marginal accuracy gains; the operational benefit arises primarily from the reliability scoring mechanism, which applies to any well-calibrated probability output. This work bridges information geometry and statistical learning, offering formal guarantees for uncertainty-aware classification in applications requiring rigorous validation.

We study streaming data with categorical features where the vocabulary of categorical feature values is changing and can even grow unboundedly over time. Feature hashing is commonly used as a pre-processing step to map these categorical values into a feature space of fixed size before learning their embeddings. While these methods have been developed and evaluated for offline or batch settings, in this paper we consider online settings. We show that deterministic embeddings are sensitive to the arrival order of categories and suffer from forgetting in online learning, leading to performance deterioration. To mitigate this issue, we propose a probabilistic hash embedding (PHE) model that treats hash embeddings as stochastic and applies Bayesian online learning to learn incrementally from data. Based on the structure of PHE, we derive a scalable inference algorithm to learn model parameters and infer/update the posteriors of hash embeddings and other latent variables. Our algorithm (i) can handle an evolving vocabulary of categorical items, (ii) is adaptive to new items without forgetting old items, (iii) is implementable with a bounded set of parameters that does not grow with the number of distinct observed values on the stream, and (iv) is invariant to the item arrival order. Experiments in classification, sequence modeling, and recommendation systems in online learning setups demonstrate the superior performance of PHE while maintaining high memory efficiency (consumes as low as 2~4 memory of a one-hot embedding table). Supplementary materials are at https://github.com/aodongli/probabilistic-hash-embeddings

Feature selection has remained a daunting challenge in machine learning and artificial intelligence, where increasingly complex, high-dimensional datasets demand principled strategies for isolating the most informative predictors. Despite widespread adoption, many established techniques suffer from notable limitations; some incur substantial computational cost, while others offer no definite statistical driven stopping criteria or assesses the significance of their importance scores. A common heuristic approach introduces multiple random noise features and retains all predictors ranked above the strongest noise feature. Although intuitive, this strategy lacks theoretical justification and depends heavily on heuristics. This paper proposes a novel feature selection method that addresses these limitations. Our approach introduces multiple random noise features and evaluates each feature's importance against the maximum importance value among these noise features incorporating a non-parametric bootstrap-based hypothesis testing framework to establish a solid theoretical foundation. We establish the conceptual soundness of our approach through statistical derivations that articulate the principles guiding the design of our algorithm. To evaluate its reliability, we generated simulated datasets under controlled statistical settings and benchmarked performance against Boruta and Knockoff-based methods, observing consistently stronger recovery of meaningful signal. As a demonstration of practical utility, we applied the technique across diverse real-world datasets, where it surpassed feature selection techniques including Boruta, RFE, and Extra Trees. Hence, the method emerges as a robust algorithm for principled feature selection, enabling the distillation of informative predictors that support reliable inference, enhanced predictive performance, and efficient computation.

Understanding the nuances in everyday language is pivotal for advancements in computational linguistics & emotions research. Traditional lexicon-based tools such as LIWC and Pattern have long served as foundational instruments in this domain. LIWC is the most extensively validated word count based text analysis tool in the social sciences and Pattern is an open source Python library offering functionalities for NLP. However, everyday language is inherently spontaneous, richly expressive, & deeply context dependent. To explore the capabilities of LLMs in capturing the valences of daily narratives in Flemish, we first conducted a study involving approximately 25,000 textual responses from 102 Dutch-speaking participants. Each participant provided narratives prompted by the question, "What is happening right now and how do you feel about it?", accompanied by self-assessed valence ratings on a continuous scale from -50 to +50. We then assessed the performance of three Dutch-specific LLMs in predicting these valence scores, and compared their outputs to those generated by LIWC and Pattern. Our findings indicate that, despite advancements in LLM architectures, these Dutch tuned models currently fall short in accurately capturing the emotional valence present in spontaneous, real-world narratives. This study underscores the imperative for developing culturally and linguistically tailored models/tools that can adeptly handle the complexities of natural language use. Enhancing automated valence analysis is not only pivotal for advancing computational methodologies but also holds significant promise for psychological research with ecologically valid insights into human daily experiences. We advocate for increased efforts in creating comprehensive datasets & finetuning LLMs for low-resource languages like Flemish, aiming to bridge the gap between computational linguistics & emotion research.

Adversarial machine learning challenges the assumption that the underlying distribution remains consistent throughout the training and implementation of a prediction model. In particular, adversarial evasion considers scenarios where adversaries adapt their data to influence particular outcomes from established prediction models, such scenarios arise in applications such as spam email filtering, malware detection and fake-image generation, where security methods must be actively updated to keep up with the ever-improving generation of malicious data. Game theoretic models have been shown to be effective at modelling these scenarios and hence training resilient predictors against such adversaries. Recent advancements in the use of pessimistic bilevel optimsiation which remove assumptions about the convexity and uniqueness of the adversary's optimal strategy have proved to be particularly effective at mitigating threats to classifiers due to its ability to capture the antagonistic nature of the adversary. However, this formulation has not yet been adapted to regression scenarios. This article serves to propose a pessimistic bilevel optimisation program for regression scenarios which makes no assumptions on the convexity or uniqueness of the adversary's solutions.