As a paradigm for sequential decision making in unknown environments, reinforcement learning (RL) has received a flurry of attention in recent years. However, the explosion of model complexity in emerging applications and the presence of nonconvexity exacerbate the challenge of achieving efficient RL in sample-starved situations, where data collection is expensive, time-consuming, or even high-stakes (e.g., in clinical trials, autonomous systems, and online advertising). How to understand and enhance the sample and computational efficacies of RL algorithms is thus of great interest. In this tutorial, we aim to introduce several important algorithmic and theoretical developments in RL, highlighting the connections between new ideas and classical topics. Employing Markov Decision Processes as the central mathematical model, we cover several distinctive RL scenarios (i.e., RL with a simulator, online RL, offline RL, robust RL, and RL with human feedback), and present several mainstream RL approaches (i.e., model-based approach, value-based approach, and policy optimization). Our discussions gravitate around the issues of sample complexity, computational efficiency, as well as algorithm-dependent and information-theoretic lower bounds from a non-asymptotic viewpoint.

Group or cluster structure on explanatory variables in machine learning problems is a very general phenomenon, which has attracted broad interest from practitioners and theoreticians alike. In this work we contribute an approach to sparse learning under such group structure, that does not require prior information on the group identities. Our paradigm is motivated by the Laplacian geometry of an underlying network with a related community structure, and proceeds by directly incorporating this into a penalty that is effectively computed via a heat-flow-based local network dynamics. The proposed penalty interpolates between the lasso and the group lasso penalties, the runtime of the heat-flow dynamics being the interpolating parameter. As such it can automatically default to lasso when the group structure reflected in the Laplacian is weak. In fact, we demonstrate a data-driven procedure to construct such a network based on the available data. Notably, we dispense with computationally intensive pre-processing involving clustering of variables, spectral or otherwise. Our technique is underpinned by rigorous theorems that guarantee its effective performance and provide bounds on its sample complexity. In particular, in a wide range of settings, it provably suffices to run the diffusion for time that is only logarithmic in the problem dimensions. We explore in detail the interfaces of our approach with key statistical physics models in network science, such as the Gaussian Free Field and the Stochastic Block Model. Our work raises the possibility of applying similar diffusion-based techniques to classical learning tasks, exploiting the interplay between geometric, dynamical and stochastic structures underlying the data.

Artificial intelligence (AI) systems increasingly inform medical decision-making, yet concerns about algorithmic bias and inequitable outcomes persist, particularly for historically marginalized populations. This paper introduces the concept of Predictive Representativity (PR), a framework of fairness auditing that shifts the focus from the composition of the data set to outcomes-level equity. Through a case study in dermatology, we evaluated AI-based skin cancer classifiers trained on the widely used HAM10000 dataset and on an independent clinical dataset (BOSQUE Test set) from Colombia. Our analysis reveals substantial performance disparities by skin phototype, with classifiers consistently underperforming for individuals with darker skin, despite proportional sampling in the source data. We argue that representativity must be understood not as a static feature of datasets but as a dynamic, context-sensitive property of model predictions. PR operationalizes this shift by quantifying how reliably models generalize fairness across subpopulations and deployment contexts. We further propose an External Transportability Criterion that formalizes the thresholds for fairness generalization. Our findings highlight the ethical imperative for post-hoc fairness auditing, transparency in dataset documentation, and inclusive model validation pipelines. This work offers a scalable tool for diagnosing structural inequities in AI systems, contributing to discussions on equity, interpretability, and data justice and fostering a critical re-evaluation of fairness in data-driven healthcare.

Training data attribution (TDA) provides insights into which training data is responsible for a learned model behavior. Gradient-based TDA methods such as influence functions and unrolled differentiation both involve a computation that resembles an inverse Hessian-vector product (iHVP), which is difficult to approximate efficiently. We introduce an algorithm (ASTRA) which uses the EKFAC-preconditioner on Neumann series iterations to arrive at an accurate iHVP approximation for TDA. ASTRA is easy to tune, requires fewer iterations than Neumann series iterations, and is more accurate than EKFAC-based approximations. Using ASTRA, we show that improving the accuracy of the iHVP approximation can significantly improve TDA performance.

Many critical decision-making tasks are now delegated to machine-learned models, and it is imperative that their decisions are trustworthy and reliable, and their outputs are consistent across similar inputs. We identify a new source of unreliable behaviors-called glitches-which may significantly impair the reliability of AI models having steep decision boundaries. Roughly speaking, glitches are small neighborhoods in the input space where the model's output abruptly oscillates with respect to small changes in the input. We provide a formal definition of glitches, and use well-known models and datasets from the literature to demonstrate that they have widespread existence and argue they usually indicate potential model inconsistencies in the neighborhood of where they are found. We proceed to the algorithmic search of glitches for widely used gradient-boosted decision tree (GBDT) models. We prove that the problem of detecting glitches is NP-complete for tree ensembles, already for trees of depth 4. Our glitch-search algorithm for GBDT models uses an MILP encoding of the problem, and its effectiveness and computational feasibility are demonstrated on a set of widely used GBDT benchmarks taken from the literature.

Model-based clustering is widely used for identifying and distinguishing types of diseases. However, modern biomedical data coming with high dimensions make it challenging to perform the model estimation in traditional cluster analysis. The incorporation of factor analyzer into the mixture model provides a way to characterize the large set of data features, but the current estimation method is computationally impractical for massive data due to the intrinsic slow convergence of the embedded algorithms, and the incapability to vary the size of the factor analyzers, preventing the implementation of a generalized mixture of factor analyzers and further characterization of the data clusters. We propose a hybrid matrix-free computational scheme to efficiently estimate the clusters and model parameters based on a Gaussian mixture along with generalized factor analyzers to summarize the large number of variables using a small set of underlying factors. Our approach outperforms the existing method with faster convergence while maintaining high clustering accuracy. Our algorithms are applied to accurately identify and distinguish types of breast cancer based on large tumor samples, and to provide a generalized characterization for subtypes of lymphoma using massive gene records.

We propose Temporal Conformal Prediction (TCP), a principled framework for constructing well-calibrated prediction intervals for non-stationary time series. TCP integrates a machine learning-based quantile forecaster with an online conformal calibration layer. This layer's thresholds are updated via a modified Robbins-Monro scheme, allowing the model to dynamically adapt to volatility clustering and regime shifts without rigid parametric assumptions. We benchmark TCP against GARCH, Historical Simulation, and static Quantile Regression across diverse financial assets. Our empirical results reveal a critical flaw in static methods: while sharp, Quantile Regression is poorly calibrated, systematically over-covering the nominal 95% target. In contrast, TCP's adaptive mechanism actively works to achieve the correct coverage level, successfully navigating the coverage-sharpness tradeoff. Visualizations during the 2020 market crash confirm TCP's superior adaptive response, and a comprehensive sensitivity analysis demonstrates the framework's robustness to hyperparameter choices. Overall, TCP offers a practical and theoretically-grounded solution to the central challenge of calibrated uncertainty quantification for time series under distribution shift, advancing the interface between statistical inference and machine learning.

The detection of gravitational waves by the LIGO-Virgo-KAGRA collaboration has ushered in a new era of observational astronomy, emphasizing the need for rapid and detailed parameter estimation and population-level analyses. Traditional Bayesian inference methods, particularly Markov chain Monte Carlo, face significant computational challenges when dealing with the high-dimensional parameter spaces and complex noise characteristics inherent in gravitational wave data. This review examines the emerging role of simulation-based inference methods in gravitational wave astronomy, with a focus on approaches that leverage machine-learning techniques such as normalizing flows and neural posterior estimation. We provide a comprehensive overview of the theoretical foundations underlying various simulation-based inference methods, including neural posterior estimation, neural ratio estimation, neural likelihood estimation, flow matching, and consistency models. We explore the applications of these methods across diverse gravitational wave data processing scenarios, from single-source parameter estimation and overlapping signal analysis to testing general relativity and conducting population studies. Although these techniques demonstrate speed improvements over traditional methods in controlled studies, their model-dependent nature and sensitivity to prior assumptions are barriers to their widespread adoption. Their accuracy, which is similar to that of conventional methods, requires further validation across broader parameter spaces and noise conditions.

Handling missing values is a common challenge in biostatistical analyses, typically addressed by imputation methods. We propose a novel, fast, and easy-to-use imputation method called missing value imputation with adversarial random forests (MissARF), based on generative machine learning, that provides both single and multiple imputation. MissARF employs adversarial random forest (ARF) for density estimation and data synthesis. To impute a missing value of an observation, we condition on the non-missing values and sample from the estimated conditional distribution generated by ARF. Our experiments demonstrate that MissARF performs comparably to state-of-the-art single and multiple imputation methods in terms of imputation quality and fast runtime with no additional costs for multiple imputation.

We present UniPhyNet, a novel neural network architecture to classify cognitive load using multimodal physiological data -- specifically EEG, ECG and EDA signals -- without the explicit need for extracting hand-crafted features. UniPhyNet integrates multiscale parallel convolutional blocks and ResNet-type blocks enhanced with channel block attention module to focus on the informative features while a bidirectional gated recurrent unit is used to capture temporal dependencies. This architecture processes and combines signals in both unimodal and multimodal configurations via intermediate fusion of learned feature maps. On the CL-Drive dataset, UniPhyNet improves raw signal classification accuracy from 70% to 80% (binary) and 62% to 74% (ternary), outperforming feature-based models, demonstrating its effectiveness as an end-to-end solution for real-world cognitive state monitoring.