Kernel Stein discrepancies (KSDs) have become a principal tool for goodness-of-fit testing, but standard KSDs are often insensitive to higher-order dependency structures, such as tail dependence, which are critical in many scientific and financial domains. We address this gap by introducing the Copula-Stein Discrepancy (CSD), a novel class of discrepancies tailored to the geometry of statistical dependence. By defining a Stein operator directly on the copula density, CSD leverages the generative structure of dependence, rather than relying on the joint density's score function. For the broad class of Archimedean copulas, this approach yields a closed-form Stein kernel derived from the scalar generator function. We provide a comprehensive theoretical analysis, proving that CSD (i) metrizes weak convergence of copula distributions, ensuring it detects any mismatch in dependence; (ii) has an empirical estimator that converges at the minimax optimal rate of $O_P(n^{-1/2})$; and (iii) is provably sensitive to differences in tail dependence coefficients. The framework is extended to general non-Archimedean copulas, including elliptical and vine copulas. Computationally, the exact CSD kernel evaluation scales linearly in dimension, while a novel random feature approximation reduces the $n$-dependence from quadratic $O(n^2)$ to near-linear $\tilde{O}(n)$, making CSD a practical and theoretically principled tool for dependence-aware inference.

Understanding the relationship between antibody sequence, structure and function is essential for the design of antibody-based therapeutics and research tools. Recently, machine learning (ML) models mostly based on the application of large language models to sequence information have been developed to predict antibody properties. Yet there are open directions to incorporate structural information, not only to enhance prediction but also to offer insights into the underlying molecular mechanisms. This chapter provides an overview of these approaches and describes two ML frameworks that integrate structural data (via graph representations) with neural networks to predict properties of antibodies: ANTIPASTI predicts binding affinity (a global property) whereas INFUSSE predicts residue flexibility (a local property). We survey the principles underpinning these models; the ways in which they encode structural knowledge; and the strategies that can be used to extract biologically relevant statistical signals that can help discover and disentangle molecular determinants of the properties of interest.

Machine learning models have achieved widespread success but often inherit and amplify historical biases, resulting in unfair outcomes. Traditional fairness methods typically impose constraints at the prediction level, without addressing underlying biases in data representations. In this work, we propose a principled framework that adjusts data representations to balance predictive utility and fairness. Using sufficient dimension reduction, we decompose the feature space into target-relevant, sensitive, and shared components, and control the fairness-utility trade-off by selectively removing sensitive information. We provide a theoretical analysis of how prediction error and fairness gaps evolve as shared subspaces are added, and employ influence functions to quantify their effects on the asymptotic behavior of parameter estimates. Experiments on both synthetic and real-world datasets validate our theoretical insights and show that the proposed method effectively improves fairness while preserving predictive performance.

We propose a Bayesian variable selection method in the framework of modal regression for heavy-tailed responses. An efficient expectation-maximization algorithm is employed to expedite parameter estimation. A test statistic is constructed to exploit the shape of the model error distribution to effectively separate informative covariates from unimportant ones. Through simulations, we demonstrate and evaluate the efficacy of the proposed method in identifying important covariates in the presence of non-Gaussian model errors. Finally, we apply the proposed method to analyze two datasets arising in genetic and epigenetic studies.

Alignment of large language models (LLMs) has predominantly relied on pairwise preference optimization, where annotators select the better of two responses to a prompt. While simple, this approach overlooks the opportunity to learn from richer forms of human feedback, such as multiwise comparisons and top-$k$ rankings. We propose Ranked Choice Preference Optimization (RCPO), a unified framework that bridges preference optimization with (ranked) choice modeling via maximum likelihood estimation. The framework is flexible, supporting both utility-based and rank-based choice models. It subsumes several existing pairwise methods (e.g., DPO, SimPO), while providing principled training objectives for richer feedback formats. We instantiate this framework with two representative ranked choice models (Multinomial Logit and Mallows-RMJ). Empirical studies on Llama-3-8B-Instruct and Gemma-2-9B-it across AlpacaEval 2 and Arena-Hard benchmarks show that RCPO consistently outperforms competitive baselines. RCPO shows how directly leveraging ranked preference data, combined with the right choice models, yields more effective alignment. It offers a versatile and extensible foundation for incorporating (ranked) choice modeling into LLM training.

Matrix-based preconditioned optimizers, such as Muon, have recently been shown to be more efficient than scalar-based optimizers for training large-scale neural networks, including large language models (LLMs). On the other hand, recent benchmarks on optimizers for LLM pre-training have demonstrated that variance-reduction techniques such as MARS can achieve substantial speedups over standard optimizers that do not employ variance reduction. In this paper, to achieve the best of both worlds, we introduce MARS-M, a new optimizer that integrates the variance reduction technique in MARS with Muon. Under standard regularity conditions, we prove that Muon-M converges to a first-order stationary point at a rate of $\tilde{\mathcal{O}}(T^{-1/3})$, which improves upon $\tilde{\mathcal{O}}(T^{-1/4})$ rate attained by Muon. Our empirical results on language modeling and computer vision tasks demonstrate that MARS-M consistently yields lower losses and improved performance across various downstream benchmarks. The implementation of MARS-M is available at https://github.com/AGI-Arena/MARS/tree/main/MARS_M.

Dropout is common in clinical studies, with up to half of patients leaving early due to side effects or other reasons. When dropout is informative (i.e., dependent on survival time), it introduces censoring bias, because of which treatment effect estimates are also biased. In this paper, we propose an assumption-lean framework to assess the robustness of conditional average treatment effect (CATE) estimates in survival analysis when facing censoring bias. Unlike existing works that rely on strong assumptions, such as non-informative censoring, to obtain point estimation, we use partial identification to derive informative bounds on the CATE. Thereby, our framework helps to identify patient subgroups where treatment is effective despite informative censoring. We further develop a novel meta-learner that estimates the bounds using arbitrary machine learning models and with favorable theoretical properties, including double robustness and quasi-oracle efficiency. We demonstrate the practical value of our meta-learner through numerical experiments and in an application to a cancer drug trial. Together, our framework offers a practical tool for assessing the robustness of estimated treatment effects in the presence of censoring and thus promotes the reliable use of survival data for evidence generation in medicine and epidemiology.

This study uses double/debiased machine learning (DML) to evaluate the impact of transitioning from lecture-based blended teaching to a flipped classroom concept. Our findings indicate effects on students' self-conception, procrastination, and enjoyment. We do not find significant positive effects on exam scores, passing rates, or knowledge retention. This can be explained by the insufficient use of the instructional approach that we can identify with uniquely detailed usage data and highlights the need for additional teaching strategies. Methodologically, we propose a powerful DML approach that acknowledges the latent structure inherent in Likert scale variables and, hence, aligns with psychometric principles.

What does Elon Musk want the world to know about "white genocide theory"? Because he's been vocal about the issue in the past-- advancing the idea, for example, that Jews are pushing "hatred against whites"--I decided to search for the term on Grokipedia, the competitor to Wikipedia that Musk launched yesterday. First, the site uses just that term,, rather than, as you would see on Wikipedia and elsewhere. Just a few sentences in, Grokipedia provides the "empirical underpinnings" of this supposed campaign to eliminate white people of European descent around the world. And the site argues that conversation about this purported genocide is systematically suppressed by the media and academia, which are "prone to ideological biases favoring multiculturalism" and "relegate the theory to fringe conspiracy status despite the observable data on population trajectories."

In Guillermo del Toro's "Frankenstein," a Vast Vision Gets Netflixed Down to Size The latest reanimation of Mary Shelley's classic tale, starring Oscar Isaac and Jacob Elordi, is a labyrinthine tour of a filmmaker's career-long obsessions. Earlier this year, Quentin Tarantino, when asked to parse the high points of his filmography in an interview, described the two-part "Kill Bill" (2003-04) as "the movie I was born to make." He added, "I think'Inglourious Basterds' is my masterpiece, but'Once Upon a Time . . . in Hollywood' is my favorite." Might these be distinctions without a difference? I'm generally wary of artistic-birthright narratives, not least because a filmmaker of remarkable talent, consistent vision, and good fortune might well wind up with multiple candidates for the honor.