Be careful asking chatbots about your health. After George Mallon had his blood drawn at a routine physical, he learned that something may be gravely wrong. The preliminary results showed he might have blood cancer. Further tests would be needed. Left in suspense, he did what so many people do these days: He opened ChatGPT.

Multi-view data analysis seeks to integrate multiple representations of the same samples in order to recover a coherent low-dimensional structure. Classical approaches often rely on feature concatenation or explicit alignment assumptions, which become restrictive under heterogeneous geometries or nonlinear distortions. In this work, we propose two geometry-aware multi-view embedding strategies grounded in Gromov-Wasserstein (GW) optimal transport. The first, termed Mean-GWMDS, aggregates view-specific relational information by averaging distance matrices and applying GW-based multidimensional scaling to obtain a representative embedding. The second strategy, referred to as Multi-GWMDS, adopts a selection-based paradigm in which multiple geometry-consistent candidate embeddings are generated via GW-based alignment and a representative embedding is selected. Experiments on synthetic manifolds and real-world datasets show that the proposed methods effectively preserve intrinsic relational structure across views. These results highlight GW-based approaches as a flexible and principled framework for multi-view representation learning.

Personalized decision policies are increasingly central in areas such as healthcare [Bertsimas et al., 2017], education[Mandeletal.,2014], andpublicpolicy[Kubeetal.,2019], wheretailoringactions to individual characteristics can improve outcomes. In many of these settings, however, actively experimenting with new policies to generate "online data" is expensive, risky, or infeasible, which motivates methods that can evaluate and optimize policies using pre-existing "offline data." A variety of work studies semiparametric efficient estimation of the value of a fixed policy from offline data [Chernozhukov et al., 2018, Dud ık et al., 2011, Jiang and Li, 2016, Kallus and Uehara, 2020, 2022, Kallus et al., 2022, Scharfstein et al., 1999]. And, a variety of work considers selecting the policy that optimizes such estimates over policies in a given class [Athey and Wager, 2021, Chernozhukov et al., 2019, Foster and Syrgkanis, 2023, Kallus, 2021, Zhang et al., 2013, Zhou et al., 2023], which generally yields rates the scale with policy class complexity, e.g., OP(N 1/2) for VC classes. Luedtke and Chambaz [2020] get regret acceleration to oP(N 1/2) by leveraging an equicontinuity argument.

Dynamical systems describe how a physical system evolves over time. Physical processes can evolve faster or slower in different environmental conditions. We use time-warping as rescaling the time in a model of a physical system. This thesis proposes a new method of transfer learning for Recurrent Neural Networks (RNNs) based on time-warping. We prove that for a class of linear, first-order differential equations known as time lag models, an LSTM can approximate these systems with any desired accuracy, and the model can be time-warped while maintaining the approximation accuracy. The Time-Warping method of transfer learning is then evaluated in an applied problem on predicting fuel moisture content (FMC), an important concept in wildfire modeling. An RNN with LSTM recurrent layers is pretrained on fuels with a characteristic time scale of 10 hours, where there are large quantities of data available for training. The RNN is then modified with transfer learning to generate predictions for fuels with characteristic time scales of 1 hour, 100 hours, and 1000 hours. The Time-Warping method is evaluated against several known methods of transfer learning. The Time-Warping method produces predictions with an accuracy level comparable to the established methods, despite modifying only a small fraction of the parameters that the other methods modify.

We study privacy-preserving sparse linear regression in the high-dimensional regime, focusing on the LASSO estimator. We analyze two widely used mechanisms for differential privacy: output perturbation, which injects noise into the estimator, and objective perturbation, which adds a random linear term to the loss function. Using approximate message passing (AMP), we characterize the typical behavior of these estimators under random design and privacy noise. To quantify privacy, we adopt typical-case measures, including the on-average KL divergence, which admits a hypothesis-testing interpretation in terms of distinguishability between neighboring datasets. Our analysis reveals that sparsity plays a central role in shaping the privacy-accuracy trade-off: stronger regularization can improve privacy by stabilizing the estimator against single-point data changes. We further show that the two mechanisms exhibit qualitatively different behaviors. In particular, for objective perturbation, increasing the noise level can have non-monotonic effects, and excessive noise may destabilize the estimator, leading to increased sensitivity to data perturbations. Our results demonstrate that AMP provides a powerful framework for analyzing privacy-accuracy trade-offs in high-dimensional sparse models.

Reinforcement learning from human feedback (RLHF) has emerged as a central framework for aligning large language models (LLMs) with human preferences. Despite its practical success, RLHF raises fundamental statistical questions because it relies on noisy, subjective, and often heterogeneous feedback to learn reward models and optimize policies. This survey provides a statistical perspective on RLHF, focusing primarily on the LLM alignment setting. We introduce the main components of RLHF, including supervised fine-tuning, reward modeling, and policy optimization, and relate them to familiar statistical ideas such as Bradley-Terry-Luce (BTL) model, latent utility estimation, active learning, experimental design, and uncertainty quantification. We review methods for learning reward functions from pairwise preference data and for optimizing policies through both two-stage RLHF pipelines and emerging one-stage approaches such as direct preference optimization. We further discuss recent extensions including reinforcement learning from AI feedback, inference-time algorithms, and reinforcement learning from verifiable rewards, as well as benchmark datasets, evaluation protocols, and open-source frameworks that support RLHF research. We conclude by highlighting open challenges in RLHF. An accompanying GitHub demo https://github.com/Pangpang-Liu/RLHF_demo illustrates key components of the RLHF pipeline.

This paper develops a penalized GMM (PGMM) framework for automatic debiased inference on functionals of nonparametric instrumental variable estimators. We derive convergence rates for the PGMM estimator and provide conditions for root-n consistency and asymptotic normality of debiased functional estimates, covering both linear and nonlinear functionals. Monte Carlo experiments on average derivative show that the PGMM-based debiased estimator performs on par with the analytical debiased estimator that uses the known closed-form Riesz representer, achieving 90-96% coverage while the plug-in estimator falls below 5%. We apply our procedure to estimate mean own-price elasticities in a semiparametric demand model for differentiated products. Simulations confirm near-nominal coverage while the plug-in severely undercovers. Applied to IRI scanner data on carbonated beverages, debiased semiparametric estimates are approximately 20% more elastic compared to the logit benchmark, and debiasing corrections are heterogeneous across products, ranging from negligible to several times the standard error.

We study high-dimensional mediation analysis in which exposures, mediators, and outcomes are all multivariate, and both exposures and mediators may be high-dimensional. We formalize this as a many (exposures)-to-many (mediators)-to-many (outcomes) (MMM) mediation analysis problem. Methodologically, MMM mediation analysis simultaneously performs variable selection for high-dimensional exposures and mediators, estimates the indirect effect matrix (i.e., the coefficient matrices linking exposure-to-mediator and mediator-to-outcome pathways), and enables prediction of multivariate outcomes. Theoretically, we show that the estimated indirect effect matrices are consistent and element-wise asymptotically normal, and we derive error bounds for the estimators. To evaluate the efficacy of the MMM mediation framework, we first investigate its finite-sample performance, including convergence properties, the behavior of the asymptotic approximations, and robustness to noise, via simulation studies. We then apply MMM mediation analysis to data from the Alzheimer's Disease Neuroimaging Initiative to study how cortical thickness of 202 brain regions may mediate the effects of 688 genome-wide significant single nucleotide polymorphisms (SNPs) (selected from approximately 1.5 million SNPs) on eleven cognitive-behavioral and diagnostic outcomes. The MMM mediation framework identifies biologically interpretable, many-to-many-to-many genetic-neural-cognitive pathways and improves downstream out-of-sample classification and prediction performance. Taken together, our results demonstrate the potential of MMM mediation analysis and highlight the value of statistical methodology for investigating complex, high-dimensional multi-layer pathways in science. The MMM package is available at https://github.com/THELabTop/MMM-Mediation.

Given $n$ independent samples from a $d$-dimensional probability distribution, our aim is to generate diffusion-based samples from a distribution obtained by tilting the original, where the degree of tilt is parametrized by $θ\in \mathbb{R}^d$. We define a plug-in estimator and show that it is minimax-optimal. We develop Wasserstein bounds between the distribution of the plug-in estimator and the true distribution as a function of $n$ and $θ$, illustrating regimes where the output and the desired true distribution are close. Further, under some assumptions, we prove the TV-accuracy of running Diffusion on these tilted samples. Our theoretical results are supported by extensive simulations. Applications of our work include finance, weather and climate modelling, and many other domains, where the aim may be to generate samples from a tilted distribution that satisfies practically motivated moment constraints.

We analyze the one-pass stochastic gradient descent dynamics of a two-layer neural network with quadratic activations in a teacher--student framework. In the high-dimensional regime, where the input dimension $N$ and the number of samples $M$ diverge at fixed ratio $α= M/N$, and for finite hidden widths $(p,p^*)$ of the student and teacher, respectively, we study the low-dimensional ordinary differential equations that govern the evolution of the student--teacher and student--student overlap matrices. We show that overparameterization ($p>p^*$) only modestly accelerates escape from a plateau of poor generalization by modifying the prefactor of the exponential decay of the loss. We then examine how unconstrained weight norms introduce a continuous rotational symmetry that results in a nontrivial manifold of zero-loss solutions for $p>1$. From this manifold the dynamics consistently selects the closest solution to the random initialization, as enforced by a conserved quantity in the ODEs governing the evolution of the overlaps. Finally, a Hessian analysis of the population-loss landscape confirms that the plateau and the solution manifold correspond to saddles with at least one negative eigenvalue and to marginal minima in the population-loss geometry, respectively.