We propose GaussDetect-LiNGAM, a novel approach for bivariate causal discovery that eliminates the need for explicit Gaussianity tests by leveraging a fundamental equivalence between noise Gaussianity and residual independence in the reverse regression. Under the standard LiNGAM assumptions of linearity, acyclicity, and exogeneity, we prove that the Gaussianity of the forward-model noise is equivalent to the independence between the regressor and residual in the reverse model. This theoretical insight allows us to replace fragile and sample-sensitive Gaussianity tests with robust kernel-based independence tests. Experimental results validate the equivalence and demonstrate that GaussDetect-LiNGAM maintains high consistency across diverse noise types and sample sizes, while reducing the number of tests per decision (TPD). Our method enhances both the efficiency and practical applicability of causal inference, making LiNGAM more accessible and reliable in real-world scenarios.

Online A/B testing, the gold standard for evaluating new advertising policies, consumes substantial engineering resources and risks significant revenue loss from deploying underperforming variations. This motivates the use of Off-Policy Evaluation (OPE) for rapid, offline assessment. However, applying OPE to ad auctions is fundamentally more challenging than in domains like recommender systems, where stochastic policies are common. In online ad auctions, it is common for the highest-bidding ad to win the impression, resulting in a deterministic, winner-takes-all setting. This results in zero probability of exposure for non-winning ads, rendering standard OPE estimators inapplicable. We introduce the first principled framework for OPE in deterministic auctions by repurposing the bid landscape model to approximate the propensity score. This model allows us to derive robust approximate propensity scores, enabling the use of stable estimators like Self-Normalized Inverse Propensity Scoring (SNIPS) for counterfactual evaluation. We validate our approach on the AuctionNet simulation benchmark and against 2-weeks online A/B test from a large-scale industrial platform. Our method shows remarkable alignment with online results, achieving a 92\% Mean Directional Accuracy (MDA) in CTR prediction, significantly outperforming the parametric baseline. MDA is the most critical metric for guiding deployment decisions, as it reflects the ability to correctly predict whether a new model will improve or harm performance. This work contributes the first practical and validated framework for reliable OPE in deterministic auction environments, offering an efficient alternative to costly and risky online experiments.

Federated Learning (FL) is plagued by two key challenges: high communication overhead and performance collapse on heterogeneous (non-IID) data. Analytic FL (AFL) provides a single-round, data distribution invariant solution, but is limited to linear models. Subsequent non-linear approaches, like DeepAFL, regain accuracy but sacrifice the single-round benefit. In this work, we break this tradeoff. W e propose SAFLe, a framework that achieves scalable non-linear expressivity by introducing a structured head of bucketed features and sparse, grouped embeddings. W e prove this non-linear architecture is mathematically equivalent to a high-dimensional linear regression. This key equivalence allows SAFLe to be solved with AFL's single-shot, invariant aggregation law. Empirically, SAFLe establishes a new state-of-the-art for analytic FL, significantly outperforming both linear AFL and multi-round DeepAFL in accuracy across all benchmarks, demonstrating a highly efficient and scalable solution for federated vision.

We introduce Sketch Tomography, an efficient procedure for quantum state tomography based on the classical shadow protocol used for quantum observable estimations. The procedure applies to the case where the ground truth quantum state is a matrix product state (MPS). The density matrix of the ground truth state admits a tensor train ansatz as a result of the MPS assumption, and we estimate the tensor components of the ansatz through a series of observable estimations, thus outputting an approximation of the density matrix. The procedure is provably convergent with a sample complexity that scales quadratically in the system size. We conduct extensive numerical experiments to show that the procedure outputs an accurate approximation to the quantum state. For observable estimation tasks involving moderately large subsystems, we show that our procedure gives rise to a more accurate estimation than the classical shadow protocol. We also show that sketch tomography is more accurate in observable estimation than quantum states trained from the maximum likelihood estimation formulation.

A major effort in modern high-dimensional statistics has been devoted to the analysis of linear predictors trained on nonlinear feature embeddings via empirical risk minimization (ERM). Gaussian equivalence theory (GET) has emerged as a powerful universality principle in this context: it states that the behavior of high-dimensional, complex features can be captured by Gaussian surrogates, which are more amenable to analysis. Despite its remarkable successes, numerical experiments show that this equivalence can fail even for simple embeddings -- such as polynomial maps -- under general scaling regimes. We investigate this breakdown in the setting of random feature (RF) models in the quadratic scaling regime, where both the number of features and the sample size grow quadratically with the data dimension. We show that when the target function depends on a low-dimensional projection of the data, such as generalized linear models, GET yields incorrect predictions. To capture the correct asymptotics, we introduce a Conditional Gaussian Equivalent (CGE) model, which can be viewed as appending a low-dimensional non-Gaussian component to an otherwise high-dimensional Gaussian model. This hybrid model retains the tractability of the Gaussian framework and accurately describes RF models in the quadratic scaling regime. We derive sharp asymptotics for the training and test errors in this setting, which continue to agree with numerical simulations even when GET fails. Our analysis combines general results on CLT for Wiener chaos expansions and a careful two-phase Lindeberg swapping argument. Beyond RF models and quadratic scaling, our work hints at a rich landscape of universality phenomena in high-dimensional ERM.

We frame novelty detection on path space as a hypothesis testing problem with signature-based test statistics. Using transportation-cost inequalities of Gasteratos and Jacquier (2023), we obtain tail bounds for false positive rates that extend beyond Gaussian measures to laws of RDE solutions with smooth bounded vector fields, yielding estimates of quantiles and p-values. Exploiting the shuffle product, we derive exact formulae for smooth surrogates of conditional value-at-risk (CVaR) in terms of expected signatures, leading to new one-class SVM algorithms optimising smooth CVaR objectives. We then establish lower bounds on type-$\mathrm{II}$ error for alternatives with finite first moment, giving general power bounds when the reference measure and the alternative are absolutely continuous with respect to each other. Finally, we evaluate numerically the type-$\mathrm{I}$ error and statistical power of signature-based test statistic, using synthetic anomalous diffusion data and real-world molecular biology data.

High quality data is needed to unlock the full potential of AI for end users. However finding new sources of such data is getting harder: most publicly-available human generated data will soon have been used. Additionally, publicly available data often is not representative of users of a particular system -- for example, a research speech dataset of contractors interacting with an AI assistant will likely be more homogeneous, well articulated and self-censored than real world commands that end users will issue. Therefore unlocking high-quality data grounded in real user interactions is of vital interest. However, the direct use of user data comes with significant privacy risks. Differential Privacy (DP) is a well established framework for reasoning about and limiting information leakage, and is a gold standard for protecting user privacy. The focus of this work, \emph{Differentially Private Synthetic data}, refers to synthetic data that preserves the overall trends of source data,, while providing strong privacy guarantees to individuals that contributed to the source dataset. DP synthetic data can unlock the value of datasets that have previously been inaccessible due to privacy concerns and can replace the use of sensitive datasets that previously have only had rudimentary protections like ad-hoc rule-based anonymization. In this paper we explore the full suite of techniques surrounding DP synthetic data, the types of privacy protections they offer and the state-of-the-art for various modalities (image, tabular, text and decentralized). We outline all the components needed in a system that generates DP synthetic data, from sensitive data handling and preparation, to tracking the use and empirical privacy testing. We hope that work will result in increased adoption of DP synthetic data, spur additional research and increase trust in DP synthetic data approaches.

We investigate the convergence properties of a class of iterative algorithms designed to minimize a potentially non-smooth and noisy objective function, which may be algebraically intractable and whose values may be obtained as the output of a black box. The algorithms considered can be cast under the umbrella of a generalised gradient descent recursion, where the gradient is that of a smooth approximation of the objective function. The framework we develop includes as special cases model-based and mollification methods, two classical approaches to zero-th order optimisation. The convergence results are obtained under very weak assumptions on the regularity of the objective function and involve a trade-off between the degree of smoothing and size of the steps taken in the parameter updates. As expected, additional assumptions are required in the stochastic case. We illustrate the relevance of these algorithms and our convergence results through a challenging classification example from machine learning.

We study estimation and statistical inference for reward models used in aligning large language models (LLMs). A key component of LLM alignment is reinforcement learning from human feedback (RLHF), where humans compare pairs of model-generated answers and their preferences are used to train a reward model. However, human feedback is inherently heterogeneous, creating significant challenges for reliable reward learning. To address this, we adopt a heterogeneous preference framework that jointly models the latent reward of answers and human rationality. This leads to a challenging biconvex optimization problem, which we solve via an alternating gradient descent algorithm. We establish theoretical guarantees for the resulting estimator, including its convergence and asymptotic distribution. These results enable the construction of confidence intervals for reward estimates. Leveraging these uncertainty quantification results, we conduct valid statistical comparisons between rewards and incorporate uncertainty into the best-of-$N$ (BoN) policy framework. Extensive simulations demonstrate the effectiveness of our method, and applications to real LLM data highlight the practical value of accounting for uncertainty in reward modeling for LLM alignment.

We present the winning strategy for the EVA2025 Data Challenge, which aimed to estimate the probability of extreme precipitation events. These events occurred at most once in the dataset making the challenge fundamentally one of extrapolating extreme values. Given the scarcity of extreme events, we argue that a simple, robust modeling approach is essential. We adopt univariate models instead of multivariate ones and model Peaks Over Thresholds using Extreme Value Theory. Specifically, we fit an exponential distribution to model exceedances of the target variable above a high quantile (after seasonal adjustment). The novelty of our approach lies in using martingale testing to evaluate the extrapolation power of the procedure and to agnostically select the level of the high quantile. While this method has several limitations, we believe that framing extrapolation as a game opens the door to other agnostic approaches in Extreme Value Analysis.