We address the problem of causal effect estimation in the presence of hidden confounders using nonparametric instrumental variable (IV) regression. An established approach is to use estimators based on learned spectral features, that is, features spanning the top singular subspaces of the operator linking treatments to instruments. While powerful, such features are agnostic to the outcome variable. Consequently, the method can fail when the true causal function is poorly represented by these dominant singular functions. To mitigate, we introduce Augmented Spectral Feature Learning, a framework that makes the feature learning process outcome-aware. Our method learns features by minimizing a novel contrastive loss derived from an augmented operator that incorporates information from the outcome. By learning these task-specific features, our approach remains effective even under spectral misalignment. We provide a theoretical analysis of this framework and validate our approach on challenging benchmarks.

Evaluating rare-event forecasts is challenging because standard metrics collapse as event prevalence declines. Measures such as F1-score, AUPRC, MCC, and accuracy induce degenerate thresholds -- converging to zero or one -- and their values become dominated by class imbalance rather than tail discrimination. We develop a family of rare-event-stable (RES) metrics whose optimal thresholds remain strictly interior as the event probability approaches zero, ensuring coherent decision rules under extreme rarity. Simulations spanning event probabilities from 0.01 down to one in a million show that RES metrics maintain stable thresholds, consistent model rankings, and near-complete prevalence invariance, whereas traditional metrics exhibit statistically significant threshold drift and structural collapse. A credit-default application confirms these results: RES metrics yield interpretable probability-of-default cutoffs (4-9%) and remain robust under subsampling, while classical metrics fail operationally. The RES framework provides a principled, prevalence-invariant basis for evaluating extreme-risk forecasts.

Differential privacy is increasingly formalized through the lens of hypothesis testing via the robust and interpretable $f$-DP framework, where privacy guarantees are encoded by a baseline Blackwell trade-off function $f_{\infty} = T(P_{\infty}, Q_{\infty})$ involving a pair of distributions $(P_{\infty}, Q_{\infty})$. The problem of choosing the right privacy metric in practice leads to a central question: what is a statistically appropriate baseline $f_{\infty}$ given some prior modeling assumptions? The special case of Gaussian differential privacy (GDP) showed that, under compositions of nearly perfect mechanisms, these trade-off functions exhibit a central limit behavior with a Gaussian limit experiment. Inspired by Le Cam's theory of limits of statistical experiments, we answer this question in full generality in an infinitely divisible setting. We show that suitable composition experiments $(P_n^{\otimes n}, Q_n^{\otimes n})$ converge to a binary limit experiment $(P_{\infty}, Q_{\infty})$ whose log-likelihood ratio $L = \log(dQ_{\infty} / dP_{\infty})$ is infinitely divisible under $P_{\infty}$. Thus any limiting trade-off function $f_{\infty}$ is determined by an infinitely divisible law $P_{\infty}$, characterized by its Levy--Khintchine triplet, and its Esscher tilt defined by $dQ_{\infty}(x) = e^{x} dP_{\infty}(x)$. This characterizes all limiting baseline trade-off functions $f_{\infty}$ arising from compositions of nearly perfect differentially private mechanisms. Our framework recovers GDP as the purely Gaussian case and yields explicit non-Gaussian limits, including Poisson examples. It also positively resolves the empirical $s^2 = 2k$ phenomenon observed in the GDP paper and provides an optimal mechanism for count statistics achieving asymmetric Poisson differential privacy.

Synthetic data generation is an important tool for privacy-preserving data sharing. While diffusion models have set recent benchmarks, flow matching (FM) offers a promising alternative. This paper presents different ways to implement flow matching for tabular data synthesis. We provide a comprehensive empirical study that compares flow matching (FM and variational FM) with a state-of-the-art diffusion method (TabDDPM and TabSyn) in tabular data synthesis. We evaluate both the standard Optimal Transport (OT) and the Variance Preserving (VP) probability paths, and also compare deterministic and stochastic samplers -- something possible when learning to generate using \textit{variational} flow matching -- characterising the empirical relationship between data utility and privacy risk. Our key findings reveal that flow matching, particularly TabbyFlow, outperforms diffusion baselines. Flow matching methods also achieves better performance with remarkably low function evaluations ($\leq$ 100 steps), offering a substantial computational advantage. The choice of probability path is also crucial, as using the OT path demonstrates superior performance, while VP has potential for producing synthetic data with lower disclosure risk. Lastly, our results show that making flows stochastic not only preserves marginal distributions but, in some instances, enables the generation of high utility synthetic data with reduced disclosure risk.

We study the problem of learning disentangled signals from data using non-linear Independent Component Analysis (ICA). Motivated by advances in self-supervised learning, we propose to learn self-sufficient signals: A recovered signal should be able to reconstruct a missing value of its own from all remaining components without relying on any other signals. We formulate this problem as the minimization of a conditional KL divergence. Compared to traditional maximum likelihood estimation, our algorithm is prior-free and likelihood-free, meaning that we do not need to impose any prior on the original signals or any observational model, which often restricts the model's flexibility. To tackle the KL divergence minimization problem, we propose a sequential algorithm that reduces the KL divergence and learns an optimal de-mixing flow model at each iteration. This approach completely avoids the unstable adversarial training, a common issue in minimizing the KL divergence. Experiments on toy and real-world datasets show the effectiveness of our method.

We investigate the existence of a statistical-computational gap in multiple Gaussian graph alignment. We first generalize a previously established informational threshold from Vassaux and Massoulié (2025) to regimes where the number of observed graphs $p$ may also grow with the number of nodes $n$: when $p \leq O(n/\log(n))$, we recover the results from Vassaux and Massoulié (2025), and $p \geq Ω(n/\log(n))$ corresponds to a regime where the problem is as difficult as aligning one single graph with some unknown "signal" graph. Moreover, when $\log p = ω(\log n)$, the informational thresholds for partial and exact recovery no longer coincide, in contrast to the all-or-nothing phenomenon observed when $\log p=O(\log n)$. Then, we provide the first computational barrier in the low-degree framework for (multiple) Gaussian graph alignment. We prove that when the correlation $ρ$ is less than $1$, up to logarithmic terms, low degree non-trivial estimation fails. Our results suggest that the task of aligning $p$ graphs in polynomial time is as hard as the problem of aligning two graphs in polynomial time, up to logarithmic factors. These results characterize the existence of a statistical-computational gap and provide another example in which polynomial-time algorithms cannot handle complex combinatorial bi-dimensional structures.

Replicability is a fundamental challenge in reinforcement learning (RL), as RL algorithms are empirically observed to be unstable and sensitive to variations in training conditions. To formally address this issue, we study \emph{list replicability} in the Probably Approximately Correct (PAC) RL framework, where an algorithm must return a near-optimal policy that lies in a \emph{small list} of policies across different runs, with high probability. The size of this list defines the \emph{list complexity}. We introduce both weak and strong forms of list replicability: the weak form ensures that the final learned policy belongs to a small list, while the strong form further requires that the entire sequence of executed policies remains constrained. These objectives are challenging, as existing RL algorithms exhibit exponential list complexity due to their instability. Our main theoretical contribution is a provably efficient tabular RL algorithm that guarantees list replicability by ensuring the list complexity remains polynomial in the number of states, actions, and the horizon length. We further extend our techniques to achieve strong list replicability, bounding the number of possible policy execution traces polynomially with high probability. Our theoretical result is made possible by key innovations including (i) a novel planning strategy that selects actions based on lexicographic order among near-optimal choices within a randomly chosen tolerance threshold, and (ii) a mechanism for testing state reachability in stochastic environments while preserving replicability. Finally, we demonstrate that our theoretical investigation sheds light on resolving the \emph{instability} issue of RL algorithms used in practice. In particular, we show that empirically, our new planning strategy can be incorporated into practical RL frameworks to enhance their stability.

The Influence Maximization (IM) problem aims to select a set of seed nodes within a given budget to maximize the spread of influence in a social network. However, real-world social networks have several structural inequalities, such as dominant majority groups and underrepresented minority groups. If these inequalities are not considered while designing IM algorithms, the outcomes might be biased, disproportionately benefiting majority groups while marginalizing minorities. In this work, we address this gap by designing a fairness-aware IM method using Reinforcement Learning (RL) that ensures equitable influence outreach across all communities, regardless of protected attributes. Fairness is incorporated using a maximin fairness objective, which prioritizes improving the outreach of the least-influenced group, pushing the solution toward an equitable influence distribution. We propose a novel fairness-aware deep RL method, called DQ4FairIM, that maximizes the expected number of influenced nodes by learning an RL policy. The learnt policy ensures that minority groups formulate the IM problem as a Markov Decision Process (MDP) and use deep Q-learning, combined with the Structure2Vec network embedding, earning together with Structure2Vec network embedding to solve the MDP. We perform extensive experiments on synthetic benchmarks and real-world networks to compare our method with fairness-agnostic and fairness-aware baselines. The results show that our method achieves a higher level of fairness while maintaining a better fairness-performance trade-off than baselines. Additionally, our approach learns effective seeding policies that generalize across problem instances without retraining, such as varying the network size or the number of seed nodes.

Given a training dataset, the goal of dataset distillation is to derive a synthetic dataset such that models trained on the latter perform as well as those trained on the training dataset. In this work, we develop and analyze an efficient dataset distillation algorithm for supervised learning, specifically regression in $\mathbb{R}^d$, based on matching the losses on the training and synthetic datasets with respect to a fixed set of randomly sampled regressors without any model training. Our first key contribution is a novel performance guarantee proving that our algorithm needs only $\tilde{O}(d^2)$ sampled regressors to derive a synthetic dataset on which the MSE loss of any bounded linear model is nearly the same as its MSE loss on the given training data. In particular, the model optimized on the synthetic data has close to minimum loss on the training data, thus performing nearly as well as the model optimized on the latter. Complementing this, we also prove a matching lower bound of $Ω(d^2)$ for the number of sampled regressors showing the tightness of our analysis. Our second contribution is to extend our algorithm to offline RL dataset distillation by matching the Bellman loss, unlike previous works which used a behavioral cloning objective. This is the first such method which leverages both, the rewards and the next state information, available in offline RL datasets, without any policy model optimization. Our algorithm generates a synthetic dataset whose Bellman loss with respect to any linear action-value predictor is close to the latter's Bellman loss on the offline RL training dataset. Therefore, a policy associated with an action-value predictor optimized on the synthetic dataset performs nearly as well as that derived from the one optimized on the training data. We conduct experiments to validate our theoretical guarantees and observe performance gains.

Hierarchical clustering is a fundamental machine-learning technique for grouping data points into dendrograms. However, existing hierarchical clustering methods encounter two primary challenges: 1) Most methods specify dendrograms without a global objective. 2) Graph-based methods often neglect the significance of graph structure, optimizing objectives on complete or static predefined graphs. In this work, we propose Hyperbolic Continuous Structural Entropy neural networks, namely HypCSE, for structure-enhanced continuous hierarchical clustering. Our key idea is to map data points in the hyperbolic space and minimize the relaxed continuous structural entropy (SE) on structure-enhanced graphs. Specifically, we encode graph vertices in hyperbolic space using hyperbolic graph neural networks and minimize approximate SE defined on graph embeddings. To make the SE objective differentiable for optimization, we reformulate it into a function using the lowest common ancestor (LCA) on trees and then relax it into continuous SE (CSE) by the analogy of hyperbolic graph embeddings and partitioning trees. To ensure a graph structure that effectively captures the hierarchy of data points for CSE calculation, we employ a graph structure learning (GSL) strategy that updates the graph structure during training. Extensive experiments on seven datasets demonstrate the superior performance of HypCSE.