pwc-archive/papers-with-abstracts huggingface dataset:
A General-Purpose Theorem for High-Probability Bounds of Stochastic Approximation with Polyak Averaging
Authors: Sajad Khodadadian, Martin Zubeldia
Date: 2025-05-27 00:00:00
Tasks: Q-Learning

Polyak-Ruppert averaging is a widely used technique to achieve the optimal asymptotic variance of stochastic approximation (SA) algorithms, yet its high-probability performance guarantees remain underexplored in general settings. In this paper, we present a general framework for establishing non-asymptotic concentration bounds for the error of averaged SA iterates. Our approach assumes access to individual concentration bounds for the unaveraged iterates and yields a sharp bound on the averaged iterates. We also construct an example, showing the tightness of our result up to constant multiplicative factors. As direct applications, we derive tight concentration bounds for contractive SA algorithms and for algorithms such as temporal difference learning and Q-learning with averaging, obtaining new bounds in settings where traditional analysis is challenging.
Langevin SDEs have unique transient dynamics
Authors: Vincent Guan, Joseph Janssen, Nicolas Lanzetti, Antonio Terpin, Geoffrey Schiebinger, Elina Robeva
Date: 2025-05-27 00:00:00

The overdamped Langevin stochastic differential equation (SDE) is a classical physical model used for chemical, genetic, and hydrological dynamics. In this work, we prove that the drift and diffusion terms of a Langevin SDE are jointly identifiable from temporal marginal distributions if and only if the process is observed out of equilibrium. This complete characterization of structural identifiability removes the long-standing assumption that the diffusion must be known to identify the drift. We then complement our theory with experiments in the finite sample setting and study the practical identifiability of the drift and diffusion, in order to propose heuristics for optimal data collection.
A ZeNN architecture to avoid the Gaussian trap
Authors: Luís Carvalho, João L. Costa, José Mourão, Gonçalo Oliveira
Date: 2025-05-26 00:00:00

We propose a new simple architecture, Zeta Neural Networks (ZeNNs), in order to overcome several shortcomings of standard multi-layer perceptrons (MLPs). Namely, in the large width limit, MLPs are non-parametric, they do not have a well-defined pointwise limit, they lose non-Gaussian attributes and become unable to perform feature learning; moreover, finite width MLPs perform poorly in learning high frequencies. The new ZeNN architecture is inspired by three simple principles from harmonic analysis: i) Enumerate the perceptons and introduce a non-learnable weight to enforce convergence; ii) Introduce a scaling (or frequency) factor; iii) Choose activation functions that lead to near orthogonal systems. We will show that these ideas allow us to fix the referred shortcomings of MLPs. In fact, in the infinite width limit, ZeNNs converge pointwise, they exhibit a rich asymptotic structure beyond Gaussianity, and perform feature learning. Moreover, when appropriate activation functions are chosen, (finite width) ZeNNs excel at learning high-frequency features of functions with low dimensional domains.
Learning with Expected Signatures: Theory and Applications
Authors: Lorenzo Lucchese, Mikko S. Pakkanen, Almut E. D. Veraart
Date: 2025-05-26 00:00:00
Tasks: Time Series

The expected signature maps a collection of data streams to a lower dimensional representation, with a remarkable property: the resulting feature tensor can fully characterize the data generating distribution. This "model-free" embedding has been successfully leveraged to build multiple domain-agnostic machine learning (ML) algorithms for time series and sequential data. The convergence results proved in this paper bridge the gap between the expected signature's empirical discrete-time estimator and its theoretical continuous-time value, allowing for a more complete probabilistic interpretation of expected signature-based ML methods. Moreover, when the data generating process is a martingale, we suggest a simple modification of the expected signature estimator with significantly lower mean squared error and empirically demonstrate how it can be effectively applied to improve predictive performance.
Liouville PDE-based sliced-Wasserstein flow for fair regression
Authors: Pilhwa Lee, Jayshawn Cooper
Date: 2025-05-22 00:00:00
Tasks: Density Estimation, Fairness, regression

The sliced Wasserstein flow (SWF), a nonparametric and implicit generative gradient flow, is applied to fair regression. We have improved the SWF in a few aspects. First, the stochastic diffusive term from the Fokker-Planck equation-based Monte Carlo is transformed to Liouville partial differential equation (PDE)-based transport with density estimation, however, without the diffusive term. Now, the computation of the Wasserstein barycenter is approximated by the SWF barycenter with the prescription of Kantorovich potentials for the induced gradient flow to generate its samples. These two efforts improve the convergence in training and testing SWF and SWF barycenters with reduced variance. Applying the generative SWF barycenter for fair regression demonstrates competent profiles in the accuracy-fairness Pareto curves.
Efficient Training of Neural SDEs Using Stochastic Optimal Control
Authors: Rembert Daems, Manfred Opper, Guillaume Crevecoeur, Tolga Birdal
Date: 2025-05-22 00:00:00
Tasks: Variational Inference

We present a hierarchical, control theory inspired method for variational inference (VI) for neural stochastic differential equations (SDEs). While VI for neural SDEs is a promising avenue for uncertainty-aware reasoning in time-series, it is computationally challenging due to the iterative nature of maximizing the ELBO. In this work, we propose to decompose the control term into linear and residual non-linear components and derive an optimal control term for linear SDEs, using stochastic optimal control. Modeling the non-linear component by a neural network, we show how to efficiently train neural SDEs without sacrificing their expressive power. Since the linear part of the control term is optimal and does not need to be learned, the training is initialized at a lower cost and we observe faster convergence.
On Transferring Transferability: Towards a Theory for Size Generalization
Authors: Eitan Levin, Yuxin Ma, Mateo Díaz, Soledad Villar
Date: 2025-05-29 00:00:00

Many modern learning tasks require models that can take inputs of varying sizes. Consequently, dimension-independent architectures have been proposed for domains where the inputs are graphs, sets, and point clouds. Recent work on graph neural networks has explored whether a model trained on low-dimensional data can transfer its performance to higher-dimensional inputs. We extend this body of work by introducing a general framework for transferability across dimensions. We show that transferability corresponds precisely to continuity in a limit space formed by identifying small problem instances with equivalent large ones. This identification is driven by the data and the learning task. We instantiate our framework on existing architectures, and implement the necessary changes to ensure their transferability. Finally, we provide design principles for designing new transferable models. Numerical experiments support our findings.
Spectral Mixture Kernels for Bayesian Optimization
Authors: Yi Zhang, Cheng Hua
Date: 2025-05-23 00:00:00
Tasks: Bayesian Optimization

Bayesian Optimization (BO) is a widely used approach for solving expensive black-box optimization tasks. However, selecting an appropriate probabilistic surrogate model remains an important yet challenging problem. In this work, we introduce a novel Gaussian Process (GP)-based BO method that incorporates spectral mixture kernels, derived from spectral densities formed by scale-location mixtures of Cauchy and Gaussian distributions. This method achieves a significant improvement in both efficiency and optimization performance, matching the computational speed of simpler kernels while delivering results that outperform more complex models and automatic BO methods. We provide bounds on the information gain and cumulative regret associated with obtaining the optimum. Extensive numerical experiments demonstrate that our method consistently outperforms existing baselines across a diverse range of synthetic and real-world problems, including both low- and high-dimensional settings.
The Strong, Weak and Benign Goodhart's law. An independence-free and paradigm-agnostic formalisation
Authors: Adrien Majka, El-Mahdi El-Mhamdi
Date: 2025-05-29 00:00:00

Goodhart's law is a famous adage in policy-making that states that ``When a measure becomes a target, it ceases to be a good measure''. As machine learning models and the optimisation capacity to train them grow, growing empirical evidence reinforced the belief in the validity of this law without however being formalised. Recently, a few attempts were made to formalise Goodhart's law, either by categorising variants of it, or by looking at how optimising a proxy metric affects the optimisation of an intended goal. In this work, we alleviate the simplifying independence assumption, made in previous works, and the assumption on the learning paradigm made in most of them, to study the effect of the coupling between the proxy metric and the intended goal on Goodhart's law. Our results show that in the case of light tailed goal and light tailed discrepancy, dependence does not change the nature of Goodhart's effect. However, in the light tailed goal and heavy tailed discrepancy case, we exhibit an example where over-optimisation occurs at a rate inversely proportional to the heavy tailedness of the discrepancy between the goal and the metric. %
Joint estimation of smooth graph signals from partial linear measurements
Authors: Hemant Tyagi
Date: 2025-05-29 00:00:00

Given an undirected and connected graph $G$ on $T$ vertices, suppose each vertex $t$ has a latent signal $x_t \in \mathbb{R}^n$ associated to it. Given partial linear measurements of the signals, for a potentially small subset of the vertices, our goal is to estimate $x_t$'s. Assuming that the signals are smooth w.r.t $G$, in the sense that the quadratic variation of the signals over the graph is small, we obtain non-asymptotic bounds on the mean squared error for jointly recovering $x_t$'s, for the smoothness penalized least squares estimator. In particular, this implies for certain choices of $G$ that this estimator is weakly consistent (as $T \rightarrow \infty$) under potentially very stringent sampling, where only one coordinate is measured per vertex for a vanishingly small fraction of the vertices. The results are extended to a ``multi-layer'' ranking problem where $x_t$ corresponds to the latent strengths of a collection of $n$ items, and noisy pairwise difference measurements are obtained at each ``layer'' $t$ via a measurement graph $G_t$. Weak consistency is established for certain choices of $G$ even when the individual $G_t$'s are very sparse and disconnected.
Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean-Field Games
Authors: Antonio Ocello, Daniil Tiapkin, Lorenzo Mancini, Mathieu Laurière, Eric Moulines
Date: 2025-05-28 00:00:00
Tasks: Decision Making, Reinforcement Learning (RL)

We introduce Mean-Field Trust Region Policy Optimization (MF-TRPO), a novel algorithm designed to compute approximate Nash equilibria for ergodic Mean-Field Games (MFG) in finite state-action spaces. Building on the well-established performance of TRPO in the reinforcement learning (RL) setting, we extend its methodology to the MFG framework, leveraging its stability and robustness in policy optimization. Under standard assumptions in the MFG literature, we provide a rigorous analysis of MF-TRPO, establishing theoretical guarantees on its convergence. Our results cover both the exact formulation of the algorithm and its sample-based counterpart, where we derive high-probability guarantees and finite sample complexity. This work advances MFG optimization by bridging RL techniques with mean-field decision-making, offering a theoretically grounded approach to solving complex multi-agent problems.
Principled Out-of-Distribution Generalization via Simplicity
Authors: Jiawei Ge, Amanda Wang, Shange Tang, Chi Jin
Date: 2025-05-28 00:00:00
Tasks: Image Generation, Out-of-Distribution Generalization

Modern foundation models exhibit remarkable out-of-distribution (OOD) generalization, solving tasks far beyond the support of their training data. However, the theoretical principles underpinning this phenomenon remain elusive. This paper investigates this problem by examining the compositional generalization abilities of diffusion models in image generation. Our analysis reveals that while neural network architectures are expressive enough to represent a wide range of models -- including many with undesirable behavior on OOD inputs -- the true, generalizable model that aligns with human expectations typically corresponds to the simplest among those consistent with the training data. Motivated by this observation, we develop a theoretical framework for OOD generalization via simplicity, quantified using a predefined simplicity metric. We analyze two key regimes: (1) the constant-gap setting, where the true model is strictly simpler than all spurious alternatives by a fixed gap, and (2) the vanishing-gap setting, where the fixed gap is replaced by a smoothness condition ensuring that models close in simplicity to the true model yield similar predictions. For both regimes, we study the regularized maximum likelihood estimator and establish the first sharp sample complexity guarantees for learning the true, generalizable, simple model.
GLAMP: An Approximate Message Passing Framework for Transfer Learning with Applications to Lasso-based Estimators
Authors: Longlin Wang, Yanke Song, Kuanhao Jiang, Pragya Sur
Date: 2025-05-28 00:00:00
Tasks: Denoising, Transfer Learning

Approximate Message Passing (AMP) algorithms enable precise characterization of certain classes of random objects in the high-dimensional limit, and have found widespread applications in fields such as statistics, deep learning, genetics, and communications. However, existing AMP frameworks cannot simultaneously handle matrix-valued iterates and non-separable denoising functions. This limitation prevents them from precisely characterizing estimators that draw information from multiple data sources with distribution shifts. In this work, we introduce Generalized Long Approximate Message Passing (GLAMP), a novel extension of AMP that addresses this limitation. We rigorously prove state evolution for GLAMP. GLAMP significantly broadens the scope of AMP, enabling the analysis of transfer learning estimators that were previously out of reach. We demonstrate the utility of GLAMP by precisely characterizing the risk of three Lasso-based transfer learning estimators: the Stacked Lasso, the Model Averaging Estimator, and the Second Step Estimator. We also demonstrate the remarkable finite sample accuracy of our theory via extensive simulations.
Handling bounded response in high dimensions: a Horseshoe prior Bayesian Beta regression approach
Authors: The Tien Mai
Date: 2025-05-28 00:00:00
Tasks: regression, Variable Selection

Bounded continuous responses -- such as proportions -- arise frequently in diverse scientific fields including climatology, biostatistics, and finance. Beta regression is a widely adopted framework for modeling such data, due to the flexibility of the Beta distribution over the unit interval. While Bayesian extensions of Beta regression have shown promise, existing methods are limited to low-dimensional settings and lack theoretical guarantees. In this work, we propose a novel Bayesian approach for high-dimensional sparse Beta regression framework that employs a tempered posterior. Our method incorporates the Horseshoe prior for effective shrinkage and variable selection. Most notable, we propose a novel Gibbs sampling algorithm using P\'olya-Gamma augmentation for efficient inference in Beta regression model. We also provide the first theoretical results establishing posterior consistency and convergence rates for Bayesian Beta regression. Through extensive simulation studies in both low- and high-dimensional scenarios, we demonstrate that our approach outperforms existing alternatives, offering improved estimation accuracy and model interpretability. Our method is implemented in the R package ``betaregbayes" available on Github.
Scalable and adaptive prediction bands with kernel sum-of-squares
Authors: Louis Allain, Sébastien da Veiga, Brian Staber
Date: 2025-05-27 00:00:00
Tasks: Conformal Prediction

Conformal Prediction (CP) is a popular framework for constructing prediction bands with valid coverage in finite samples, while being free of any distributional assumption. A well-known limitation of conformal prediction is the lack of adaptivity, although several works introduced practically efficient alternate procedures. In this work, we build upon recent ideas that rely on recasting the CP problem as a statistical learning problem, directly targeting coverage and adaptivity. This statistical learning problem is based on reproducible kernel Hilbert spaces (RKHS) and kernel sum-of-squares (SoS) methods. First, we extend previous results with a general representer theorem and exhibit the dual formulation of the learning problem. Crucially, such dual formulation can be solved efficiently by accelerated gradient methods with several hundreds or thousands of samples, unlike previous strategies based on off-the-shelf semidefinite programming algorithms. Second, we introduce a new hyperparameter tuning strategy tailored specifically to target adaptivity through bounds on test-conditional coverage. This strategy, based on the Hilbert-Schmidt Independence Criterion (HSIC), is introduced here to tune kernel lengthscales in our framework, but has broader applicability since it could be used in any CP algorithm where the score function is learned. Finally, extensive experiments are conducted to show how our method compares to related work. All figures can be reproduced with the accompanying code.
A Kernelised Stein Discrepancy for Assessing the Fit of Inhomogeneous Random Graph Models
Authors: Anum Fatima, Gesine Reinert
Date: 2025-05-27 00:00:00

Complex data are often represented as a graph, which in turn can often be viewed as a realisation of a random graph, such as of an inhomogeneous random graph model (IRG). For general fast goodness-of-fit tests in high dimensions, kernelised Stein discrepancy (KSD) tests are a powerful tool. Here, we develop, test, and analyse a KSD-type goodness-of-fit test for IRG models that can be carried out with a single observation of the network. The test is applicable to a network of any size and does not depend on the asymptotic distribution of the test statistic. We also provide theoretical guarantees.
Moment Expansions of the Energy Distance
Authors: Ian Langmore
Date: 2025-05-27 00:00:00
Tasks: Sensitivity

The energy distance is used to test distributional equality, and as a loss function in machine learning. While $D^2(X, Y)=0$ only when $X\sim Y$, the sensitivity to different moments is of practical importance. This work considers $D^2(X, Y)$ in the case where the distributions are close. In this regime, $D^2(X, Y)$ is more sensitive to differences in the means $\bar{X}-\bar{Y}$, than differences in the covariances $\Delta$. This is due to the structure of the energy distance and is independent of dimension. The sensitivity to on versus off diagonal components of $\Delta$ is examined when $X$ and $Y$ are close to isotropic. Here a dimension dependent averaging occurs and, in many cases, off diagonal correlations contribute significantly less. Numerical results verify these relationships hold even when distributional assumptions are not strictly met.
Kernel Quantile Embeddings and Associated Probability Metrics
Authors: Masha Naslidnyk, Siu Lun Chau, François-Xavier Briol, Krikamol Muandet
Date: 2025-05-26 00:00:00

Embedding probability distributions into reproducing kernel Hilbert spaces (RKHS) has enabled powerful nonparametric methods such as the maximum mean discrepancy (MMD), a statistical distance with strong theoretical and computational properties. At its core, the MMD relies on kernel mean embeddings to represent distributions as mean functions in RKHS. However, it remains unclear if the mean function is the only meaningful RKHS representation. Inspired by generalised quantiles, we introduce the notion of kernel quantile embeddings (KQEs). We then use KQEs to construct a family of distances that: (i) are probability metrics under weaker kernel conditions than MMD; (ii) recover a kernelised form of the sliced Wasserstein distance; and (iii) can be efficiently estimated with near-linear cost. Through hypothesis testing, we show that these distances offer a competitive alternative to MMD and its fast approximations.
Anytime-valid, Bayes-assisted,Prediction-Powered Inference
Authors: Valentin Kilian, Stefano Cortinovis, François Caron
Date: 2025-05-23 00:00:00
Tasks: Prediction, valid

Given a large pool of unlabelled data and a smaller amount of labels, prediction-powered inference (PPI) leverages machine learning predictions to increase the statistical efficiency of standard confidence interval procedures based solely on labelled data, while preserving their fixed-time validity. In this paper, we extend the PPI framework to the sequential setting, where labelled and unlabelled datasets grow over time. Exploiting Ville's inequality and the method of mixtures, we propose prediction-powered confidence sequence procedures that are valid uniformly over time and naturally accommodate prior knowledge on the quality of the predictions to further boost efficiency. We carefully illustrate the design choices behind our method and demonstrate its effectiveness in real and synthetic examples.
Wasserstein Transfer Learning
Authors: Kaicheng Zhang, Sinian Zhang, Doudou Zhou, Yidong Zhou
Date: 2025-05-23 00:00:00
Tasks: Transfer Learning

Transfer learning is a powerful paradigm for leveraging knowledge from source domains to enhance learning in a target domain. However, traditional transfer learning approaches often focus on scalar or multivariate data within Euclidean spaces, limiting their applicability to complex data structures such as probability distributions. To address this, we introduce a novel framework for transfer learning in regression models, where outputs are probability distributions residing in the Wasserstein space. When the informative subset of transferable source domains is known, we propose an estimator with provable asymptotic convergence rates, quantifying the impact of domain similarity on transfer efficiency. For cases where the informative subset is unknown, we develop a data-driven transfer learning procedure designed to mitigate negative transfer. The proposed methods are supported by rigorous theoretical analysis and are validated through extensive simulations and real-world applications.