GenAI4ELab/papercli-papers huggingface dataset:
Infinite-Dimensional Diffusion Models
Authors: Jakiw Pidstrigach; Youssef Marzouk; Sebastian Reich; Sven Wang
Venue: JMLR 2024 (main)

Abstract: Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standard approach is first to discretize and then to apply diffusion models to the discretized data. While such approaches are practically appealing, the performance of the resulting algorithms typically deteriorates as discretization parameters are refined. In this paper, we instead directly formulate diffusion-based generative models in infinite dimensions and apply them to the generative modelling of functions. We prove that our formulations are well posed in the infinite-dimensional setting and provide dimension-independent distance bounds from the sample to the target measure. Using our theory, we also develop guidelines for the design of infinite-dimensional diffusion models. For image distributions, these guidelines are in line with current canonical choices. For other distributions, however, we can improve upon these canonical choices.  We demonstrate these results  both theoretically and empirically, by applying the algorithms to data distributions on manifolds and to distributions arising in Bayesian inverse problems or simulation-based inference.
Estimation of the Order of Non-Parametric Hidden Markov Models using the Singular Values of an Integral Operator
Authors: Marie Du Roy de Chaumaray; Salima El Kolei; Marie-Pierre Etienne; Matthieu Marbac
Venue: JMLR 2024 (main)

Abstract: Interested in estimating the order of a finite-state Hidden Markov Model (HMM) with non-parametric emission distributions from a single observed sequence, we introduce a new method that only requires full rank transition matrix and linear independence between the emission distributions. This method relies on the equality between the order of the HMM and the rank of a specific integral operator. Since only the empirical counter-part of the singular values of the operator can be obtained, a thresholding procedure is proposed. At a non-asymptotic level, an upper-bound on the probability of overestimating the order of the HMM is provided. At an asymptotic level, the consistency of the estimator is established. In addition, we introduce a general heuristic that can be successfully applied to several problems in spectral analysis for designing a data-driven procedure for the threshold. The approach has the advantage of not requiring any knowledge of an upper-bound on the order of the HMM. Moreover, different types of data (including circular or mixed-type data) can be managed. The relevance of the approach is illustrated on numerical experiments and on real data considering multivariate data with directional variables.
Stochastic-Constrained Stochastic Optimization with Markovian Data
Authors: Yeongjong Kim; Dabeen Lee
Venue: JMLR 2024 (main)

Abstract: This paper considers stochastic-constrained stochastic optimization where the stochastic constraint is to satisfy that the expectation of a random function is below a certain threshold. In particular, we study the setting where data samples are drawn from a Markov chain and thus are not independent and identically distributed. We generalize the drift-plus-penalty framework, a primal-dual stochastic gradient method developed for the i.i.d. case, to the Markov chain sampling setting. We propose three variants of drift-plus-penalty; two are for the case when the mixing time of the underlying Markov chain is known while the other is for the case of unknown mixing time. In fact, our algorithms apply to a more general setting of constrained online convex optimization where the sequence of constraint functions follows a Markov chain. The algorithms are adaptive in that the first two work without knowledge of the time horizon while the third uses AdaGrad-style algorithm parameters, which is of independent interest. We demonstrate the effectiveness of our proposed methods through numerical experiments on classification with fairness constraints.
PyDMD: A Python Package for Robust Dynamic Mode Decomposition
Authors: Sara M. Ichinaga; Francesco Andreuzzi; Nicola Demo; Marco Tezzele; Karl Lapo; Gianluigi Rozza; Steven L. Brunton; J. Nathan Kutz
Venue: JMLR 2024 (main)

Abstract: The dynamic mode decomposition (DMD) is a powerful data-driven modeling technique that reveals coherent spatiotemporal patterns from dynamical system snapshot observations. PyDMD is a Python package that implements DMD and several of its major optimizations and methodological extensions. In this paper, we introduce the version 1.0 release of PyDMD, which includes new data preprocessors, plotting tools, and a number of cutting-edge DMD methods specifically designed to handle real-world data that may be noisy, multi-scale, parameterized, prohibitively high-dimensional, and even strongly nonlinear. The package is friendly to install, thoroughly-documented, supplemented with extensive code examples, and modularly-structured to support future additions. The entire codebase is released under the MIT license and is available at https://github.com/PyDMD/PyDMD.
Countering the Communication Bottleneck in Federated Learning: A Highly Efficient Zero-Order Optimization Technique
Authors: Elissa Mhanna; Mohamad Assaad
Venue: JMLR 2024 (main)

Abstract: Federated learning (FL) is a creative technique that enables multiple edge devices to train a model without revealing raw data. However, several issues hinder the practical implementation of FL, especially in wireless environments. These issues comprise the limited capacity of the upload transmission link between the edge devices and the aggregator, as well as the wireless disturbances. To address these challenges, we develop a zero-order (ZO) communication-efficient framework for FL. While in standard FL, each device must upload a long vector containing the gradient or the model per communication round, our novel ZO method incorporates a two-point gradient estimator, which requires uploading only two scalars. What also sets our approach apart is that it directly incorporates wireless perturbations into the learning, eliminating the need for additional computational resources to remove their impact. In this work, we overcome the technical and analytical challenges associated with FL problems and ZO methods, comprehensively study our algorithm, and prove it converges almost surely under different conditions, convexity and non-convexity, noise-free and noisy environments. We then find theoretical bounds on the convergence rate when the objective is strongly convex, non-convex, and $\kappa$-gradient-dominated that compete with first-order (FO) or centralized methods under the same settings. Finally, we provide experimental results demonstrating the effectiveness of our algorithm, considering relevant examples. We provide an example illustrating the amount of communication saved due to its efficiency compared to its FO counterpart.
Mean-Field Games With Finitely Many Players: Independent Learning and Subjectivity
Authors: Bora Yongacoglu; GÃ¼rdal Arslan; Serdar YÃ¼ksel
Venue: JMLR 2024 (main)

Abstract: Independent learners are agents that employ single-agent algorithms in multi-agent systems, intentionally ignoring the effect of other strategic agents. This paper studies mean-field games from a decentralized learning perspective with two aims: (i) to identify structure that can guide algorithm design, and (ii) to understand emergent behaviour in systems of independent learners. We study a new model of partially observed mean-field games with finitely many players, local action observability, and partial observations of the global state. Specific observation channels considered include (a) global observability, (b) mean-field observability, (c) compressed mean-field observability, and (d) only local observability. We establish conditions under which the control problem of a given agent is equivalent to a fully observed MDP, as well as conditions under which the control problem is equivalent only to a POMDP. Using the connection to MDPs, we prove the existence of perfect equilibrium among memoryless stationary policies under mean-field observability.  Using the connection to POMDPs, we prove convergence of learning iterates obtained by independent learners under any of our observation channels. We interpret the limiting values as subjective value functions, which an agent believes to be relevant to its control problem. These subjective value functions are used to propose subjective Q-equilibrium, a new solution concept whose existence is proved under mean-field or global observability. Furthermore, we provide a decentralized independent learning algorithm, and by adapting the recently developed theory of satisficing paths to allow for subjectivity, we prove that it drives play to subjective Q-equilibrium. Our algorithm is decentralized, in that it uses only local information for learning and allows players to use different, heterogeneous policies during play. As such, it departs from the conventional representative agent approach common to other algorithms for mean-field games.
Fourier Neural Operators for Arbitrary Resolution Climate Data Downscaling
Authors: Qidong Yang; Alex Hernandez-Garcia; Paula Harder; Venkatesh Ramesh; Prasanna Sattigeri; Daniela Szwarcman; Campbell D. Watson; David Rolnick
Venue: JMLR 2024 (main)

Abstract: Climate simulations are essential in guiding our understanding of climate change and responding to its effects. However, it is computationally expensive to resolve complex climate processes at high spatial resolution. As one way to speed up climate simulations, neural networks have been used to downscale climate variables from fast-running low-resolution simulations, but high-resolution training data are often unobtainable or scarce, greatly limiting accuracy. In this work, we propose a downscaling method based on the Fourier neural operator. It is trained using a low upsampling factor and then can zero-shot (without additional training) downscale its input to arbitrary unseen high resolution. Evaluated both on ERA5 climate model data and on the Navier-Stokes equation solution data, our downscaling model significantly outperforms state-of-the-art convolutional and generative adversarial downscaling models, both in standard single-resolution downscaling and in zero-shot generalization to higher upsampling factors. Furthermore, we show that our method also outperforms state-of-the-art data-driven partial differential equation solvers on Navier-Stokes equations. Overall, our work bridges the gap between simulation of a physical process and interpolation of low-resolution output, showing that it is possible to combine both approaches and significantly improve upon each other.
High Probability and Risk-Averse Guarantees for a Stochastic Accelerated Primal-Dual Method
Authors: Yassine Laguel; Necdet Serhat Aybat; Mert GÃ¼rbÃ¼zbalaban
Venue: JMLR 2024 (main)

Abstract: We consider stochastic strongly-convex-strongly-concave (SCSC) saddle point (SP) problems which frequently arise in applications ranging from distributionally robust learning to game theory and fairness in machine learning. We focus on the recently developed stochastic accelerated primal-dual algorithm (SAPD), which admits optimal complexity in several settings as an accelerated algorithm. We provide high probability guarantees for convergence to a neighborhood of the saddle point that reflects accelerated convergence behavior. We also provide an analytical formula for the limiting covariance matrix of the iterates for a class of stochastic SCSC quadratic problems where the gradient noise is additive and Gaussian. This allows us to develop lower bounds for this class of quadratic problems which show that our analysis is tight in terms of the high probability bound dependence on the problem parameters. We also provide a risk-averse convergence analysis characterizing the âConditional Value at Riskâ, the âEntropic Value at Riskâ, and the Ï2-divergence of the distance to the saddle point for the iterate sequence, highlighting the trade-offs between the bias and the risk associated with an approximate solution obtained by terminating the algorithm at any iteration.
Efficiently Escaping Saddle Points in Bilevel Optimization
Authors: Minhui Huang; Xuxing Chen; Kaiyi Ji; Shiqian Ma; Lifeng Lai
Venue: JMLR 2025 (main)

Abstract: Bilevel optimization is one of the fundamental problems in machine learning and optimization. Recent theoretical developments in bilevel optimization focus on finding the first-order stationary points for nonconvex-strongly-convex cases. In this paper, we analyze algorithms that can escape saddle points in nonconvex-strongly-convex bilevel optimization. Specifically, we show that the perturbed approximate implicit differentiation (AID) with a warm start strategy finds an $\epsilon$-approximate local minimum of bilevel optimization in $\tilde{O}(\epsilon^{-2})$ iterations with high probability. Moreover, we propose an inexact NEgative-curvature-Originated-from-Noise Algorithm (iNEON), an algorithm that can escape saddle point and find local minimum of stochastic bilevel optimization. As a by-product, we provide the first nonasymptotic analysis of perturbed multi-step gradient descent ascent (GDmax) algorithm that converges to local minimax point for minimax problems.
Bayes Meets Bernstein at the Meta Level: an Analysis of Fast Rates in Meta-Learning with PAC-Bayes
Authors: Charles Riou; Pierre Alquier; Badr-Eddine ChÃ©rief-Abdellatif
Venue: JMLR 2025 (main)

Abstract: Bernstein's condition is a key assumption that guarantees fast rates in machine learning. For example, under this condition, the Gibbs posterior with prior $\pi$ has an excess risk in $O(d_{\pi}/n)$, as opposed to $O(\sqrt{d_{\pi}/n})$ in the general case, where $n$ denotes the number of observations and $d_{\pi}$ is a complexity parameter which depends on the prior $\pi$. In this paper, we examine the Gibbs posterior in the context of meta-learning, i.e., when learning the prior $\pi$ from $T$ previous tasks. Our main result is that Bernstein's condition always holds at the meta level, regardless of its validity at the observation level. This implies that the additional cost to learn the Gibbs prior $\pi$, which will reduce the term $d_\pi$ across tasks, is in $O(1/T)$, instead of the expected $O(1/\sqrt{T})$. We further illustrate how this result improves on the standard rates in three different settings: discrete priors, Gaussian priors and mixture of Gaussian priors.
DisC2o-HD: Distributed causal inference with covariates shift for analyzing real-world high-dimensional data
Authors: Jiayi Tong; Jie Hu; George Hripcsak; Yang Ning; Yong Chen
Venue: JMLR 2025 (main)

Abstract: High-dimensional healthcare data, such as electronic health records (EHR) data and claims data, present two primary challenges due to the large number of variables and the need to consolidate data from multiple clinical sites. The third key challenge is the potential existence of heterogeneity in terms of covariate shift. In this paper, we propose a distributed learning algorithm accounting for covariate shift to estimate the average treatment effect (ATE) for high-dimensional data, named DisC2o-HD. Leveraging the surrogate likelihood method, our method calibrates the estimates of the propensity score and outcome models to approximately attain the desired covariate balancing property, while accounting for the covariate shift across multiple clinical sites. We show that our distributed covariate balancing propensity score estimator can approximate the pooled estimator, which is obtained by pooling the data from multiple sites together. The proposed estimator remains consistent if either the propensity score model or the outcome regression model is correctly specified. The semiparametric efficiency bound is achieved when both the propensity score and the outcome models are correctly specified. We conduct simulation studies to demonstrate the performance of the proposed algorithm; additionally, we conduct an empirical study to present the readiness of implementation and validity.
Deep Out-of-Distribution Uncertainty Quantification via Weight Entropy Maximization
Authors: Antoine de Mathelin; FranÃ§ois Deheeger; Mathilde Mougeot; Nicolas Vayatis
Venue: JMLR 2025 (main)

Abstract: This paper deals with uncertainty quantification and out-of-distribution detection in deep learning using Bayesian and ensemble methods. It proposes a practical solution to the lack of prediction diversity observed recently for standard approaches when used out-of-distribution (Ovadia et al., 2019; Liu et al., 2021). Considering that this issue is mainly related to a lack of weight diversity, we claim that standard methods sample in "over-restricted" regions of the weight space due to the use of "over-regularization" processes, such as weight decay and zero-mean centered Gaussian priors. We propose to solve the problem by adopting the maximum entropy principle for the weight distribution, with the underlying idea to maximize the weight diversity. Under this paradigm, the epistemic uncertainty is described by the weight distribution of maximal entropy that produces neural networks "consistent" with the training observations. Considering stochastic neural networks, a practical optimization is derived to build such a distribution, defined as a trade-off between the average empirical risk and the weight distribution entropy. We provide both theoretical and numerical results to assess the efficiency of the approach. In particular, the proposed algorithm appears in the top three best methods in all configurations of an extensive out-of-distribution detection benchmark including more than thirty competitors.
Enhancing Graph Representation Learning with Localized Topological Features
Authors: Zuoyu Yan; Qi Zhao; Ze Ye; Tengfei Ma; Liangcai Gao; Zhi Tang; Yusu Wang; Chao Chen
Venue: JMLR 2025 (main)

Abstract: Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be beneficial to explicitly extract and incorporate high-order topological and geometric information into these models. In this paper, we propose a principled approach to extract the rich connectivity information of graphs based on the theory of persistent homology. Our method utilizes the topological features to enhance the representation learning of graph neural networks and achieve state-of-the-art performance on various node classification and link prediction benchmarks. We also explore the option of end-to-end learning of the topological features, i.e., treating topological computation as a differentiable operator during learning. Our theoretical analysis and empirical study provide insights and potential guidelines for employing topological features in graph learning tasks.
Memory Gym: Towards Endless Tasks to Benchmark Memory Capabilities of Agents
Authors: Marco Pleines; Matthias Pallasch; Frank Zimmer; Mike Preuss
Venue: JMLR 2025 (main)

Abstract: Memory Gym presents a suite of 2D partially observable environments, namely Mortar Mayhem, Mystery Path, and Searing Spotlights, designed to benchmark memory capabilities in decision-making agents. These environments, originally with finite tasks, are expanded into innovative, endless formats, mirroring the escalating challenges of cumulative memory games such as âI packed my bagâ. This progression in task design shifts the focus from merely assessing sample efficiency to also probing the levels of memory effectiveness in dynamic, prolonged scenarios. To address the gap in available memory-based Deep Reinforcement Learning baselines, we introduce an implementation within the open-source CleanRL library that integrates Transformer-XL (TrXL) with Proximal Policy Optimization. This approach utilizes TrXL as a form of episodic memory, employing a sliding window technique. Our comparative study between the Gated Recurrent Unit (GRU) and TrXL reveals varied performances across our finite and endless tasks. TrXL, on the finite environments, demonstrates superior effectiveness over GRU, but only when utilizing an auxiliary loss to reconstruct observations. Notably, GRU makes a remarkable resurgence in all endless tasks, consistently outperforming TrXL by significant margins. Website and Source Code: https://marcometer.github.io/jmlr_2024.github.io/
A Random Matrix Approach to Low-Multilinear-Rank Tensor Approximation
Authors: Hugo Lebeau; Florent Chatelain; Romain Couillet
Venue: JMLR 2025 (main)

Abstract: This work presents a comprehensive understanding of the estimation of a planted low-rank signal from a general spiked tensor model near the computational threshold. Relying on standard tools from the theory of large random matrices, we characterize the large-dimensional spectral behavior of the unfoldings of the data tensor and exhibit relevant signal-to-noise ratios governing the detectability of the principal directions of the signal. These results allow to accurately predict the reconstruction performance of truncated multilinear SVD (MLSVD) in the non-trivial regime. This is particularly important since it serves as an initialization of the higher-order orthogonal iteration (HOOI) scheme, whose convergence to the best low-multilinear-rank approximation depends entirely on its initialization. We give a sufficient condition for the convergence of HOOI and show that the number of iterations before convergence tends to $1$ in the large-dimensional limit.
Adaptive Client Sampling in Federated Learning via Online Learning with Bandit Feedback
Authors: Boxin Zhao; Lingxiao Wang; Ziqi Liu; Zhiqiang Zhang; Jun Zhou; Chaochao Chen; Mladen Kolar
Venue: JMLR 2025 (main)

Abstract: Due to the high cost of communication, federated learning (FL) systems need to sample a subset of clients that are involved in each round of training. As a result, client sampling plays an important role in FL systems as it affects the convergence rate of optimization algorithms used to train machine learning models. Despite its importance, there is limited work on how to sample clients effectively. In this paper, we cast client sampling as an online learning task with bandit feedback, which we solve with an online stochastic mirror descent (OSMD) algorithm designed to minimize the sampling variance. We then theoretically show how our sampling method can improve the convergence speed of federated optimization algorithms over the widely used uniform sampling. Through both simulated and real data experiments, we empirically illustrate the advantages of the proposed client sampling algorithm over uniform sampling and existing online learning-based sampling strategies. The proposed adaptive sampling procedure is applicable beyond the FL problem studied here and can be used to improve the performance of stochastic optimization procedures such as stochastic gradient descent and stochastic coordinate descent.