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DiFuseR: A Distributed Sketch-based Influence maximization algorithm for GPUs

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arXiv 2024年

作者： Göktürk, Gökhan Kaya, Kamer Faculty of Engineering and Natural Sciences Sabancı University Istanbul34956 Turkey Center of Excellence in Data Analytics Sabancı University Turkey

Influence maximization (IM) aims to find a given number of "seed" vertices that can effectively maximize the expected spread under a given diffusion model. Due to the NP-Hardness of finding an optimal seed set, approximation algorithms are often used for IM. However, these algorithms require a large number of simulations to find good seed sets. In this work, we propose DiFuseR, a blazing-fast, high-quality IM algorithm that can run on multiple GPUs in a distributed setting. DiFuseR is designed to increase GPU utilization, reduce inter-node communication, and minimize overlapping data/computation among the nodes. Based on the experiments with various graphs, containing some of the largest networks available, and diffusion settings, the proposed approach is found to be 3.2× and 12× faster on average on a single GPU and 8 GPUs, respectively. It can achieve up to 8× and 233.7× speedup on the same hardware settings. Furthermore, thanks to its smart load-balancing mechanism, on 8 GPUs, it is on average 5.6× faster compared to its single-GPU performance. © 2024, CC BY.

关键词： expectation maximization algorithm

Prophet Inequalities: Separating Random Order from Order Selection

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arXiv 2023年

作者： Giambartolomei, Giordano Mallmann-Trenn, Frederik Saona, Raimundo King’s College London United Kingdom Institute of Science and Technology Austria

Prophet inequalities are a central object of study in optimal stopping theory. A gambler is sent values in an online fashion, sampled from an instance of independent distributions, in an adversarial, random or selected order, depending on the model. When observing each value, the gambler either accepts it as a reward or irrevocably rejects it and proceeds to observe the next value. The goal of the gambler, who cannot see the future, is maximising the expected value of the reward while competing against the expectation of a prophet (the offline maximum). In other words, one seeks to maximise the gambler-to-prophet ratio of the expectations. The model, in which the gambler selects the arrival order first, and then observes the values, is known as Order Selection. In this model a ratio of 0.7251 is attainable for any instance. Recently, this has been improved up to 0.7258 by Bubna and Chiplunkar (2023). If the gambler chooses the arrival order (uniformly) at random, we obtain the Random Order model. The worst case ratio over all possible instances has been extensively studied for at least 40 years. In a computer-assisted proof, Bubna and Chiplunkar (2023) also showed that this ratio is at most 0.7254 for the Random Order model, thus establishing for the first time that carefully choosing the order, instead of simply taking it at random, benefits the gambler. We give an alternative, non-simulation-assisted proof of this fact, by showing mathematically that in the Random Order model, no algorithm can achieve a ratio larger than 0.7235. This sets a new state-of-the-art hardness for this model, and establishes more formally that there is a real benefit in choosing the order. Copyright © 2023, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Simultaneous Estimation of Many Sparse Networks via Hierarchical Poisson Log-Normal Model

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arXiv 2024年

作者： Ge, Changhao Li, Hongzhe Graduate Group of Applied Mathematics and Computational Science University of Pennsylvania United States Department of Biostatistics Epidemiology and Informatics University of Pennsylvania United States

The advancement of single-cell RNA-sequencing (scRNA-seq) technologies allow us to study the individual level cell-type-specific gene expression networks by direct inference of genes’ conditional independence structures. scRNA-seq data facilitates the analysis of gene expression data across different conditions or samples, enabling simultaneous estimation of condition- or sample-specific gene networks. Since the scRNA-seq data are count data with many zeros, existing network inference methods based on Gaussian graphs cannot be applied to such single cell data directly. We propose a hierarchical Poisson Log-Normal model to simultaneously estimate many such networks to effectively incorporate the shared network structures. We develop an efficient simultaneous estimation method that uses the variational EM and alternating direction method of multipliers (ADMM) algorithms, optimized for parallel processing. Simulation studies show this method outperforms traditional methods in network structure recovery and parameter estimation across various network models. We apply the method to two single cell RNA-seq datasets, a yeast single-cell gene expression dataset measured under 11 different environmental conditions, and a single-cell gene expression data from 13 inflammatory bowel disease patients. We demonstrate that simultaneous estimation can uncover a wider range of conditional dependence networks among genes, offering deeper insights into gene expression mechanisms. © 2024, CC BY.

关键词： expectation maximization algorithm

Multi-modal Image and Radio Frequency Fusion for Optimizing Vehicle Positioning

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arXiv 2024年

作者： Huan, Ouwen Luo, Tao Chen, Mingzhe Beijing Laboratory of Advanced Information Network Beijing University of Posts and Telecommunications Beijing100876 China Department of Electrical and Computer Engineering Institute for Data Science and Computing University of Miami Coral GablesFL33146 United States

In this paper, a multi-modal vehicle positioning framework that jointly localizes vehicles with channel state information (CSI) and images is designed. In particular, we consider an outdoor scenario where each vehicle can communicate with only one BS, and hence, it can upload its estimated CSI to only its associated BS. Each BS is equipped with a set of cameras, such that it can collect a small number of labeled CSI, a large number of unlabeled CSI, and the images taken by cameras. To exploit the unlabeled CSI data and position labels obtained from images, we design an meta-learning based hard expectation-maximization (EM) algorithm. Specifically, since we do not know the corresponding relationship between unlabeled CSI and the multiple vehicle locations in images, we formulate the calculation of the training objective as a minimum matching problem. To reduce the impact of label noises caused by incorrect matching between unlabeled CSI and vehicle locations obtained from images and achieve better convergence, we introduce a weighted loss function on the unlabeled datasets, and study the use of a meta-learning algorithm for computing the weighted loss. Subsequently, the model parameters are updated according to the weighted loss function of unlabeled CSI samples and their matched position labels obtained from images. Simulation results show that the proposed method can reduce the positioning error by up to 61% compared to a baseline that does not use images and uses only CSI fingerprint for vehicle positioning. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

EM algorithms for optimization problems with polynomial objectives

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arXiv 2024年

作者： Asai, Kensuke Gotoh, Jun-Ya Coincheck Inc. Tokyo Japan Department of Data Science for Business Innovation Chuo University Tokyo Japan

The EM (expectation-maximization) algorithm is regarded as an MM (Majorization-Minimization) algorithm for maximum likelihood estimation of statistical models. Expanding this view, this paper demonstrates that by choosing an appropriate probability distribution, even nonstatistical optimization problem can be cast as a negative log-likelihood-like minimization problem, which can be approached by an EM (or MM) algorithm. When a polynomial objective is optimized over a simple polyhedral feasible set and an exponential family distribution is employed, the EM algorithm can be reduced to a natural gradient descent of the employed distribution with a constant step size. This is demonstrated through three examples. In this paper, we demonstrate the global convergence of specific cases with some exponential family distributions in a general form. In instances when the feasible set is not sufficiently simple, the use of MM algorithms can nevertheless be adequately described. When the objective is to minimize a convex quadratic function and the constraints are polyhedral, global convergence can also be established based on the existing results for an entropy-like proximal point algorithm. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

GreediRIS: Scalable Influence maximization using Distributed Streaming Maximum Cover

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arXiv 2024年

作者： Barik, Reet Cappa, Wade Ferdous, S.M. Minutoli, Marco Halappanavar, Mahantesh Kalyanaraman, Ananth Washington State University WA99164 United States Pacific Northwest National Laboratory RichlandWA99354 United States

Influence maximization—the problem of identifying a subset of k influential seeds (vertices) in a network—is a classical problem in network science with numerous applications. The problem is NP-hard, but there exist efficient polynomial time approximations. However, scaling these algorithms still remain a daunting task due to the complexities associated with steps involving stochastic sampling and large-scale aggregations. In this paper, we present a new parallel distributed approximation algorithm for influence maximization with provable approximation guarantees. Our approach, which we call GreediRIS, leverages the RandGreedi framework—a state-of-the-art approach for distributed submodular optimization—for solving a step that computes a maximum k cover. GreediRIS combines distributed and streaming models of computations, along with pruning techniques, to effectively address the communication bottlenecks of the algorithm. Experimental results on up to 512 nodes (32K cores) of the NERSC Perlmutter supercomputer show that GreediRIS can achieve good strong scaling performance, preserve quality, and significantly outperform the other state-of-the-art distributed implementations. For instance, on 512 nodes, the most performant variant of GreediRIS achieves geometric mean speedups of 28.99× and 36.35× for two different diffusion models, over a state-of-the-art parallel implementation. We also present a communication-optimized version of GreediRIS that further improves the speedups by two orders of magnitude. © 2024, CC BY-NC-ND.

关键词： expectation maximization algorithm

Fearless Stochasticity in expectation Propagation

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arXiv 2024年

作者： So, Jonathan Turner, Richard E. University of Cambridge United Kingdom The Alan Turing Institute

expectation propagation (EP) is a family of algorithms for performing approximate inference in probabilistic models. The updates of EP involve the evaluation of moments-expectations of certain functions-which can be estimated from Monte Carlo (MC) samples. However, the updates are not robust to MC noise when performed naively, and various prior works have attempted to address this issue in different ways. In this work, we provide a novel perspective on the moment-matching updates of EP;namely, that they perform natural-gradient-based optimisation of a variational objective. We use this insight to motivate two new EP variants, with updates that are particularly well-suited to MC estimation. They remain stable and are most sample-efficient when estimated with just a single sample. These new variants combine the benefits of their predecessors and address key weaknesses. In particular, they are easier to tune, offer an improved speed-accuracy trade-off, and do not rely on the use of debiasing estimators. We demonstrate their efficacy on a variety of probabilistic inference tasks. © 2024, CC BY.

关键词： expectation maximization algorithm

SimPro: A Simple Probabilistic Framework Towards Realistic Long-Tailed Semi-Supervised Learning

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arXiv 2024年

作者： Du, Chaoqun Han, Yizeng Huang, Gao Department of Automation BNRist Tsinghua University Beijing China

Recent advancements in semi-supervised learning have focused on a more realistic yet challenging task: addressing imbalances in labeled data while the class distribution of unlabeled data remains both unknown and potentially mismatched. Current approaches in this sphere often presuppose rigid assumptions regarding the class distribution of unlabeled data, thereby limiting the adaptability of models to only certain distribution ranges. In this study, we propose a novel approach, introducing a highly adaptable framework, designated as SimPro, which does not rely on any predefined assumptions about the distribution of unlabeled data. Our framework, grounded in a probabilistic model, innovatively refines the expectation-maximization (EM) algorithm by explicitly decoupling the modeling of conditional and marginal class distributions. This separation facilitates a closed-form solution for class distribution estimation during the maximization phase, leading to the formulation of a Bayes classifier. The Bayes classifier, in turn, enhances the quality of pseudo-labels in the expectation phase. Remarkably, the SimPro framework not only comes with theoretical guarantees but also is straightforward to implement. Moreover, we introduce two novel class distributions broadening the scope of the evaluation. Our method showcases consistent state-of-the-art performance across diverse benchmarks and data distribution scenarios. Our code is available at https://***/ LeapLabTHU/SimPro. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

OPTIMIZING BACKWARD POLICIES IN GFLOWNETS VIA TRAJECTORY LIKELIHOOD maximization

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arXiv 2024年

作者： Gritsaev, Timofei Morozov, Nikita Samsonov, Sergey Tiapkin, Daniil HSE University Russia Constructor University Bremen Germany CMAP CNRS École polytechnique Institut Polytechnique de Paris France Université Paris-Saclay CNRS Laboratoire de mathématiques d’Orsay France

Generative Flow Networks (GFlowNets) are a family of generative models that learn to sample objects with probabilities proportional to a given reward function. The key concept behind GFlowNets is the use of two stochastic policies: a forward policy, which incrementally constructs compositional objects, and a backward policy, which sequentially deconstructs them. Recent results show a close relationship between GFlowNet training and entropy-regularized reinforcement learning (RL) problems with a particular reward design. However, this connection applies only in the setting of a fixed backward policy, which might be a significant limitation. As a remedy to this problem, we introduce a simple backward policy optimization algorithm that involves direct maximization of the value function in an entropy-regularized Markov Decision Process (MDP) over intermediate rewards. We provide an extensive experimental evaluation of the proposed approach across various benchmarks in combination with both RL and GFlowNet algorithms and demonstrate its faster convergence and mode discovery in complex environments. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm