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Randomized block Krylov method for approximation of truncated tensor SVD

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arXiv 2025年

作者： Kooshkghazi, Malihe Nobakht Ahmadi-Asl, Salman de Almeida, André L.F. Lab of Machine Learning and Knowledge Representation Innopolis University Innopolis420500 Russia Department of Teleinformatics Engineering Federal University of Ceara Fortaleza Brazil

This paper is devoted to studying the application of the block Krylov subspace method for approximation of the truncated tensor SVD (T-SVD). The theoretical results of the proposed randomized approach are presented. Several experimental experiments using synthetics and real-world data are conducted to verify the efficiency and feasibility of the proposed randomized approach, and the numerical results show that the proposed method provides promising results. Applications of the proposed approach to data completion and data compression are presented. © 2025, CC BY.

关键词： Numerical methods

Low-Rank Matrix and Tensor Decomposition Using Randomized Two-Sided Subspace Iteration With Application to Video Reconstruction

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Low-Rank Matrix and Tensor Decomposition Using Randomized Tw...

IEEE International Conference on Image Processing

作者： Maboud F. Kaloorazi Salman Ahmadi-Asl Susanto Rahardja School of Electronic Engineering Xi’an Shiyou University China Lab of Machine Learning and Knowledge Representation Innopolis University Russia Engineering Cluster Singapore Institute of Technology Singapore

ISBN: (数字)9798350349399

ISBN: (纸本)9798350349405

The low-rank approximation of big data matrices and tensors plays a pivotal role in many modern applications. Recently, the randomized subspace iteration has shown to be a powerful tool in approximating large matrices. In this paper we present a rank-revealing, two-sided variant of the randomized subspace iteration. Novelty of our work lies in the utilization of the unpivoted QR factorization, rather than the singular value decomposition (SVD), for factorizing the compressed matrix. We provide bounds on the rank-revealingness of our algorithm as well as bounds on the error of the low-rank approximations, in both 2- and Frobenius norm. In addition, we employ the proposed algorithm to efficiently compute the low rank tensor decomposition using the truncated higher-order SVD. We conduct tests on (i) two classes of matrices, and (ii) synthetic data tensor and real dataset to demonstrate the efficacy of the proposed algorithms.

关键词： Tensors Image coding Supervised learning Approximation algorithms Matrix decomposition Reliability Task analysis

Randomized algorithms for Kroncecker tensor decomposition and applications

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arXiv 2024年

作者： Ahmadi-Asl, Salman Rezaeian, Naeim de Almeida, André L.F. Liu, Yipeng Lab of Machine Learning and Knowledge Representation Innopolis University Innopolis420500 Russia Peoples’ Friendship University of Russia Moscow Russia Department of Teleinformatics Engineering Federal University of Ceara Fortaleza Brazil Chengdu611731 China

This paper proposes fast randomized algorithms for computing the Kronecker Tensor Decomposition (KTD). The proposed algorithms can decompose a given tensor into the KTD format much faster than the existing state-of-the-art algorithms. Our principal idea is to use the randomization framework to reduce computational complexity significantly. We provide extensive simulations to verify the effectiveness and performance of the proposed randomized algorithms with several orders of magnitude acceleration compared to the deterministic one. Our simulations use synthetics and real-world datasets with applications to tensor completion, video/image compression, image denoising, and image super-resolution. © 2024, CC BY.

关键词： Tensors

RepFair-GAN: Mitigating representation Bias in GANs Using Gradient Clipping

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arXiv 2022年

作者： Kenfack, Patrik Joslin Sabbagh, Kamil Rivera, Adín Ramírez Khan, Adil Machine Learning and Knowledge Representation Lab Innopolis University Innopolis Russia Departments of Informatics University of Oslo Oslo Norway

Fairness has become an essential problem in many domains of machine learning (ML), such as classification, natural language processing, and Generative Adversarial Networks (GANs). In this research effort, we study the unfairness of GANs. We formally define a new fairness notion for generative models in terms of the distribution of generated samples sharing the same protected attributes (gender, race, etc.). The defined fairness notion (representational fairness) requires the distribution of the sensitive attributes at the test time to be uniform, and, in particular for GAN model, we show that this fairness notion is violated even when the dataset contains equally represented groups, i.e., the generator favors generating one group of samples over the others at the test time. In this work, we shed light on the source of this representation bias in GANs along with a straightforward method to overcome this problem. We first show on two widely used datasets (MNIST, SVHN) that when the norm of the gradient of one group is more important than the other during the discriminator’s training, the generator favors sampling data from one group more than the other at test time. We then show that controlling the groups’ gradient norm by performing group-wise gradient norm clipping in the discriminator during the training leads to a more fair data generation in terms of representational fairness compared to existing models while preserving the quality of generated samples. © 2022, CC BY.

关键词： Generative adversarial networks

Domain generalization using ensemble learning

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arXiv 2021年

作者： Mesbah, Yusuf Ibrahim, Youssef Youssry Khan, Adil Mehood Machine Learning and Knowledge Representation Lab Innopolis University Tatarstan Russia

Domain generalization is a sub-field of transfer learning that aims at bridging the gap between two different domains in the absence of any knowledge about the target domain. Our approach tackles the problem of a model's weak generalization when it is trained on a single source domain. From this perspective, we build an ensemble model on top of base deep learning models trained on a single source to enhance the generalization of their collective prediction. The results achieved thus far have demonstrated promising improvements of the ensemble over any of its base learners. Copyright © 2021, The Authors. All rights reserved.

关键词： Deep learning

NONNEGATIVE TENSOR DECOMPOSITION VIA COLlabORATIVE NEURODYNAMIC OPTIMIZATION

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arXiv 2024年

作者： Ahmadi-Asl, Salman Leplat, Valentin Phan, Anh-Huy Cichocki, Andrzej Lab of Machine Learning and Knowledge Representation Innopolis University Innopolis Russia Skolkovo Institute of Science and Technology Center for Artificial Intelligence Technology Moscow Russia Innopolis University Innopolis Russia Systems Research Institute of Polish Academy of Science Warsaw Poland

This paper introduces a novel collaborative neurodynamic model for computing nonnegative Canonical Polyadic Decomposition (CPD). The model relies on a system of recurrent neural networks to solve the underlying nonconvex optimization problem associated with nonnegative CPD. Additionally, a discrete-time version of the continuous neural network is developed. To enhance the chances of reaching a potential global minimum, the recurrent neural networks are allowed to communicate and exchange information through particle swarm optimization (PSO). Convergence and stability analyses of both the continuous and discrete neurodynamic models are thoroughly examined. Experimental evaluations are conducted on random and real-world datasets to demonstrate the effectiveness of the proposed approach. © 2024, CC BY.

关键词： Particle swarm optimization (PSO)

Impact of Model Ensemble on the Fairness of Classifiers in machine learning

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Impact of Model Ensemble on the Fairness of Classifiers in M...

2021 International Conference on Applied Artificial Intelligence, ICAPAI 2021

作者： Kenfack, Patrik Joslin Khan, Adil Mehmood Ahsan Kazmi, S.M. Hussain, Rasheed Oracevic, Alma Khattak, Asad Masood Networks and Blockchain Lab Innopolis University Innopolis Russia Machine Learning and Knowledge Representation Lab Innopolis University Innopolis Russia College of Technological Innovation Zayed University Abu Dhabi United Arab Emirates

ISBN: (纸本)9781728159348

machine learning (ML) models are trained using historical data that may contain stereotypes of the society (biases). These biases will be inherently learned by the ML models which might eventually result in discrimination against certain subjects, for instance, people with certain protected characteristics (race, gender, age, religion, etc.). Since the decision provided by ML models might affect people's lives, fairness of these models becomes crucially important. When training a model with fairness constraints, a significant loss in accuracy relative to the unconstrained model may be unavoidable. Reducing the trade-off between fairness and accuracy is an active research question within the fair ML community, i.e., to provide models with high accuracy with as little bias as possible. In this paper, we extensively investigate the fairness metrics over different ML models and study the impact of ensemble models on fairness. To this end, we compare different ensemble strategies and empirically show which strategy is preferable for different fairness metrics. Furthermore, we also propose a novel weighting technique that allows a balance between fairness and accuracy. In essence, we assign weights such that they are proportional to classifiers' performance in term of fairness and accuracy. Our experimental results show that our weighting technique reduces the trade-off between fairness and accuracy in ensemble models. © 2021 IEEE.

关键词： machine learning

Adversarial stacked auto-encoders for fair representation learning

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arXiv 2021年

作者： Kenfack, Patrik Joslin Khan, Adil Mehmood Hussain, Rasheed Kazmi, S.M. Ahsan Networks and Blockchain Lab Innopolis University Innopolis Russia Machine Learning and Knowledge Representation Lab Innopolis University Innopolis Russia

Training machine learning models with the only accuracy as a final goal may promote prejudices and discriminatory behaviors embedded in the data. One solution is to learn latent representations that fulfill specific fairness metrics. Different types of learning methods are employed to map data into the fair representational space. The main purpose is to learn a latent representation of data that scores well on a fairness metric while maintaining the usability for the downstream task. In this paper, we propose a new fair representation learning approach that leverages different levels of representation of data to tighten the fairness bounds of the learned representation. Our results show that stacking different auto-encoders and enforcing fairness at different latent spaces result in an improvement of fairness compared to other existing approaches. © 2021, CC BY.

关键词： learning systems

Efficient Algorithms for Low Tubal Rank Tensor Approximation with Applications to Image Compression, Super-Resolution and Deep learning

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arXiv 2024年

作者： Ahmadi-Asl, Salman Rezaeian, Naeim Caiafa, Cesar F. de Almeida, André L.F. Lab of Machine Learning and Knowledge Representation Innopolis University Innopolis420500 Russia Peoples’ Friendship University of Russia Moscow Russia Instituto Argentino de Radioastronomia—CCT La Plata CONICET/CIC-PBA/UNLP Villa Elisa1894 Argentina Department of Teleinformatics Engineering Federal University of Ceara Fortaleza Brazil

In this paper we propose efficient randomized fixed-precision techniques for low tubal rank approximation of tensors. The proposed methods are faster and more efficient than the existing fixed-precision algorithms for approximating the truncated tensor SVD (T-SVD). Besides, there are a few works on randomized single-pass algorithms for computing low tubal rank approximation of tensors, none of them experimentally reports the robustness of such algorithms for low-rank approximation of real-world data tensors e.g., images and videos. The current single-pass algorithms for tensors are generalizations of those developed for matrices to tensors. However, the single-pass randomized algorithms for matrices have been recently improved and stabilized. Motivated by this progress, in this paper, we also generalize them to the tensor case based on the tubal product (T-product). We conduct extensive simulations to study the robustness of them compared with the existing single-pass randomized algorithms. In particular, we experimentally found that single-pass algorithms with the sketching parameters of equal sizes usually lead to ill-conditioned tensor least-squares problems and inaccurate results. It is experimentally shown that our proposed single-pass algorithms are robust in this sense. Numerical results demonstrate that under the same conditions (setting the same hyper-parameters), our proposed algorithms provide better performance. Three applications to image compression, super-resolution problem and deep learning are also presented. © 2024, CC BY.

关键词： Tensors