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Distributed Approximate Matrix Computations

Sarzaeem, Mohammad Amin | 2025

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 58595 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Aref, Mohammad Reza; Yassaee Meybodi, Mohammad Hossein
  7. Abstract:
  8. Matrix computations are the fundamental operations in fields such as machine learning and optimization. With the rapid growth of data dimensions, performing these computations in a centralized manner has become increasingly infeasible. Hence, distributed computation has emerged as an efficient approach to enhance both speed and scalability. To address inherent challenges of distributed processing—such as slow nodes (stragglers) and privacy preservation—utilizing appropriate coding structures is essential. Due to the critical role of matrix multiplication, numerous coded distributed methods have been proposed. Most of these approaches focus on exact recovery of the product; however, in practice, data is often noisy, and enforcing exact reconstruction imposes strict constraints on the system, significantly increasing the number of required processors. This limitation has motivated a growing body of research on distributed approximate matrix multiplication. These methods employ techniques such as data compression to reduce processor requirements while ensuring approximate recovery. Nevertheless, many of these approaches suffer from theoretical deficiencies or are effective only under specific conditions. In this work, we present a fundamental study of distributed approximate matrix multiplication and propose efficient frameworks by leveraging sketching techniques, optimization-based methods, and differential privacy. Furthermore, building on these approaches, we introduce a method for distributed computation of matrix inversion
  9. Keywords:
  10. Differential Privacy ; Matrix Sketching ; Coded Distributed Computing ; Approximate Matrix Multiplication ; Privacy Preserving ; Data Compression

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