# Lossy compression of matrices by black-box optimisation of mixed integer nonlinear programming

arXiv: https://arxiv.org/abs/2204.10579 · HTML: https://mlsanity.com/paper/2204.10579/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 29 references that are in the map.
- First posted on arXiv 22 Apr 2022.

## Builds on (most cited first, 10 of 10)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Combinatorial Bayesian Optimization using the Graph Cartesian Product](https://mlsanity.com/paper/1902.00448/) (2019)
- [Bayesian Optimization of Combinatorial Structures](https://mlsanity.com/paper/1806.08838/) (2018)
- [Combining Latent Space and Structured Kernels for Bayesian Optimization over Combinatorial Spaces](https://mlsanity.com/paper/2111.01186/) (2021)
- [Mixed-Variable Bayesian Optimization](https://mlsanity.com/paper/1907.01329/) (2019)
- [Nonnegative/binary matrix factorization with a D-Wave quantum annealer](https://mlsanity.com/paper/1704.01605/) (2017)
- [Application of QUBO solver using black-box optimization to structural design for resonance avoidance](https://mlsanity.com/paper/2204.04906/) (2022)
- [Kernels over Sets of Finite Sets using RKHS Embeddings, with Application to Bayesian (Combinatorial) Optimization](https://mlsanity.com/paper/1910.04086/) (2019)
- [Bayesian Variational Optimization for Combinatorial Spaces](https://mlsanity.com/paper/2011.02004/) (2020)
- [Lossy compression of statistical data using quantum annealer](https://mlsanity.com/paper/2110.02142/) (2021)

## Built on by (most cited first, 6 of 6)

- [Random Postprocessing for Combinatorial Bayesian Optimization](https://mlsanity.com/paper/2309.02842/) (2023)
- [Real-Time Black-Box Optimization for Dynamic Discrete Environments Using Embedded Ising Machines](https://mlsanity.com/paper/2506.16924/) (2025)
- [Efficient Bit Labeling in Factorization Machines with Annealing for Traveling Salesman Problem](https://mlsanity.com/paper/2407.02091/) (2024)
- [Subsampling Factorization Machine Annealing](https://mlsanity.com/paper/2508.08778/) (2025)
- [Quantum Computing and AI: Perspectives on Advanced Automation in Science and Engineering](https://mlsanity.com/paper/2505.10012/) (2025)
- [Wall-Clock Complexity for Zeroth-Order Optimization with Tunable Oracle Fidelity](https://mlsanity.com/paper/2605.31346/) (2026)

## Abstract (arXiv)

In edge computing, suppressing data size is a challenge for machine learning models that perform complex tasks such as autonomous driving, in which computational resources (speed, memory size and power) are limited. Efficient lossy compression of matrix data has been introduced by decomposing it into the product of an integer and real matrices. However, its optimisation is difficult as it requires simultaneous optimisation of an integer and real variables. In this paper, we improve this optimisation by utilising recently developed black-box optimisation (BBO) algorithms with an Ising solver for integer variables. In addition, the algorithm can be used to solve mixed-integer programming problems that are linear and non-linear in terms of real and integer variables, respectively. The differences between the choice of Ising solvers (simulated annealing, quantum annealing and simulated quenching) and the strategies of the BBO algorithms (BOCS, FMQA and their variations) are discussed for further development of the BBO techniques.