Linear Autoencoders (LAEs) have shown strong performance in state-of-the-art recommender systems. However, this success remains largely empirical, with limited theoretical understanding. In this paper, we investigate the generalizability -- a theoretical measure of model performance in statistical learning -- of multivariate linear regression and LAEs. We first propose a PAC-Bayes bound for multivariate linear regression, extending the earlier bound for single-output linear regression by Shalaeva et al., and establish sufficient conditions for its convergence. We then show that LAEs, when evaluated under a relaxed mean squared error, can be interpreted as constrained multivariate linear regression models on bounded data, to which our bound adapts. Furthermore, we develop theoretical methods to improve the computational efficiency of optimizing the LAE bound, enabling its practical evaluation on large models and real-world datasets. Experimental results demonstrate that our bound is tight and correlates well with practical ranking metrics such as Recall@K and NDCG@K.

Earth observation (EO) data provenance is vital for facilitating data sharing and cooperative processing. However, existing techniques for managing EO data provenance still have various weaknesses, including decentralization, traceability, transparency, tamper-proofing, and security protection. Despite being a transformative solution in various domains, the potential of blockchain technology in EO data provenance remains largely unexplored. This article introduces a blockchain-based solution for EO data provenance, aiming to facilitate data sharing and traceability. We have implemented a prototype based on the blockchain technology and conducted a performance evaluation. To the best of authors' knowledge, this is the first paper to explore the application of blockchain in the management of EO data provenance.

Matrix factorization is a powerful method to implement collaborative filtering recommender systems. This article addresses two major challenges, privacy and efficiency, which matrix factorization is facing. We based our work on DS-ADMM, a distributed matrix factorization algorithm with decent efficiency, to achieve the following two pieces of work: (1) Integrated local differential privacy paradigm into DS-ADMM to provide the privacy-preserving property; (2) Introduced a stochastic quantized function to reduce transmission overheads in ADMM to further improve efficiency. We named our work DS-ADMM++, in which one ’+’ refers to differential privacy, and the other ’+’ refers to quantized techniques. DS-ADMM++ is the first to perform efficient and private matrix factorization under the scenarios of differential privacy and DS-ADMM. We conducted experiments with benchmark data sets to demonstrate that our approach provides differential privacy and excellent scalability with a decent loss of accuracy.

A simplified approach to accelerate matrix factorization of big data is to parallelize it. A commonly used method is to divide the matrix into multiple non-intersecting blocks and concurrently calculate them. This operation causes the Load balance problem, which significantly impacts parallel performance and is a big concern. A general belief is that the load balance across blocks is impossible by balancing rows and columns separately. We challenge the belief by proposing an approach of “Balanced Partitioning (BaPa)”. We demonstrate under what circumstance independently balancing rows and columns can lead to the balanced intersection of rows and columns, why, and how. We formally prove the feasibility of BaPa by observing the variance of rating numbers across blocks, and empirically validate its soundness by applying it to two standard parallel matrix factorization algorithms, DSGD and CCD++. Besides, we establish a mathematical model of “Imbalance Degree” to explain further why BaPa works well. BaPa is applied to synchronous parallel matrix factorization, but as a general load balance solution, it has significant application potential.

The latest implementation of the fully homomorphic encryption algorithm (FHEW), FHEW-V2, takes about 0.12 s for a bootstrapping on a single-node computer. It seems much faster than the previous implementations. However, the 30-bit homomorphic addition requires 270 times of bootstrapping; plus those spent on key generation, the total elapsed time climbs to 55 seconds, which is unacceptable. In this article, we reveal how to further optimize FHEW-V2 by focusing on efficiently constructing homomorphic full adders. We tackle inefficiency in FHEW-V2 by massive efforts: First, we explore FHEW-V2 and locate hotspots; second, we leverage the heterogeneous parallel computing model of multicore CPU and GPUs to remove the hotspots to improve performance. The empirical results show that a 30-bit homomorphic addition is completed in 23.8753 s after optimization, gaining an overall speedup of 2.2845; and a 6-bit homomorphic multiplication costs 25.8438, gaining an overall speedup of 2.2435. The 2.2845 speedup is a rough integration of a 13.248 speedup for the key generation and a 1.672 speedup for the bootstrapping; the 2.2435 speedup is a rough integration of the same key generation and a 1.675 speedup for the bootstrapping. We also reveal the strengths and weaknesses of FHEW-V2 by comparing it with a state-of-the-art somewhat homomorphic encryption algorithm, microsoft's simple encrypted arithmetic library (SEAL).