Subsampled online matrix factorization with convergence guarantees
This work addresses the computational bottleneck of handling very large matrices in machine learning, offering a practical solution for big data applications.
The authors tackled the problem of scaling matrix factorization to massive datasets exceeding 1TB by developing an algorithm that streams and subsamples matrix columns, achieving large speed-ups compared to non-subsampling methods due to feature redundancy in high-dimensional settings.
We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains morethan 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low complexity per iteration andreasonable memory footprint. In contrast to previous online matrix factorization methods, our approach relies on low-dimensional statistics from past iterates to control the extra variance introduced by subsampling. We present a convergence analysis that guarantees us to reach a stationary point of the problem. Large speed-ups can be obtained compared to previous online algorithms that do not perform subsampling, thanks to the feature redundancy that often exists in high-dimensional settings.