Compressed linear algebra for large-scale machine learning

Large-scale machine learning algorithms are often iterative, using repeated read-only data access and I/O-bound matrix-vector multiplications to converge to an optimal model. It is crucial for performance to fit the data into single-node or distributed main memory and enable fast matrix-vector operations on in-memory data. General-purpose, heavy- and lightweight compression techniques struggle to achieve both good compression ratios and fast decompression speed to enable block-wise uncompressed operations. Therefore, we initiate work—inspired by database compression and sparse matrix formats—on value-based compressed linear algebra (CLA), in which heterogeneous, lightweight database compression techniques are applied to matrices, and then linear algebra operations such as matrix-vector multiplication are executed directly on the compressed representation. We contribute effective column compression schemes, cache-conscious operations, and an efficient sampling-based compression algorithm. Our experiments show that CLA achieves in-memory operations performance close to the uncompressed case and good compression ratios, which enables fitting substantially larger datasets into available memory. We thereby obtain significant end-to-end performance improvements up to \(9.2\mathrm{x}\).