Large-scale machine learning (ML) algorithms are often iterative, using repeated read-only data access and I/Obound 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. General-purpose, heavy-and lightweight compression techniques struggle to achieve both good compression ratios and fast decompression speed to enable block-wise uncompressed operations. Hence, we initiate work on compressed linear algebra (CLA), in which lightweight database compression techniques are applied to matrices and then linear algebra operations such as matrix-vector multiplication are executed directly on the compressed representations. 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 that allow us to fit larger datasets into available memory. We thereby obtain significant end-to-end performance improvements up to 26x or reduced memory requirements.
Recent work on compressed linear algebra (CLA) shows that columnar compression for matrices (tables) could help reduce file sizes for linear algebra-based ML programs in SystemML REF .
Compressed Linear Algebra for Large-Scale Machine Learning
PVLDB
PVLDB
Computer Science