Compressed Linear Algebra for Declarative Large-Scale Machine Learning

Large-scale Machine Learning (ML) algorithms are often iterative, using repeated read-only data access and I/O-bound matrix-vector multiplications. Hence, it is crucial for performance to fit the data into single-node or distributed main memory to enable fast matrix-vector operations. General-purpose compression struggles to achieve both good compression ratios and fast decompression for block-wise uncompressed operations. Therefore, we introduce Compressed Linear Algebra (CLA) for lossless matrix compression. CLA encodes matrices with lightweight, value-based compression techniques and executes linear algebra operations directly on the compressed representations. We contribute effective column compression schemes, cache-conscious operations, and an efficient sampling-based compression algorithm. Our experiments show good compression ratios and operations performance close to the uncompressed case, which enables fitting larger datasets into available memory. We thereby obtain significant end-to-end performance improvements. Large-scale ML leverages large data collections to find interesting patterns or build robust predictive models.7 Applications range from traditional regression, classification, and clustering to user recommendations and deep learning for unstructured data. The labeled data required to train these ML models is now abundant, thanks to feedback loops in data products and weak supervision techniques. Many ML systems exploit data-parallel frameworks such as Spark20 or Flink2 for parallel model training and scoring on commodity hardware. It remains challenging, however, to train ML models on massive labeled data sets in a cost-effective manner.