τDQ: Tensor Methods for Data Quality Validation in Business Intelligence via GPU-Accelerated Completion and Decomposition

Abstract

We introduce τDQ (tau-DQ), a GPU-accelerated framework for detecting missing and potentially inaccurate data in business intelligence through tensor methods. Unlike conventional profiling that validates individual fields, τDQ identifies struc- tural anomalies in multi-dimensional relationships. Tensor completion surfaces gaps—expected combinations that are missing from the data. Tensor decomposition flags suspicious values—records that exist but don’t fit the low-rank structure of valid busi- ness data. Together, these techniques catch data quality failures invisible to rule-based validation: the missing regional coverage, the transaction that shouldn’t exist, the KPI attribution that violates hierarchy.τDQ achieves 25–30× speedup over Spark-RAPIDS while detecting 73% more structural defects than traditional approaches.