Dual-Bound FORCE: Conditional Row-Contribution Bounds for Streaming Normalized Transformed-Scatter Sketches

Source abstract

High-dimensional monitoring and subspace analysis require contamination-resistant dependence summaries with subquadratic state complexity. Coordinatewise clipping limits individual entries but allows total row contribution to grow with dimension. Dual-Bound Fast Outlier-Robust Correlation Estimation combines fixed median-based calibration, coordinate clipping, parallel and residual contraction, and Frequent Directions sketching to estimate a normalized transformed second moment. Conditional on calibration, an exact-arithmetic companion has a simultaneous row envelope and an error decomposition for sampling, whole-row replacement, and sketch approximation. The implemented dense output is the Gram matrix of a column-normalized sketch factor, which is positive semidefinite in exact arithmetic and shares its factor with the subspace route. Active and peak calibration states are linear in dimension for fixed rank and calibration size before dense-output materialization. Minimax development over 112 configurations selected the reported parameter tuple. In matched-window synthetic experiments, Dual-Bound reduced mean projection error by 0.0858 under casewise and 0.0150 under coordinatewise Cauchy replacement relative to a tuned median-absolute-deviation version of Sketch-based Fast Outlier-Robust Correlation Estimation; clean and bounded structural differences were −0.0015 and −0.0020. Results depended on configuration and mechanism. External projection and donor-balanced reconstruction errors remained between 0.97 and 1.00, so biological recovery and population validation were not demonstrated. The analysis provides no unconditional calibration or convergence guarantee, no useful guarantee in terms of the cell-fault fraction, and no end-to-end implementation or unconditional floating-point guarantee. These results establish a focused design for conditional transformed-scatter sketching in high-dimensional streams.