A novel, computationally tractable algorithm flags in big matrices every column associated in any way with others or a dependent variable, with much higher power when columns are linked like mutations in chromosomes

Scanning exhaustively a big data matrix DM for subsets of independent variables IVs that are associated with a dependent variable DV is computationally tractable only for 1- and 2-IV effects. I present a highly computationally tractable Participation-In-Association Score (PAS) that in a DM with markers flags every column that is strongly associated with others. PAS examines no column subsets and its computational cost grows linearly with DM columns, remaining reasonable even in million-column DMs. PAS exploits how associations of markers in DM rows cause matches associations in the rows' pairwise comparisons. For every such comparison with a match at a tested column, PAS computes the other matches by modifying the comparison's total matches (scored once per DM), yielding a distribution of conditional matches that is perturbed by associations of the tested column. Equally tractable is dvPAS that flags DV-associated IVs by permuting the markers in the DV. P values are obtained by permutation and Sidak-corrected for multiple tests, bypassing model selection. Simulations show that i) PAS and dvPAS generate uniform-(0,1)-distributed type I error in null DMs and ii) detect randomly encountered binary and trinary models of significant n-column association and n-IV association with a binary DV, respectively, with power in the order of magnitude of exhaustive evaluation's and false positives that are uniform-(0,1)-distributed or straightforwardly tuned to be so. Power to detect 2-way DV-associated 100-marker+ runs is non-parametrically ultimate but that to detect pure n-column associations and pure n-IV DV associations sinks exponentially as n increases. Power increases about twofold in trinary vs. binary DMs and in a major way when there are background associations like between mutations in chromosomes, specially in trinary DMs where dvPAS filters said background most effectively.