  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.
