  We derandomize G. Valiant's [J. ACM 62 (2015) Art. 13] subquadratic-time
algorithm for finding outlier correlations in binary data. Our derandomized
algorithm gives deterministic subquadratic scaling essentially for the same
parameter range as Valiant's randomized algorithm, but the precise constants we
save over quadratic scaling are more modest. Our main technical tool for
derandomization is an explicit family of correlation amplifiers built via a
family of zigzag-product expanders in Reingold, Vadhan, and Wigderson [Ann. of
Math. 155 (2002) 157--187]. We say that a function
$f:\{-1,1\}^d\rightarrow\{-1,1\}^D$ is a correlation amplifier with threshold
$0\leq\tau\leq 1$, error $\gamma\geq 1$, and strength $p$ an even positive
integer if for all pairs of vectors $x,y\in\{-1,1\}^d$ it holds that (i)
$|\langle x,y\rangle|<\tau d$ implies $|\langle
f(x),f(y)\rangle|\leq(\tau\gamma)^pD$; and (ii) $|\langle x,y\rangle|\geq\tau
d$ implies $\bigl(\frac{\langle x,y\rangle}{\gamma d}\bigr)^pD
  \leq\langle f(x),f(y)\rangle\leq
  \bigl(\frac{\gamma\langle x,y\rangle}{d}\bigr)^pD$.
