  It is usual to consider data protection and learnability as conflicting
objectives. This is not always the case: we show how to jointly control
inference --- seen as the attack --- and learnability by a noise-free process
that mixes training examples, the Crossover Process (cp). One key point is that
the cp~is typically able to alter joint distributions without touching on
marginals, nor altering the sufficient statistic for the class. In other words,
it saves (and sometimes improves) generalization for supervised learning, but
can alter the relationship between covariates --- and therefore fool measures
of nonlinear independence and causal inference into misleading ad-hoc
conclusions. For example, a cp~can increase / decrease odds ratios, bring
fairness or break fairness, tamper with disparate impact, strengthen, weaken or
reverse causal directions, change observed statistical measures of dependence.
For each of these, we quantify changes brought by a cp, as well as its
statistical impact on generalization abilities via a new complexity measure
that we call the Rademacher cp~complexity. Experiments on a dozen readily
available domains validate the theory.
