Paul Roussel

Nicolas Grislain, Paul Roussel, Victoria de Sainte Agathe

This paper introduces Qrlew, an open source library that can parse SQL queries into Relations -- an intermediate representation -- that keeps track of rich data types, value ranges, and row ownership; so that they can easily be rewritten into differentially-private equivalent and turned back into SQL queries for execution in a variety of standard data stores. With Qrlew, a data practitioner can express their data queries in standard SQL; the data owner can run the rewritten query without any technical integration and with strong privacy guarantees on the output; and the query rewriting can be operated by a privacy-expert who must be trusted by the owner, but may belong to a separate organization.

Christian J. Walder, Paul Roussel, Richard Nock et al.

We introduce a family of pairwise stochastic gradient estimators for gradients of expectations, which are related to the log-derivative trick, but involve pairwise interactions between samples. The simplest example of our new estimator, dubbed the fundamental trick estimator, is shown to arise from either a) introducing and approximating an integral representation based on the fundamental theorem of calculus, or b) applying the reparameterisation trick to an implicit parameterisation under infinitesimal perturbation of the parameters. From the former perspective we generalise to a reproducing kernel Hilbert space representation, giving rise to a locality parameter in the pairwise interactions mentioned above, yielding our representer trick estimator. The resulting estimators are unbiased and shown to offer an independent component of useful information in comparison with the log-derivative estimator. We provide a further novel theoretical analysis which further characterises the variance reduction afforded by the new techniques. Promising analytical and numerical examples confirm the theory and intuitions behind the new estimators.