  In this paper, we present a study of a kernel-based consensual aggregation on
randomly projected high-dimensional features of predictions for regression. The
aggregation scheme is composed of two steps: the high-dimensional features of
predictions, given by a large number of regression estimators, are randomly
projected into a smaller subspace using Johnson-Lindenstrauss Lemma in the
first step, and a kernel-based consensual aggregation is implemented on the
projected features in the second step. We theoretically show that the
performance of the aggregation scheme is close to the performance of the
aggregation implemented on the original high-dimensional features, with high
probability. Moreover, we numerically illustrate that the aggregation scheme
upholds its performance on very large and highly correlated features of
predictions given by different types of machines. The aggregation scheme allows
us to flexibly merge a large number of redundant machines, plainly constructed
without model selection or cross-validation. The efficiency of the proposed
method is illustrated through several experiments evaluated on different types
of synthetic and real datasets.
