Consensual Aggregation on Random Projected High-dimensional Features for Regression

TL;DR

This paper introduces a kernel-based consensual aggregation method for high-dimensional regression predictions, utilizing random projections to reduce dimensionality while maintaining performance, and demonstrates its effectiveness on synthetic and real datasets.

Contribution

The paper proposes a novel aggregation scheme combining random projections and kernel methods, enabling efficient merging of many predictors without model selection or cross-validation.

Findings

Performance close to original high-dimensional aggregation with high probability

Effective on large, highly correlated feature sets from diverse models

Demonstrated robustness and efficiency on synthetic and real data

Abstract

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.