# Consensual Aggregation on Random Projected High-dimensional Features for Regression

arXiv: https://arxiv.org/abs/2204.02606 · HTML: https://mlsanity.com/paper/2204.02606/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 55 references that are in the map.
- First posted on arXiv 6 Apr 2022.

## Builds on (most cited first, 5 of 5)

- [COBRA: A Combined Regression Strategy](https://mlsanity.com/paper/1303.2236/) (2013)
- [Pycobra: A Python Toolbox for Ensemble Learning and Visualisation](https://mlsanity.com/paper/1707.00558/) (2017)
- [Aggregation using input-output trade-off](https://mlsanity.com/paper/1803.03166/) (2018)
- [Statistical learning for wind power : a modeling and stability study towards forecasting](https://mlsanity.com/paper/1610.01000/) (2016)
- [Non-linear aggregation of filters to improve image denoising](https://mlsanity.com/paper/1904.00865/) (2019)

## Abstract (arXiv)

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.