This post was co-written with Baptiste Rocca. This old saying expresses pretty well the underlying idea that rules the very powerful "ensemble methods" in machine learning. Roughly, ensemble learning methods, that often trust the top rankings of many machine learning competitions (including Kaggle's competitions), are based on the hypothesis that combining multiple models together can often produce a much more powerful model. The purpose of this post is to introduce various notions of ensemble learning. We will give the reader some necessary keys to well understand and use related methods and be able to design adapted solutions when needed.

In this article supervised learning problems are solved using soft rule ensembles. We first review the importance sampling learning ensembles (ISLE) approach that is useful for generating hard rules. The soft rules are then obtained with logistic regression from the corresponding hard rules. In order to deal with the perfect separation problem related to the logistic regression, Firth's bias corrected likelihood is used. Various examples and simulation results show that soft rule ensembles can improve predictive performance over hard rule ensembles.

Ensembles over neural network weights trained from different random initialization, known as deep ensembles, achieve state-of-the-art accuracy and calibration. The recently introduced batch ensembles provide a drop-in replacement that is more parameter efficient. In this paper, we design ensembles not only over weights, but over hyperparameters to improve the state of the art in both settings. For best performance independent of budget, we propose hyper-deep ensembles, a simple procedure that involves a random search over different hyperparameters, themselves stratified across multiple random initializations. Its strong performance highlights the benefit of combining models with both weight and hyperparameter diversity.

Ensemble methods are meta-algorithms that combine several machine learning techniques into one predictive model in order to decrease variance (bagging), bias (boosting), or improve predictions (stacking). Most ensemble methods use a single base learning algorithm to produce homogeneous base learners, i.e. learners of the same type, leading to homogeneous ensembles. There are also some methods that use heterogeneous learners, i.e. learners of different types, leading to heterogeneous ensembles. In order for ensemble methods to be more accurate than any of its individual members, the base learners have to be as accurate as possible and as diverse as possible. Bagging stands for bootstrap aggregation.

Model inversion (MI), where an adversary abuses access to a trained Machine Learning (ML) model in order to infer sensitive information about the model's original training data, has gotten a lot of attention in recent years. The trained model under assault is frequently frozen during MI and used to direct the training of a generator, such as a Generative Adversarial Network, to rebuild the distribution of the model's original training data. As a result, scrutiny of the capabilities of MI techniques is essential for the creation of appropriate protection techniques. Reconstruction of training data with high quality using a single model is complex. However, existing MI literature does not consider targeting many models simultaneously, which could offer the adversary extra information and viewpoints.