5/20/2023 0 Comments Nextime ensemble![]() Boosting sequentially reweights the training samples forcing the model to attend to the training examples with higher loss values.Bagging bootstraps the training set, estimates many copies of a model on the resulting samples, and then averages their predictions.There are several approaches to building ensembles: In addition to that, ensembling can hurt interpretability of more transparent machine learning algorithms like decision trees by blurring the decision boundaries of individual models - this point does not really apply to neural networks for which the issue of interpretability arises already on the individual model level. Why almost, though? Because there is always a lingering problem of computational cost given how resource hungry the most powerful models (yes, neural networks) are. Given that ensembling and diversification are conceptually related, and in some problems, the two are mathematically equivalent, I decided to give the post its title. “Diversification is the only free lunch in finance” is the quote attributed to Harry Markowitz, the father of the Modern Portfolio Theory. This resonates with me deeply, as I am a finance professional-ensembling is akin to building a robust portfolio consisting of many individual assets and sacrificing higher expected returns on some of them in favor of an overall reduction in risk by diversifying investments. ![]() Strong ensembles comprise models that are accurate, performing well on their own, yet diverse in the sense of making different mistakes. ConclusionĪn ensemble is a collection of models designed to outperform every single one of them by combining their predictions. Ensembles of Neural Networks: the Role of Loss Surface Geometry V. Building Ensembles of Neural Networks IV. Ensembling improves the performance of neural networks not only by dampening their inherent sensitivity to noise but also by combining qualitatively different and uncorrelated solutions.There are ensemble methods that admit realistic target functions which are not suitable as direct optimization objectives for ML models (think of using cross-entropy for training while being interested in some other metric like accuracy).Strong ensembles consist of models that are both accurate and diverse.Towards the end of the post, I discuss the effectiveness of ensemble methods in deep learning in the context of the current literature on the loss surface geometry of neural networks. I then introduce a simple ensemble optimization algorithm and demonstrate how to apply it to build ensembles of neural networks with Python and PyTorch. I begin with a brief overview of some common ensemble techniques and outline their weaknesses. In this post, I cover the somewhat overlooked topic of ensemble optimization. I am grateful to Tetyana Drobot and Igor Pozdeev for their comments and suggestions. A notebook accompanying this post can be found here.
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