Last Updated on August 6, 2019 Training a deep neural network that can generalize well to new data is a challenging problem. A model with too little capacity cannot learn the problem, whereas a model with too much capacity can learn it too well and overfit the training dataset. Both cases result in a model that does not generalize well. A modern approach to reducing generalization error is to use a larger model that may be required to use regularization […]

Last Updated on August 6, 2019 How to Improve Performance By Combining Predictions From Multiple Models. Deep learning neural networks are nonlinear methods. They offer increased flexibility and can scale in proportion to the amount of training data available. A downside of this flexibility is that they learn via a stochastic training algorithm which means that they are sensitive to the specifics of the training data and may find a different set of weights each time they are trained, which […]

Last Updated on August 28, 2020 Deep learning neural network models are highly flexible nonlinear algorithms capable of learning a near infinite number of mapping functions. A frustration with this flexibility is the high variance in a final model. The same neural network model trained on the same dataset may find one of many different possible “good enough” solutions each time it is run. Model averaging is an ensemble learning technique that reduces the variance in a final neural network […]

Last Updated on August 25, 2020 Ensemble learning are methods that combine the predictions from multiple models. It is important in ensemble learning that the models that comprise the ensemble are good, making different prediction errors. Predictions that are good in different ways can result in a prediction that is both more stable and often better than the predictions of any individual member model. One way to achieve differences between models is to train each model on a different subset […]

Last Updated on August 25, 2020 Predictive modeling problems where the training dataset is small relative to the number of unlabeled examples are challenging. Neural networks can perform well on these types of problems, although they can suffer from high variance in model performance as measured on a training or hold-out validation datasets. This makes choosing which model to use as the final model risky, as there is no clear signal as to which model is better than another toward […]

Last Updated on August 25, 2020 A modeling averaging ensemble combines the prediction from each model equally and often results in better performance on average than a given single model. Sometimes there are very good models that we wish to contribute more to an ensemble prediction, and perhaps less skillful models that may be useful but should contribute less to an ensemble prediction. A weighted average ensemble is an approach that allows multiple models to contribute to a prediction in […]

Last Updated on August 28, 2020 Model averaging is an ensemble technique where multiple sub-models contribute equally to a combined prediction. Model averaging can be improved by weighting the contributions of each sub-model to the combined prediction by the expected performance of the submodel. This can be extended further by training an entirely new model to learn how to best combine the contributions from each submodel. This approach is called stacked generalization, or stacking for short, and can result in […]

Last Updated on August 25, 2020 Supervised learning is challenging, although the depths of this challenge are often learned then forgotten or willfully ignored. This must be the case, because dwelling too long on this challenge may result in a pessimistic outlook. In spite of the challenge, we continue to wield supervised learning algorithms and they perform well in practice. Fundamental to the challenge of supervised learning, are the concerns: How much data is needed to reasonably approximate the unknown […]

Last Updated on August 28, 2020 Model ensembles can achieve lower generalization error than single models but are challenging to develop with deep learning neural networks given the computational cost of training each single model. An alternative is to train multiple model snapshots during a single training run and combine their predictions to make an ensemble prediction. A limitation of this approach is that the saved models will be similar, resulting in similar predictions and predictions errors and not offering […]

Last Updated on August 28, 2020 The training process of neural networks is a challenging optimization process that can often fail to converge. This can mean that the model at the end of training may not be a stable or best-performing set of weights to use as a final model. One approach to address this problem is to use an average of the weights from multiple models seen toward the end of the training run. This is called Polyak-Ruppert averaging […]