How To Prevent Overfitting Machine Learning

How to Avert Overfitting in Deep Learning Neural Networks

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 as well much capacity can learn information technology too well and overfit the training dataset. Both cases result in a model that does not generalize well.

A modernistic arroyo to reducing generalization error is to utilize a larger model that may be required to use regularization during training that keeps the weights of the model small. These techniques not only reduce overfitting, but they can as well lead to faster optimization of the model and better overall performance.

In this mail, you will observe the trouble of overfitting when training neural networks and how it tin be addressed with regularization methods.

Afterward reading this post, y'all will know:

• Underfitting can easily exist addressed by increasing the chapters of the network, but overfitting requires the use of specialized techniques.
• Regularization methods similar weight decay provide an easy style to control overfitting for large neural network models.
• A modern recommendation for regularization is to use early stopping with dropout and a weight constraint.

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A Gentle Introduction to Regularization to Reduce Overfitting and Improve Generalization Fault
Photo past jaimilee.beale, some rights reserved.

Overview

This tutorial is divided into 4 parts; they are:

1. The Problem of Model Generalization and Overfitting
2. Reduce Overfitting past Constraining Model Complexity
3. Methods for Regularization
4. Regularization Recommendations

The Problem of Model Generalization and Overfitting

The objective of a neural network is to take a final model that performs well both on the information that we used to train it (due east.g. the training dataset) and the new data on which the model will be used to brand predictions.

The cardinal claiming in motorcar learning is that we must perform well on new, previously unseen inputs — not just those on which our model was trained. The ability to perform well on previously unobserved inputs is called generalization.

— Folio 110, Deep Learning, 2016.

We require that the model learn from known examples and generalize from those known examples to new examples in the future. Nosotros use methods similar a train/examination divide or chiliad-fold cross-validation simply to estimate the power of the model to generalize to new data.

Learning and too generalizing to new cases is hard.

As well petty learning and the model will perform poorly on the training dataset and on new data. The model will underfit the problem. Too much learning and the model volition perform well on the training dataset and poorly on new data, the model will overfit the trouble. In both cases, the model has not generalized.

• Underfit Model. A model that fails to sufficiently learn the trouble and performs poorly on a training dataset and does not perform well on a holdout sample.
• Overfit Model. A model that learns the grooming dataset as well well, performing well on the training dataset but does not perform well on a hold out sample.
• Good Fit Model. A model that suitably learns the training dataset and generalizes well to the erstwhile out dataset.

A model fit can exist considered in the context of the bias-variance trade-off.

An underfit model has high bias and low variance. Regardless of the specific samples in the training data, it cannot larn the problem. An overfit model has low bias and loftier variance. The model learns the training data besides well and functioning varies widely with new unseen examples or even statistical noise added to examples in the training dataset.

In order to generalize well, a system needs to be sufficiently powerful to approximate the target role. If it is too simple to fit even the training data then generalization to new data is also likely to be poor. […] An overly complex system, however, may be able to estimate the data in many dissimilar ways that give similar errors and is unlikely to choose the one that will generalize all-time …

— Folio 241, Neural Smithing: Supervised Learning in Feedforward Artificial Neural Networks, 1999.

We tin address underfitting by increasing the capacity of the model. Capacity refers to the power of a model to fit a multifariousness of functions; more than capacity, means that a model can fit more than types of functions for mapping inputs to outputs. Increasing the capacity of a model is easily achieved by changing the structure of the model, such equally adding more layers and/or more nodes to layers.

Because an underfit model is so easily addressed, information technology is more than mutual to take an overfit model.

An overfit model is easily diagnosed by monitoring the performance of the model during training by evaluating it on both a preparation dataset and on a holdout validation dataset. Graphing line plots of the operation of the model during grooming, called learning curves, volition show a familiar pattern.

For case, line plots of the loss (that we seek to minimize) of the model on train and validation datasets will bear witness a line for the training dataset that drops and may plateau and a line for the validation dataset that drops at first, then at some betoken begins to rise over again.

Every bit training progresses, the generalization error may subtract to a minimum and so increase once more as the network adapts to idiosyncrasies of the grooming data.

— Page 250, Neural Smithing: Supervised Learning in Feedforward Artificial Neural Networks, 1999.

A learning curve plot tells the story of the model learning the problem until a point at which information technology begins overfitting and its power to generalize to the unseen validation dataset begins to go worse.

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Reduce Overfitting by Constraining Model Complication

At that place are two ways to approach an overfit model:

1. Reduce overfitting by grooming the network on more than examples.
2. Reduce overfitting by changing the complexity of the network.

A do good of very deep neural networks is that their performance continues to better as they are fed larger and larger datasets. A model with a well-nigh-infinite number of examples will eventually plateau in terms of what the chapters of the network is capable of learning.

A model tin overfit a preparation dataset because it has sufficient capacity to do so. Reducing the capacity of the model reduces the likelihood of the model overfitting the grooming dataset, to a point where information technology no longer overfits.

The capacity of a neural network model, it'due south complication, is defined past both it'due south structure in terms of nodes and layers and the parameters in terms of its weights. Therefore, we tin can reduce the complexity of a neural network to reduce overfitting in one of ii ways:

1. Change network complexity by irresolute the network construction (number of weights).
2. Change network complexity by changing the network parameters (values of weights).

In the instance of neural networks, the complexity tin can be varied past changing the number of adaptive parameters in the network. This is chosen structural stabilization. […] The second master approach to controlling the complexity of a model is through the employ of regularization which involves the addition of a penalty term to the error function.

— Page 332, Neural Networks for Blueprint Recognition, 1995.

For example, the structure could be tuned such every bit via filigree search until a suitable number of nodes and/or layers is found to reduce or remove overfitting for the trouble. Alternately, the model could be overfit and pruned by removing nodes until information technology achieves suitable performance on a validation dataset.

Information technology is more mutual to instead constrain the complication of the model by ensuring the parameters (weights) of the model remain small-scale. Small parameters suggest a less complex and, in turn, more stable model that is less sensitive to statistical fluctuations in the input data.

Large weighs tend to cause sharp transitions in the [activation] functions and thus big changes in output for small changes in inputs.

— Page 269, Neural Smithing: Supervised Learning in Feedforward Artificial Neural Networks, 1999.

It is more common to focus on methods that constrain the size of the weights in a neural network considering a single network construction can exist defined that is nether-constrained, e.thousand. has a much larger capacity than is required for the problem, and regularization can be used during training to ensure that the model does not overfit. In such cases, operation tin can even be better as the additional capacity can be focused on better learning generalizable concepts in the problem.

Techniques that seek to reduce overfitting (reduce generalization error) past keeping network weights minor are referred to as regularization methods. More than specifically, regularization refers to a class of approaches that add additional information to transform an ill-posed trouble into a more stable well-posed problem.

A problem is said to be ill-posed if pocket-size changes in the given information cause big changes in the solution. This instability with respect to the data makes solutions unreliable considering minor measurement errors or uncertainties in parameters may exist greatly magnified and lead to wildly different responses. […] The idea behind regularization is to apply supplementary information to restate an ill-posed trouble in a stable form.

— Page 266, Neural Smithing: Supervised Learning in Feedforward Artificial Neural Networks, 1999.

Regularization methods are so widely used to reduce overfitting that the term "regularization" may be used for any method that improves the generalization error of a neural network model.

Regularization is whatever modification we brand to a learning algorithm that is intended to reduce its generalization error but non its grooming error. Regularization is ane of the key concerns of the field of machine learning, rivaled in its importance merely by optimization.

— Folio 120, Deep Learning, 2016.

Regularization Methods for Neural Networks

The simplest and peradventure most common regularization method is to add a penalty to the loss role in proportion to the size of the weights in the model.

1. Weight Regularization (weight decay): Penalize the model during training based on the magnitude of the weights.

This will encourage the model to map the inputs to the outputs of the training dataset in such a manner that the weights of the model are kept modest. This arroyo is called weight regularization or weight decay and has proven very constructive for decades for both simpler linear models and neural networks.

A uncomplicated alternative to gathering more data is to reduce the size of the model or better regularization, by adjusting hyperparameters such as weight disuse coefficients …

— Page 427, Deep Learning, 2016.

Beneath is a listing of five of the most common boosted regularization methods.

1. Activity Regularization: Penalize the model during training base on the magnitude of the activations.
2. Weight Constraint: Constrain the magnitude of weights to be within a range or below a limit.
3. Dropout: Probabilistically remove inputs during training.
4. Dissonance: Add statistical noise to inputs during training.
5. Early Stopping: Monitor model operation on a validation fix and stop training when performance degrades.

Most of these methods have been demonstrated (or proven) to approximate the effect of adding a penalisation to the loss function.

Each method approaches the problem differently, offering benefits in terms of a mixture of generalization operation, configurability, and/or computational complexity.

Regularization Recommendations

This section outlines some recommendations for using regularization methods for deep learning neural networks.

Y'all should always consider using regularization, unless you accept a very large dataset, e.g. big-data scale.

Unless your training set contains tens of millions of examples or more, you lot should include some mild forms of regularization from the start.

— Page 426, Deep Learning, 2016.

A practiced general recommendation is to pattern a neural network construction that is under-constrained and to use regularization to reduce the likelihood of overfitting.

… controlling the complexity of the model is not a uncomplicated matter of finding the model of the right size, with the right number of parameters. Instead, … in practical deep learning scenarios, nosotros almost e'er practice find—that the all-time fitting model (in the sense of minimizing generalization error) is a large model that has been regularized accordingly.

— Page 229, Deep Learning, 2016.

Early on stopping should well-nigh universally exist used in improver to a method to keep weights small during training.

Early on stopping should exist used almost universally.

— Folio 426, Deep Learning, 2016.

Some more specific recommendations include:

• Classical: utilise early stopping and weight decay (L2 weight regularization).
• Alternate: use early on stopping and added noise with a weight constraint.
• Modern: use early stopping and dropout, in improver to a weight constraint.

These recommendations would suit Multilayer Perceptrons and Convolutional Neural Networks.

Some recommendations for recurrent neural nets include:

• Classical: use early stopping with added weight noise and a weight constraint such as maximum norm.
• Modern: use early on stopping with a backpropagation-through-time-aware version of dropout and a weight constraint.

There are no argent bullets when it comes to regularization and systematic experimentation is strongly encouraged.

Further Reading

This section provides more than resource on the topic if you are looking to get deeper.

Books

• Affiliate vii Regularization for Deep Learning, Deep Learning, 2016.
• Section five.5. Regularization in Neural Networks, Blueprint Recognition and Machine Learning, 2006.
• Chapter xvi, Heuristics for Improving Generalization, Neural Smithing: Supervised Learning in Feedforward Artificial Neural Networks, 1999.
• Chapter 9 Learning and Generalization, Neural Networks for Pattern Recognition, 1995.

Articles

• What is overfitting and how can I avoid information technology? Neural Network FAQ.
• Regularization (mathematics), Wikipedia.

Summary

In this post, yous discovered the problem of overfitting when training neural networks and how it can be addressed with regularization methods.

Specifically, you learned:

• Underfitting tin can easily exist addressed past increasing the capacity of the network, but overfitting requires the use of specialized techniques.
• Regularization methods like weight decay provide an easy way to control overfitting for large neural network models.
• A modern recommendation for regularization is to employ early on stopping with dropout and a weight constraint.

Practice you have whatsoever questions?
Ask your questions in the comments below and I volition practice my best to answer.

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