One of the biggest problems that data scientists or machine learning engineers face is the complexity involved in creating algorithms that perform well on training data as well as new inputs. A lot of techniques are used in machine learning to minimize or completely eliminate the test error. This is done, on some occasions, without caring too much about the increased training error. All these techniques put together are commonly referred to as regularization.
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In simpler terms, regularization is changes made to a learning algorithm to minimize its generalization error without focusing too much on reducing its training error. There are several regularization techniques available, with each working on a different aspect of a learning algorithm or neural network, and each leading to a different outcome.
There are regularization techniques that put additional restrictions on a learning model, such as constraints on the parameter values. There are those that put restrictions on the parameter values. If the regularization technique is chosen carefully, it can lead to an improved performance on the test data model.
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Why do we need neural network regularization?
Deep neural networks are complex learning models that are exposed to overfitting, owing to their flexible nature of memorizing individual training set patterns instead of taking a generalized approach towards unrecognizable data. This is why neural network regularization is so important. It helps you keep the learning model easy-to-understand to allow the neural network to generalize data it can’t recognize.
Let’s understand this with an example. Suppose we have a dataset that includes both input and output values. Let us also assume there is a true relation between these values. Now, one of the objectives of deep learning is to establish an approximate relationship between input and output values. So, for every data set, there exist two models that can help us in defining this relationship – simple model and complex model.
In the simple model, there exists a straight line that just includes two parameters that define the relationship in question. A graphical representation of this model will feature a straight line that closely passes through the centre of the data set in question, ensuring that there is very little distance between the line and the points below and above it.
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On the other hand, the complex model has several parameters, depending on the data set. It follows the polynomial equation, which allows it to pass through every training data point. With the gradual increase in complexity, the training error will reach zero value and the model will memorize the individual patterns of the data set. Unlike simple models that aren’t too different from one another even when they are trained on different data sets, the same can’t be said about complex models.
What are Bias and Variance?
In simple terms, bias is a measure of the distance that exists between the true population line and the average of the models that are trained on different data sets. Bias has a very important role in deciding whether or not we are going to have a good prediction interval. It does this by figuring how close the average function has come to the true relationship.
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Variance quantifies the estimate variation for an average function. Variance determines how much deviation a model that is being modelled on a specific data set shows when it is trained on different data sets through its entire prediction journey. Whether an algorithm has high bias or high variance, we can make several modifications to get it to perform better.
How can we deal with high Bias?
- Train it for longer periods of time
- Use a bigger network with hidden units or layers
- Try better neural network architecture or advanced optimization algorithms
How can we deal with high variance (overfitting)?
- Addition of data
- Find better neural network architecture
With existing deep learning algorithms, we are free to continue to train larger neural networks to minimize the bias without having any influence whatsoever on the variance. Similarly, we can continue to add data to minimize variance without having any impact on the value of the bias. Also, if we are dealing with both high bias and high variance, we can bring both those values down by using the right deep learning regularization technique.
As discussed, an increase in model complexity results in an increase in the value of variance and decrease in that of bias. With the right regularization technique, you can work towards reducing both testing and training error, and thus allow an ideal trade-off between variance and bias.
Here are three of the most common regularization techniques:
1. Dataset Augmentation
What is the easiest way to generalize? The answer is quite simple, but its implementation it isn’t. You just need to train that model on a lager data set. However, this isn’t viable in most situations as we mostly deal with limited data. The best possible solution that can be performed for several machine learning problems is to create synthetic or fake data to add to your existing data set. So if you are dealing with image data, the easiest ways of creating synthetic data include scaling, pixel translation of the picture, and rotation.
2. Early stopping
A very common training scenario that leads to overfitting is when a model is trained on a relatively larger data set. In this situation, the training of the model for a larger period of time wouldn’t result in its increased generalization capability; it would instead lead to overfitting.
After a certain point in the training process and after a significant reduction in the training error, there comes a time when the validation error starts to increase. This signifies that overfitting has started. By using the Early Stopping technique, we stop the training of the models and hold the parameters as they are as soon as we see an increase in the validation error.
3. L1 and L2
L1 and L2 make the Weight Penalty regularization technique that is quite commonly used to train models. It works on an assumption that makes models with larger weights more complex than those with smaller weights. The role of the penalties in all of this is to ensure that the weights are either zero or very small. The only exception is when big gradients are present to counteract. Weight Penalty is also referred to as Weight Decay, which signifies the decay of weights to a smaller unit or zero.
L1 norm: It allows some weights to be big and drives some towards zero. It penalizes a weight’s true value.
L2 norm: It drives all weights towards smaller values. It penalizes a weight’s square value.
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What is L1’s advantage over L2 regularization?
Since L1 regularization lowers the beta coefficients or makes them smaller to almost zero, it is essential for terminating unimportant features. L2 regularization on the other hand, lessens the weights uniformly and is only applied when multicollinearity is present in the data itself. L1 regularization can therefore be used for feature selection, giving it an advantage over L2 regularization.
What are the benefits and challenges of data augmentation?
The benefits include improving the accuracy of predicting models by the addition of more training data, preventing data from becoming scarce for better models, and increasing the ability of models to generalize an output. It also reduces the cost of collecting data and then labelling it. Challenges include developing new research to create synthetic data with advanced applications for data augmentation domains. Also, if real datasets contain biases, then the augmented data will also contain the biases.
How do we handle high bias and high variance?
Dealing with high bias means training data sets for longer periods of time. For that, a bigger network should be used with hidden layers. Also, better neural networks should be applied. To handle high variance, regularization has to be initiated, additional data has to be added, and, similarly, a better neural network architecture has to be framed.