gradient descent

What is gradient descent?

Gradient descent is an optimization algorithm that refines a machine learning model's parameters to create a more accurate model. The goal is to reduce a model's error or cost function when testing against an input variable and the expected result. It's called gradient because it is analogous to measuring how steep a hill might be and descent because, with this approach, the goal is to get to a lower error or cost function.

Making slight variations to a machine learning model is analogous to experiencing changes in the incline when stepping away from the top of a hill. The gradient represents a combination of the direction and steepness of a step toward the lowest possible error rate in the machine learning model. The learning rate, which refers to the impact of changes to a given variable on the error rate, is also a critical component. If the learning rate is too high, the training process may miss things, but if it is too low, it requires more time to reach the lowest point. In practice, a given machine learning problem might have many more dimensions than you might find with a real hill.

Many other approaches can help machine learning algorithms explore feature variations, including Newton's method, genetic algorithms and simulated annealing. However, gradient descent is often a first choice because it is easy to implement and scales well. Its principles are applicable across various domains and types of data.

Why gradient descent is important in machine learning

Gradient descent helps the machine learning training process explore how changes in model parameters affect accuracy across many variations. A parameter is a mathematical expression that calculates the impact of a given variable on the result. For example, temperature might have a greater effect on ice cream sales on hot days, but past a certain point, its impact lessens. Price might have a greater impact on cooler days but less on hot ones.

Sometimes, slight changes to various combinations of parameters don't make the model any more accurate. This is called a local optimum. Ideally, the machine learning algorithm finds the global optimum -- that is, the best possible solution across all the data. But, sometimes, a model that is not as good as the global optimum is suitable, especially if it is quicker and cheaper.

Gradient descent makes it easier to iteratively test and explore variations in a model's parameters and thus get closer to the global optimum faster. It can also help machine learning models explore variations of complex functions with many parameters and help data scientists frame different ways of training a model for a large training data set.

Sometimes, a machine learning algorithm can get stuck on a local optimum. Gradient descent provides a little bump to the existing algorithm to find a better solution that is a little closer to the global optimum. This is comparable to descending a hill in the fog into a small valley, while recognizing you have not walked far enough to reach the mountain's bottom. A step in any direction takes you up the edge of a little valley. A little momentum is required to get far enough to scale the edge from where you can find another edge that might take you even further toward the bottom. In the case of gradient descent, it takes you further toward the bottom to create a more accurate model.

How does gradient descent work?

Putting gradient descent to work starts by identifying a high-level goal, such as ice cream sales, and encoding it in a way that can guide a given machine learning algorithm, such as optimal pricing based on weather predictions. Let's walk through how this might work in practice:

1. Identify a goal. Create a model that minimizes the error in predicting the profits of ice cream sales.
2. Initialize parameters. Start by assigning a higher weight to the importance of temperature on hot days but less on cold days.
3. Minimize losses. Identify which features, such as the weights of temperature and price, affect the model's performance. Assess how much the current model's predictions vary from previous results, and then use this information to adjust the features in the next round of iterations.
4. Update parameters. Subtract a fraction of the gradient from each parameter based on the learning rate, which determines the magnitude of changes. For example, temperature may have a lower learning rate than price changes in a model for predicting peak ice cream profits in the summer.
5. Repeat. Repeat the process until the model fails to improve despite new variations.

Types of gradient descent

There are two main types of gradient descent techniques and then a hybrid between the two:

1. Batch gradient descent. The model's parameters are updated after computing the loss function across the entire data set. It can yield the best results because parameters are only updated after considering the entire training data set. However, it can be slow and expensive for larger data sets as the model's error rate needs to be calculated for the entire training data set.
2. Stochastic gradient descent. After each training example, the model's parameters are updated. It's much faster since parameters are updated more frequently. However, it can miss opportunities to converge on a suitable local optimum because of the frequent pace of parameter changes.
3. Mini-batch gradient descent. The model's parameters are updated after processing the training data set in small batches. It combines the stability of batch gradient descent with the speed of stochastic gradient descent. However, data scientists must spend more time selecting the appropriate batch size, which can affect convergence rate and performance.

Benefits of gradient descent

Gradient descent is one of the first techniques that data scientists consider for optimizing the training of machine learning algorithms that explore the impact of iteratively adjusting the weight of features. Here is why:

• Scalability. Gradient descent can efficiently explore the impact of small adjustments of feature weights when training on large data sets. It can also take advantage of the parallel processing capabilities of graphics processing units to accelerate this process.
• Efficiency. It minimizes the memory requirements for exploring lots of feature weight variations.
• Flexibility. Its straightforward implementation process makes it applicable to a wide range of machine learning algorithms, including neural networks, logistic regression, linear regression and support vector machine algorithms.
• Simplicity. The basic concepts are straightforward, making them accessible to beginners, and are available in most machine learning tools. Gradient descent also makes it easy to understand how models are improving over time, which can simplify the debugging process.
• Adaptability. Modern variants enable data scientists to adjust the learning rate for different features that can improve convergence rates and adapt to various data. In addition, it can enable fine-tuning for sparse data sets required to provide better results for edge conditions.

Challenges of gradient descent

Data scientists and developers face many challenges in getting the best results when using gradient descent. These include the following:

• Learning rate. It is important to fine-tune the learning rate or the pace of change across different iterations for the various features. The learning rate can miss opportunities to train the most accurate algorithm if set too high. If it is too low, more iterations are required.
• Local optimum. Gradient descent tends to get stuck, generating models that can't be improved with minor changes. In particular, saddle points can emerge where small changes don't look better or worse.
• Convergence. In some cases, improvement can slow down or oscillate, making it hard to evolve a better model across iterations.
• Efficiency. It's important to balance the technique for a given data set and problem. Batch gradient processes require a full pass through the data for each update, which slows the process. However, stochastic gradient descent can introduce noise into the update, making the update process more erratic and harder to track.
• Data quality. Variations in data quality can lead to inefficient updates and poorer convergence. Careful feature selection and engineering are required to help mitigate these issues.