Optimization problems are a very important part of machine learning algorithms, and the core of almost every machine learning algorithm is dealing with optimization problems.
In this article, I will introduce some of the most commonly used optimization algorithms in the field of machine learning. After reading this article, you will understand:
• What is the gradient descent method?
• How to apply the gradient descent method to a linear regression model?
• How to use the gradient descent method to process large-scale data?
• Some tips for gradient descent
let's start!
Gradient descentThe gradient descent method is an optimization algorithm for finding parameter values ​​that minimize the cost function. When we can't find the optimal solution of a function through analytical calculations (such as linear algebra operations), we can use the gradient descent method to solve the problem.
Intuition experience of gradient descent
Imagine a large bowl that you often use to eat cereals or store, and the cost function is shaped like the shape of the bowl.
Any random position on the surface of the bowl represents the cost value corresponding to the current coefficient, and the bottom of the bowl represents the cost function value corresponding to the optimal solution set. The goal of the gradient descent method is to continually try different coefficient values, then evaluate the cost function and select the parameter values ​​that can reduce the cost function. Repeat the iterative calculation of the above steps until convergence, we can get the optimal solution corresponding to the minimum cost function value.
Gradient descent processThe gradient descent method first needs to set an initial parameter value. Usually, we set the initial value to zero (coefficient=0coefficient=0), and then we need to calculate the cost function cost=f(coefficient)cost=f(coefficient) or cost. =evaluate(f(coefficient))cost=evaluate(f(coefficient)). Then we need to calculate the derivative of the function (the derivative is a concept of calculus, which is the slope value at a point in the function) and set the value of the learning efficiency parameter (alpha).
Coefficient=coefficient−(alpha∗delta)
Repeat the above process until the parameter values ​​converge, so that we can get the optimal solution of the function.
You can see how simple the idea of ​​the gradient descent method is. You only need to know the gradient value of the cost function or the function that needs to be optimized. Next I will show how to apply the gradient descent method to the field of machine learning.
Batch gradient descent
The goal of all supervised machine learning algorithms is to use known independent variable (X) data to predict the value of the dependent variable (Y). All classification and regression models are dealing with this problem.
Machine learning algorithms use a statistic to characterize the fit of the objective function. Although different algorithms have different objective function representations and different coefficient values, they have a common goal—to get the best parameter values ​​by optimizing the objective function.
Linear regression models and logistic regression models are classic cases of using gradient descent methods to find the best parameter values.
We can use a variety of measures to evaluate the fit of the machine learning model to the objective function. The cost function method measures the fit of the model by calculating the degree of difference between the predicted and actual values ​​of each training set (such as the sum of squared residuals).
We can calculate the derivative value corresponding to each parameter in the cost function, and then iteratively calculate through the above update equation.
After each iteration of the gradient descent method, we need to calculate the cost function and its derivative. Each iterative calculation process is called a batch, so this form of gradient descent is also known as the batch gradient descent method.
The batch gradient descent method is a common gradient descent method in the field of machine learning.
Stochastic gradient descent
When dealing with large-scale data, the gradient descent method is very computationally inefficient. Because the gradient descent method needs to calculate the prediction of the training set in each iteration, it takes a long time when the amount of data is very large. When you are dealing with large-scale data, you can use the stochastic gradient descent method to improve computational efficiency. The algorithm differs from the gradient descent method described above in that it performs a coefficient update process for each random training sample, rather than performing a coefficient update process after each batch of samples has been computed.
The first step of the stochastic gradient descent method requires that the samples of the training set be randomly ordered, in order to disturb the update process of the coefficients. Since we will update the coefficient values ​​after each training instance ends, the coefficient values ​​and cost function values ​​will appear as random jumps. By disturbing the order of the coefficient update process, we can take advantage of the nature of this random walk to avoid the problem of non-convergence of the model.
In addition to the inconsistent calculation of the cost function, the coefficient update process of the stochastic gradient descent method is exactly the same as the gradient descent method described above. For large-scale data, the convergence rate of the stochastic gradient descent method is significantly higher than other algorithms. Usually, you only need a small number of iterations to get a relatively good fitting parameter.
Some suggestions for the gradient descent method
This section lists several tips that can help you better understand the gradient descent algorithm in machine learning:
• Draw a curve of cost functions over time: collect and plot the cost function values ​​obtained during each iteration. For the gradient descent method, each iteration calculation reduces the cost function value. If you can't reduce the cost function value, you can try to reduce the learning efficiency value.
• Learning efficiency: The learning efficiency value in the gradient descent algorithm is usually 0.1, 0.001 or 0.0001. You can try different values ​​and choose the best learning efficiency value.
• Standardized processing: If the cost function is not skewed, then the gradient descent method will converge quickly. Concealment You can standardize input variables in advance.
• Draw a cost-average trend graph: The update process of the stochastic gradient descent method usually introduces some random noise, so we can consider the change of the process error mean of 10, 100 or 1000 update processes to measure the convergence trend of the algorithm.
to sum up
This article mainly introduces the gradient descent method in machine learning. By reading this article, you learned:
• Optimization theory is a very important part of machine learning.
• The gradient descent method is a simple optimization algorithm that you can apply to many machine learning algorithms.
• The batch gradient descent method first calculates the derivative values ​​of all parameters before performing the parameter update process.
• The stochastic gradient descent method is to calculate the derivative from each training instance and perform the parameter update process.
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