What is the stochastic gradient descent algorithm in Python?

What is the stochastic gradient descent algorithm in Python?

The stochastic gradient descent algorithm is a common algorithm used to optimize machine learning models. Its purpose is to minimize the loss function. This algorithm is called "random" because it uses randomization to help avoid getting stuck in a local optimum when training the model. In this article, we will introduce how the stochastic gradient descent algorithm works and how to implement it in Python.

The gradient descent algorithm is an iterative algorithm used to minimize the loss function. In each iteration, it moves the current parameters a small step towards the negative gradient of the loss function. This process will continue until certain stopping conditions are reached.

Code example:

# 随机梯度下降算法实现
def stochastic_gradient_descent(X, y, alpha=0.01, iterations=100):
    m, n = X.shape
    theta = np.zeros(n)
    for i in range(iterations):
        rand_idx = np.random.randint(m)
        xi = X[rand_idx]
        yi = y[rand_idx]
        hypothesis = np.dot(xi, theta)
        loss = hypothesis - yi
        gradient = np.dot(xi.T, loss)
        theta -= alpha * gradient
    return theta

In the above code, we use the stochastic gradient descent algorithm to solve the parameter theta of the linear regression model between the data set X and the target variable y. Specifically, for each iteration we will randomly select a row of data samples xi and the corresponding target value yi from the data set, and calculate the error between the value predicted by the current theta and the true value. Then, we will calculate the derivative of this error with respect to each feature, and then multiply it by the learning rate alpha to get the change in the current theta. Finally, we will apply this change to the current theta to get the updated theta value.

At the same time, we also need to note that the stochastic gradient descent algorithm requires less computing resources than the batch gradient descent algorithm. This is because we are only processing a small portion of the data in each iteration rather than the entire dataset. Because this technique of reducing the data set can be of great use when the data dimensionality is high, stochastic gradient descent algorithms are often used in practice to optimize machine learning models.

To summarize, the stochastic gradient descent algorithm is an iterative algorithm for optimizing machine learning models. It avoids falling into a local optimal solution when training the model by selecting samples in the data set in random order. In Python, we can use libraries such as NumPy to implement the stochastic gradient descent algorithm.

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