Stochastic Gradient Descent" (SGD)的MLA格式
时间: 2023-02-14 15:29:03 浏览: 91
"Stochastic Gradient Descent" (SGD). (n.d.). Retrieved from [URL]
其中, "n.d."表示没有可用的发布日期, [URL]为文章或资料来源的网址。
相关问题
Derive the stochastic gradient descent algorithm
The stochastic gradient descent (SGD) algorithm is a popular optimization algorithm used in machine learning. It is an iterative algorithm that updates the model parameters in small steps based on the gradient of the loss function with respect to the parameters. The algorithm works as follows:
1. Initialize the model parameters randomly.
2. Set the learning rate, which determines the step size of the updates.
3. For each training example:
- Compute the gradient of the loss function with respect to the parameters using the current example.
- Update the model parameters by subtracting the gradient multiplied by the learning rate.
The key difference between SGD and regular gradient descent is that in SGD, the gradient is computed and the parameters are updated for each training example, rather than for the entire training set. This makes the algorithm faster and more scalable for large datasets.
The stochastic aspect of the algorithm comes from the fact that the training examples are sampled randomly from the training set, rather than being processed in a fixed order. This randomness can help the algorithm escape from local minima and find better solutions.
Here is the pseudocode for the SGD algorithm:
```
Input: Training set (X, Y), learning rate α, number of iterations T
Output: Model parameters θ
Initialize θ randomly
for t = 1 to T do
Sample a training example (x, y) from (X, Y) randomly
Compute the gradient ∇θ L(θ; x, y) using the current example
Update the parameters: θ ← θ - α * ∇θ L(θ; x, y)
end for
return θ
```
小批量随机梯度下降(Mini-batch Stochastic Gradient Descent,Mini-batch SGD)。
小批量随机梯度下降(Mini-batch SGD)是一种梯度下降法的变体,它是一种介于批量梯度下降(Batch Gradient Descent)和随机梯度下降(Stochastic Gradient Descent)之间的方法。Mini-batch SGD 取样一小部分训练集数据来计算梯度并更新模型参数,这个小部分被称为 mini-batch。
相比于批量梯度下降,Mini-batch SGD 可以更快地更新模型参数,因为它每次只考虑一小部分数据。而相比于随机梯度下降,Mini-batch SGD 可以更稳定地更新模型参数,因为它计算的是一小部分数据的平均梯度,而不是单个数据的梯度。
通常,在实践中,Mini-batch SGD 的 mini-batch 大小通常在几十到几百之间。