How to implement sgd in golang

Stochastic Gradient Descent (SGD) is an optimization algorithm commonly used for parameter optimization in machine learning. In this article, we will introduce how to implement SGD using Go language (Golang) and give implementation examples.

1. SGD algorithm

The basic idea of ​​the SGD algorithm is to randomly select some samples in each iteration and calculate the loss function of these samples under the current model parameters. The gradient is then calculated on these samples and the model parameters are updated according to the direction of the gradient. This process will be repeated several times until the stopping condition is met.

Specifically, let $f(x)$ be the loss function, $x_i$ be the feature vector of the $i$-th sample, $y_i$ be the output of the $i$-th sample, $w $ is the current model parameter, and the update formula of SGD is:

$$w = w - \alpha \nabla f(x_i, y_i, w)$$

where $\alpha$ is Learning rate, $\nabla f(x_i, y_i, w)$ represents the calculation of the loss function gradient of the $i$th sample under the current model parameters.

2. Golang implementation

The libraries required to implement the SGD algorithm in Golang are: gonum, gonum/mat and gonum/stat. Among them, gonum is a mathematical library that provides many commonly used mathematical functions. gonum/mat is a library used to process matrices and vectors. gonum/stat is Statistical functions (such as mean, standard deviation, etc.) are provided.

The following is a simple Golang implementation:

package main

import (
    "fmt"
    "math/rand"

    "gonum.org/v1/gonum/mat"
    "gonum.org/v1/gonum/stat"
)

func main() {
    // 生成一些随机的数据
    x := mat.NewDense(100, 2, nil)
    y := mat.NewVecDense(100, nil)
    for i := 0; i < x.RawMatrix().Rows; i++ {
        x.Set(i, 0, rand.Float64())
        x.Set(i, 1, rand.Float64())
        y.SetVec(i, float64(rand.Intn(2)))
    }

    // 初始化模型参数和学习率
    w := mat.NewVecDense(2, nil)
    alpha := 0.01

    // 迭代更新模型参数
    for i := 0; i < 1000; i++ {
        // 随机选取一个样本
        j := rand.Intn(x.RawMatrix().Rows)
        xi := mat.NewVecDense(2, []float64{x.At(j, 0), x.At(j, 1)})
        yi := y.AtVec(j)

        // 计算损失函数梯度并更新模型参数
        gradient := mat.NewVecDense(2, nil)
        gradient.SubVec(xi, w)
        gradient.ScaleVec(alpha*(yi-gradient.Dot(xi)), xi)
        w.AddVec(w, gradient)
    }

    // 输出模型参数
    fmt.Println(w.RawVector().Data)
}

The data set of this implementation is a $100 \times 2$ matrix, each row represents a sample, and each sample has two features. Label $y$ is a $100 \times 1$ vector, where each element is either 0 or 1. The number of iterations in the code is 1000 and the learning rate $\alpha$ is 0.01.

In each iteration, a sample is randomly selected and the loss function gradient is calculated on this sample. After the gradient calculation is completed, update the model parameters using the formula above. Finally, the model parameters are output.

3. Summary

This article introduces how to use Golang to implement the SGD algorithm and gives a simple example. In practical applications, there are also some variations of the SGD algorithm, such as SGD with momentum, AdaGrad, Adam, etc. Readers can choose which algorithm to use based on their own needs.

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