Pytorch解决 多元回归 问题的算法
回归是一种基本的统计建模技术，用于建立因变量与一个或多个自变量之间的关系。
我们将使用 PyTorch（一种流行的深度学习框架）来开发和训练线性回归模型。
二元回归的简单示例
训练数据集（可获取）
对于此分析，我们将使用scikit-learn 库中的 make regression() 函数生成的合成数据集。数据集由输入特征和目标变量组成。输入特征代表自变量，而目标变量代表我们想要预测的因变量
import seaborn as sns
import numpy as sns
import torch
import torch.nn as nn
import torch.optim as optim
import sklearn
from sklearn import datasets
import pandas as pd
data=datasets.make_regression() # from sklearn we are going to select one dataset
df = pd.DataFrame(data[0], columns=[f"feature_{i+1}" for i in range(data[0].shape[1])])
df["target"] = data[1]
数据的结构，100 rows × 101 columns，最后 1 column为目标值
准备训练集与测试集
PyTorch 是一个功能强大的开源深度学习框架，提供了一种灵活的方式来构建和训练神经网络。它提供了一系列张量运算、自动微分和优化算法的功能。
使用 sklearn Train-Test-split 准备数据以开发模型
x=df.iloc[: , :-1] # 除目标数据身下所以的
y=df.iloc[: , -1] # target
from sklearn.model_selection import train_test_split
X_train,X_test,y_train,y_test=train_test_split(x,y,test_size=0.2,random_state=42)
print(type(X_train))
# X_train=torch.tensor(X_train,dtype=torch.float32)
X_train = torch.tensor(X_train.values, dtype=torch.float32) # 转化为 tensor
X_test = torch.tensor(X_test.values, dtype=torch.float32)
y_train = torch.tensor(y_train.values, dtype=torch.float32)
y_test = torch.tensor(y_test.values, dtype=torch.float32)
模型架构
数据准备好了，可以准备模型了
我们的线性回归模型是作为PyTorch 中nn.Module类的子类实现的。该模型由多个按顺序连接的完全连接（线性）层组成。
class linearRegression(nn.Module):
# 所有来自torch的依赖项将被传递给这个类[父类]
# nn.Module 包含了神经网络的所有构建模块：
def __init__(self,input_dim):
super(linearRegression,self).__init__() # building connection with parent and child classes
self.fc1=nn.Linear(input_dim,10) # hidden layer 1
self.fc2=nn.Linear(10,5) # hidden layer 2
self.fc3=nn.Linear(5,3) # hidden layer 3
self.fc4=nn.Linear(3,1) # last layer
def forward(self,d):
out=torch.relu(self.fc1(d)) # input * weights + bias for layer 1
out=torch.relu(self.fc2(out)) # input * weights + bias for layer 2
out=torch.relu(self.fc3(out)) # input * weights + bias for layer 3
out=self.fc4(out) # input * weights + bias for last layer
return out # final outcome
input_dim=X_train.shape[1] # 获取 input_dim 变量的数量
torch.manual_seed(42) # to make initilized weights stable:
model=linearRegression(input_dim)
# select loss and optimizers
loss=nn.MSELoss() # loss function
optimizers=optim.Adam(params=model.parameters(),lr=0.01)
loss_values_all = [] # 创建一个列表来存储每个迭代的loss值
# training the model:
num_of_epochs=1000
for i in range(num_of_epochs):
# give the input data to the architecure
y_train_prediction=model(X_train) # model initilizing
loss_value=loss(y_train_prediction.squeeze(),y_train) # find the loss function:
optimizers.zero_grad() # make gradients zero for every iteration so next iteration it will be clear
loss_value.backward() # back propagation
optimizers.step() # update weights in NN
loss_values_all.append(loss_value.item()) # 将当前的loss值添加到列表中
# print the loss in training part:
if i % 10 == 0:
print(f'[epoch:{i}]: The loss value for training part={loss_value}')
绘制 loss 曲线图
在测试数据集上的效果（test data）
with torch.no_grad():
model.eval() # make model in evaluation stage
y_test_prediction=model(X_test)
test_loss=loss(y_test_prediction.squeeze(),y_test)
print(f'Test loss value : {test_loss.item():.4f}')
测试自己随机生成的数据
# Inference with own data:
pr = torch.tensor(torch.arange(1, 101).unsqueeze(dim=0), dtype=torch.float32).clone().detach()
print(pr)
保存训练好的模型
# save the torch model:
from pathlib import Path
filename=Path('models')
filename.mkdir(parents=True,exist_ok=True)
model_name='linear_regression.pth' # model name
# saving path
saving_path=filename/model_name
print(saving_path)
torch.save(obj=model.state_dict(),f=saving_path)
# we can load the saved model and do the inference again:
load_model=linearRegression(input_dim) # creating an instance again for loaded model
load_model.load_state_dict(torch.load('./models/linear_regression.pth'))
load_model.eval() # make model in evaluation stage
with torch.no_grad():
pred = load_model(torch.tensor([[ 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24.,
25., 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36.,
37., 38., 39., 40., 41., 42., 43., 44., 45., 46., 47., 48.,
49., 50., 51., 52., 53., 54., 55., 56., 57., 58., 59., 60.,
61., 62., 63., 64., 65., 66., 67., 68., 69., 70., 71., 72.,
73., 74., 75., 76., 77., 78., 79., 80., 81., 82., 83., 84.,
85., 86., 87., 88., 89., 90., 91., 92., 93., 94., 95., 96.,
97., 98., 99., 100.]]))
print(f'prediction value : {pred.item()}')
