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。

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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]

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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
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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()}')