[Pytorch]多层感知机（MLP）回归的实现、训练与评估

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前言

MLP是一种常用的前馈神经网络，使用了BP算法的MLP可以被称为BP神经网络。MLP的隐节点采用输入向量与权向量的内积作为激活函数的自变量，激活函数采用Relu函数。各参数对网络的输出具有同等地位的影响，因此MLP是对非线性映射的全局逼近。除了使用Sklearn提供的MLPRegressor函数以外，我们可以通过Pytorch建立自定义程度更高的人工神经网络。本文将不再对MLP的理论基础进行赘述，而将介绍MLP的具体建立方法。

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一、网络主体构建

通过继承nn.Moudule类对MLP进行逐层建立

1.网络构建

该网络输入维度为8（即八个参量），输出为一个batch，即一个批训练的样本量，并在最后对Tensor进行展平。隐藏层分比为20，20，5，输出层为1，即预测值。

import torch.nn as nn
import torch.nn.functional as F

class MLP(nn.Module):
    def __init__(self):
        super(MLP, self).__init__()
        self.hidden1 = nn.Linear(in_features = 8, out_features = 20, bias = True)
        self.hidden2 = nn.Linear(20,20)
        self.hidden3 = nn.Linear(20,5)
        self.predict = nn.Linear(5,1)
    
    def forward(self,x):
        x = F.relu(self.hidden1(x))
        x = F.relu(self.hidden2(x))
        x = F.relu(self.hidden3(x))
        output = self.predict(x)
        out = output.view(-1)

        return out

1.网络结构可视化

使用Graphviz对这个简单的MLP进行可视化。
这里输入了一个64X8的张量，即代表一次性输入了64个8参量数据

import torch
from net import MLP
from torchviz import make_dot

tensor = torch.zeros(64,8).requires_grad_(True)
model = MLP()
net = model(tensor)

net_strc = make_dot(net, params = dict(list(model.named_parameters()) + [('tensor',tensor)]))
net_strc.view()

网络结构如图：

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二、数据集构建与网络训练

1.数据集构建

这里使用了sklearn提供的fetch_california_housing数据集，该数据集输入参量为8，与网络第一层输入对应。
通过sklearn提供的StandardScaler和train_test_split函数，对输入数据进行正则化与数据集分割。

def dataset():
    house_data = fetch_california_housing()
    x_train, x_test, y_train, y_test = train_test_split(house_data.data, house_data.target, test_size = 0.3, random_state = 42)
    scale = StandardScaler()
    x_train_s = scale.fit_transform(x_train)
    x_test_s = scale.transform(x_test)

    return x_train_s, x_test_s, y_train, y_test

最终返回正则化后的训练集和验证集的输入数据，以及训练集与验证集的真值。

2.网络训练

除了载入建立好的网络与数据，我们还需要设定优化器与损失函数。在这个MLP回归网络中，我们使用随机梯度优化器（SGD）与均方误差损失函数（MSE loss）。
其中draw_plot(Full_Epoch,train_loss_list,train_acc_list,val_loss_list,val_acc_list)用于绘制模型训练过程中的loss值和ACC精度变化，精度评估使用r2_score函数，即反映了样本真值与预测样本分布的决定系数，在0~1之间。
train_one_epoch(model, loss_func, epoch, epoch_size, epoch_size_val, gen, gen_val, Full_Epoch)函数用于对网络进行一个Epoch的训练。

import matplotlib.pyplot as plt
import numpy as np
import torch
import torch.nn as nn
import torch.optim as optim
from sklearn.metrics import explained_variance_score, mean_squared_error,
                             r2_score
from torch.utils.data import DataLoader, TensorDataset
from tqdm import tqdm

from data import dataset, dataset_swc
from net import MLP

def draw_plot(Full_Epoch,train_loss_list,train_acc_list,val_loss_list,val_acc_list):
    x = range(0,Full_Epoch)
    y1 = train_loss_list
    y2 = val_loss_list
    y3 = train_acc_list
    y4 = val_acc_list
    plt.figure(figsize=(13,13))
    plt.subplot(2, 1, 1)
    plt.plot(x,train_loss_list,color="blue",label="train_loss_list Line",linewidth=2)
    plt.plot(x,val_loss_list,color="orange",label="val_loss_list Line",linewidth=2)
    plt.title("Loss_curve",fontsize = 20)
    plt.xlabel(xlabel = "Epochs", fontsize = 15)
    plt.ylabel(ylabel = "Loss", fontsize = 15)
    plt.legend()
    plt.subplot(2, 1, 2)
    plt.plot(x,train_acc_list,color="blue",label="train_acc_list Line",linewidth=2)
    plt.plot(x,val_acc_list,color="orange",label="val_acc_list Line",linewidth=2)
    plt.title("Acc_curve",fontsize = 20)
    plt.xlabel(xlabel = "Epochs", fontsize = 15)
    plt.ylabel(ylabel = "Accuracy", fontsize = 15)
    plt.legend()
    plt.savefig("Loss&acc.jpg") 

def train_one_epoch(model, loss_func, epoch, epoch_size, epoch_size_val, gen, gen_val, Full_Epoch):
    train_loss = 0
    val_loss = 0
    total_loss = 0
    total_val_loss = 0

    print(f"世代{epoch+1}开始训练")

    with tqdm(total = epoch_size, desc = f'Epoch{epoch +1}/{Full_Epoch}', postfix = dict, mininterval = 0.3) as pbar:
        for iteration, batch in enumerate(gen):
            if iteration >= epoch_size:
                break
            data, target = batch
            optimizer.zero_grad()
            output = model(data)
            loss = loss_func(output, target)
            loss.backward()
            optimizer.step()

            total_loss += loss.item()
            train_loss = total_loss / (iteration + 1)
            train_acc = r2_score(target.detach().numpy(),output.detach().numpy())

            pbar.set_postfix(**{"total_loss": train_loss, 
                                "learning_rate:": 1e-3,                
                                "Acc": train_acc})                           
            pbar.update(1) #更新进度条

    print(f"世代{epoch+1}权值更新完成")
    print(f"开始评估世代{epoch+1}")
    with tqdm(total = epoch_size_val, desc = f'Epoch{epoch +1}/{Full_Epoch}', postfix = dict, mininterval = 0.3) as pbar:
        for iteration, batch in enumerate(gen_val):
            if iteration >= epoch_size_val:
                break
            data, target = batch
            optimizer.zero_grad()
            output = model(data)
            loss = loss_func(output, target)

            total_val_loss += loss.item() 
            val_loss = total_val_loss / (iteration + 1)
            val_acc = r2_score(target.detach().numpy(),output.detach().numpy())     

            pbar.set_postfix(**{"val_loss": val_loss,
            "Acc": val_acc})                
            pbar.update(1) #更新进度条
    if epoch+1 == Full_Epoch:
        torch.save(model.state_dict(),
        'weights/mlp_weights-epoch%d-Total_loss%.4f-val_loss%.4f.pkl'%((epoch+1),train_loss,val_loss / (iteration + 1)))
        
    return train_loss, train_acc, val_loss, val_acc


if __name__ == "__main__":
    Full_Epoch = 300
    Batch_size = 64
    lr = 1e-3
    loss_and_acc_curve = True

    train_loss_list = []
    val_loss_list = []
    train_acc_list = []
    val_acc_list = []


    x_train_s, x_test_s, y_train, y_test = dataset()
    x_train_st = torch.from_numpy(x_train_s.astype(np.float32))
    x_test_st = torch.from_numpy(x_test_s.astype(np.float32))
    y_train_t = torch.from_numpy(y_train.astype(np.float32))
    y_test_t = torch.from_numpy(y_test.astype(np.float32))


    train_dataset = TensorDataset(x_train_st,y_train_t)
    test_dataset = TensorDataset(x_test_st,y_test_t)
    gen = DataLoader(train_dataset, batch_size = Batch_size, num_workers = 0,
                pin_memory = True, drop_last = True, shuffle = True)
    gen_val = DataLoader(test_dataset, batch_size = Batch_size, num_workers = 0,
                pin_memory = True, drop_last = True, shuffle = True)

    model = MLP()
    optimizer = optim.SGD(model.parameters(), lr)
    loss_func = nn.MSELoss()
    epoch_size = y_train_t.size(0) // Batch_size
    epoch_size_val = y_test_t.size(0) // Batch_size

    for epoch in range(0,Full_Epoch):
        train_loss, train_acc, val_loss, val_acc = train_one_epoch(model, loss_func, epoch, epoch_size, epoch_size_val, gen, gen_val, Full_Epoch)
        train_loss_list.append(train_loss)
        train_acc_list.append(train_acc)
        val_loss_list.append(val_loss)
        val_acc_list.append(val_acc)

    if loss_and_acc_curve:
        draw_plot(Full_Epoch,train_loss_list,train_acc_list,val_loss_list,val_acc_list)

三、网络评估

在训练300个世代后，获得网络训练过程的loss值与acc值变化曲线。

网络的loss值在200个世代后基本稳定，精度变化也一直保持在0.5~0.75之间。

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总结

虽然MLP网络极为简单，且已有函数提供了快速的建立方法，但是通过手动建立可以提高对网络构建以及参数传播的理解，为更加深层次的卷积神经网络奠定基础。