本次kaggle实战还在进行中

定义比赛用来评价模型的对数均方根误差。给定预测值${\hat{y}}_1,\dots ,{\hat{y}}_n$和对应的真实标签$y_1,\dots ,y_n$，它的定义为

$$\sqrt{\frac{1}{n}\sum _{i=1}^n{\left(\log (y_i)-\log ({\hat{y}}_i)\right)}^2}.$$

对数均方根误差的实现如下面的log_rmse(net, features, labels) 函数。

# This Python 3 environment comes with many helpful analytics libraries installed
# It is defined by the kaggle/python docker image: https://github.com/kaggle/docker-python
# For example, here's several helpful packages to load in 

import numpy as np # linear algebra
import pandas as pd # data processing, CSV file I/O (e.g. pd.read_csv)
import torch
from torch import nn

# Input data files are available in the "../input/" directory.
# For example, running this (by clicking run or pressing Shift+Enter) will list all files under the input directory

import os
# for dirname, _, filenames in os.walk('/kaggle/input'):
# for filename in filenames:
# print(os.path.join(dirname, filename))

# Any results you write to the current directory are saved as output.
        

train_data = pd.read_csv("../input/house-prices-advanced-regression-techniques/train.csv")
test_data = pd.read_csv("../input/house-prices-advanced-regression-techniques/test.csv")

print(test_data.iloc[0:4, [0, 1, 2, 3, -3, -2, -1]])
print("\n")
print(train_data.iloc[0:4, [0, 1, 2, 3, -3, -2, -1]])
# print(train_data.iloc[0])
print(train_data.shape, test_data.shape)

all_features = pd.concat((train_data.iloc[:, 1:-1], test_data.iloc[:, 1:]))

numeric_features = all_features.dtypes[all_features.dtypes != 'object'].index

all_features[numeric_features] = all_features[numeric_features].apply(lambda x: (x - x.mean()) / (x.std()))

all_features[numeric_features] = all_features[numeric_features].fillna(0)

all_features = pd.get_dummies(all_features, dummy_na=True)
# print(all_features.shape)

n_train = train_data.shape[0]

# get data tensor
train_features = torch.tensor(all_features[:n_train].values, dtype=torch.float)
test_features = torch.tensor(all_features[n_train:].values, dtype=torch.float)
train_lables = torch.tensor(train_data.SalePrice.values, dtype=torch.float)
# test_lables = torch.tensor(test_data.SalePrice.values, dtype=torch.float)

# print(train_features.shape)

class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.fc1 = nn.Linear(331, 1)
        self.relu = nn.ReLU(True)
        
    def forward(self,input):
        output = self.fc1(input)
        output = self.relu(output)
        return output
    
net = Net()
for param in net.parameters():
    nn.init.normal_(param, mean=0, std=0.01)

loss_fn = nn.MSELoss()

def log_rmse(net, features, labels):
    with torch.no_grad():
        # 将小于1的值设成1，使得取对数时数值更稳定
        clipped_preds = torch.max(net(features), torch.tensor(1.0))
        rmse = torch.sqrt(2 * loss_fn(clipped_preds.log(), labels.log()).mean())
    return rmse.item()

def train(net, train_data, train_lables, num_epochs, learning_rate, weight_decay, batch_size):
    dataset = torch.utils.data.TensorDataset(train_features, train_lables)
    train_iter = torch.utils.data.DataLoader(dataset, batch_size, shuffle=True)
    optimizer = torch.optim.Adam(params=net.parameters(), lr=learning_rate, weight_decay=weight_decay)
    net = net.float()
    for epoch in range(num_epochs):
        for X, y in dataset:
            net.train()
            X = net(X.float())
            l = loss_fn(X, y.float())
            optimizer.zero_grad()
            l.backward()
            optimizer.step()
        train_ls.append(log_rmse(net, train_features, train_lables))
# if test_labels is not None:
# test_ls.append(log_rmse(net, test_features, test_labels))
    return train_ls 

num_epochs = 50
learning_rate = 0.01
weight_decay = 0
batch_size = 64
train_ls = []

train(net, train_data, train_lables, num_epochs, learning_rate, weight_decay, batch_size)

print(train_ls[40:])

K折交叉验证

我们在模型选择、欠拟合和过拟合中介绍了$K$折交叉验证。它将被用来选择模型设计并调节超参数。下面实现了一个函数，它返回第i折交叉验证时所需要的训练和验证数据。

def get_k_fold_data(k, i, X, y):
    # 返回第i折交叉验证时所需要的训练和验证数据
    assert k > 1
    fold_size = X.shape[0] // k
    X_train, y_train = None, None
    for j in range(k):
        idx = slice(j * fold_size, (j + 1) * fold_size)
        X_part, y_part = X[idx, :], y[idx]
        if j == i:
            X_valid, y_valid = X_part, y_part
        elif X_train is None:
            X_train, y_train = X_part, y_part
        else:
            X_train = torch.cat((X_train, X_part), dim=0)
            y_train = torch.cat((y_train, y_part), dim=0)
    return X_train, y_train, X_valid, y_valid

在$K$折交叉验证中我们训练$K$次并返回训练和验证的平均误差

def k_fold(k, X_train, y_train, num_epochs,
           learning_rate, weight_decay, batch_size):
    train_l_sum, valid_l_sum = 0, 0
    for i in range(k):
        data = get_k_fold_data(k, i, X_train, y_train)
        net = get_net(X_train.shape[1])
        train_ls, valid_ls = train(net, *data, num_epochs, learning_rate,
                                   weight_decay, batch_size)
        train_l_sum += train_ls[-1]
        valid_l_sum += valid_ls[-1]
        if i == 0:
            d2l.semilogy(range(1, num_epochs + 1), train_ls, 'epochs', 'rmse',
                         range(1, num_epochs + 1), valid_ls,
                         ['train', 'valid'])
        print('fold %d, train rmse %f, valid rmse %f' % (i, train_ls[-1], valid_ls[-1]))
    return train_l_sum / k, valid_l_sum / k

模型选择

我们使用一组未经调优的超参数并计算交叉验证误差。可以改动这些超参数来尽可能减小平均测试误差。
有时候你会发现一组参数的训练误差可以达到很低，但是在$K$折交叉验证上的误差可能反而较高。这种现象很可能是由过拟合造成的。因此，当训练误差降低时，我们要观察$K$折交叉验证上的误差是否也相应降低。

k, num_epochs, lr, weight_decay, batch_size = 5, 100, 5, 0, 64
train_l, valid_l = k_fold(k, train_features, train_labels, num_epochs, lr, weight_decay, batch_size)
print('%d-fold validation: avg train rmse %f, avg valid rmse %f' % (k, train_l, valid_l))

预测并在Kaggle中提交结果

下面定义预测函数。在预测之前，我们会使用完整的训练数据集来重新训练模型，并将预测结果存成提交所需要的格式。

def train_and_pred(train_features, test_features, train_labels, test_data,
                   num_epochs, lr, weight_decay, batch_size):
    net = get_net(train_features.shape[1])
    train_ls, _ = train(net, train_features, train_labels, None, None,
                        num_epochs, lr, weight_decay, batch_size)
    d2l.semilogy(range(1, num_epochs + 1), train_ls, 'epochs', 'rmse')
    print('train rmse %f' % train_ls[-1])
    preds = net(test_features).detach().numpy()
    test_data['SalePrice'] = pd.Series(preds.reshape(1, -1)[0])
    submission = pd.concat([test_data['Id'], test_data['SalePrice']], axis=1)
    submission.to_csv('./submission.csv', index=False)
    # sample_submission_data = pd.read_csv("../input/house-prices-advanced-regression-techniques/sample_submission.csv")