使用线性回归预测波士顿房价¶

#下载数据
!wget https://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.data -O housing.data 

# 从文件导入数据
datafile = './housing.data'
housing_data = np.fromfile(datafile, sep=' ')
feature_names = ['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE','DIS', 'RAD', 'TAX', 'PTRATIO', 'B', 'LSTAT', 'MEDV']
feature_num = len(feature_names)
# 将原始数据进行Reshape，变成[N, 14]这样的形状
housing_data = housing_data.reshape([housing_data.shape[0] // feature_num, feature_num])

# 画图看特征间的关系,主要是变量两两之间的关系（线性或非线性，有无明显较为相关关系）
features_np = np.array([x[:13] for x in housing_data], np.float32)
labels_np = np.array([x[-1] for x in housing_data], np.float32)
# data_np = np.c_[features_np, labels_np]
df = pd.DataFrame(housing_data, columns=feature_names)
matplotlib.use('TkAgg')
%matplotlib inline
sns.pairplot(df.dropna(), y_vars=feature_names[-1], x_vars=feature_names[::-1], diag_kind='kde')
plt.show()

# 相关性分析
fig, ax = plt.subplots(figsize=(15, 1)) 
corr_data = df.corr().iloc[-1]
corr_data = np.asarray(corr_data).reshape(1, 14)
ax = sns.heatmap(corr_data, cbar=True, annot=True)
plt.show()

sns.boxplot(data=df.iloc[:, 0:13])

<matplotlib.axes._subplots.AxesSubplot at 0x7f0e7bbca390>

features_max = housing_data.max(axis=0)
features_min = housing_data.min(axis=0)
features_avg = housing_data.sum(axis=0) / housing_data.shape[0]

BATCH_SIZE = 20
def feature_norm(input):
    f_size = input.shape
    output_features = np.zeros(f_size, np.float32)
    for batch_id in range(f_size[0]):
        for index in range(13):
            output_features[batch_id][index] = (input[batch_id][index] - features_avg[index]) / (features_max[index] - features_min[index])
    return output_features 

# 只对属性进行归一化
housing_features = feature_norm(housing_data[:, :13])
# print(feature_trian.shape)
housing_data = np.c_[housing_features, housing_data[:, -1]].astype(np.float32)
# print(training_data[0])

# 归一化后的train_data, 看下各属性的情况
features_np = np.array([x[:13] for x in housing_data],np.float32)
labels_np = np.array([x[-1] for x in housing_data],np.float32)
data_np = np.c_[features_np, labels_np]
df = pd.DataFrame(data_np, columns=feature_names)
sns.boxplot(data=df.iloc[:, 0:13])

<matplotlib.axes._subplots.AxesSubplot at 0x7f0e7ba9ee10>

# 将训练数据集和测试数据集按照8:2的比例分开
ratio = 0.8
offset = int(housing_data.shape[0] * ratio)
train_data = housing_data[:offset]
test_data = housing_data[offset:]

import paddle.nn.functional as F 
y_preds = []
labels_list = []

def train(model):
    print('start training ... ')
    # 开启模型训练模式
    model.train()
    EPOCH_NUM = 500
    train_num = 0
    optimizer = paddle.optimizer.SGD(learning_rate=0.001, parameters=model.parameters())
    for epoch_id in range(EPOCH_NUM):
        # 在每轮迭代开始之前，将训练数据的顺序随机的打乱
        np.random.shuffle(train_data)
        # 将训练数据进行拆分，每个batch包含20条数据
        mini_batches = [train_data[k: k+BATCH_SIZE] for k in range(0, len(train_data), BATCH_SIZE)]
        for batch_id, data in enumerate(mini_batches):
            features_np = np.array(data[:, :13], np.float32)
            labels_np = np.array(data[:, -1:], np.float32)
            features = paddle.to_tensor(features_np)
            labels = paddle.to_tensor(labels_np)
            # 前向计算
            y_pred = model(features)
            cost = F.mse_loss(y_pred, label=labels)
            train_cost = cost.numpy()[0]
            # 反向传播
            cost.backward()
            # 最小化loss，更新参数
            optimizer.step()
            # 清除梯度
            optimizer.clear_grad()
            
            if batch_id%30 == 0 and epoch_id%50 == 0:
                print("Pass:%d,Cost:%0.5f"%(epoch_id, train_cost))

            train_num = train_num + BATCH_SIZE
            train_nums.append(train_num)
            train_costs.append(train_cost)
        
model = Regressor()
train(model)

start training ... 
Pass:0,Cost:609.66571
Pass:50,Cost:34.14360
Pass:100,Cost:98.01004
Pass:150,Cost:19.73042
Pass:200,Cost:66.26864
Pass:250,Cost:25.50872
Pass:300,Cost:76.24126
Pass:350,Cost:18.54617
Pass:400,Cost:49.38592
Pass:450,Cost:15.36817

matplotlib.use('TkAgg')
%matplotlib inline
draw_train_process(train_nums, train_costs)

# 获取预测数据
INFER_BATCH_SIZE = 100

infer_features_np = np.array([data[:13] for data in test_data]).astype("float32")
infer_labels_np = np.array([data[-1] for data in test_data]).astype("float32")

infer_features = paddle.to_tensor(infer_features_np)
infer_labels = paddle.to_tensor(infer_labels_np)
fetch_list = model(infer_features)

sum_cost = 0
for i in range(INFER_BATCH_SIZE):
    infer_result = fetch_list[i][0]
    ground_truth = infer_labels[i]
    if i % 10 == 0:
        print("No.%d: infer result is %.2f,ground truth is %.2f" % (i, infer_result, ground_truth))
    cost = paddle.pow(infer_result - ground_truth, 2)
    sum_cost += cost
mean_loss = sum_cost / INFER_BATCH_SIZE
print("Mean loss is:", mean_loss.numpy())

No.0: infer result is 11.93,ground truth is 8.50
No.10: infer result is 4.97,ground truth is 7.00
No.20: infer result is 14.26,ground truth is 11.70
No.30: infer result is 16.12,ground truth is 11.70
No.40: infer result is 13.31,ground truth is 10.80
No.50: infer result is 15.40,ground truth is 14.90
No.60: infer result is 18.79,ground truth is 21.40
No.70: infer result is 15.40,ground truth is 13.80
No.80: infer result is 18.12,ground truth is 20.60
No.90: infer result is 21.37,ground truth is 24.50
Mean loss is: [12.069371]

def plot_pred_ground(pred, ground):
    plt.figure()   
    plt.title("Predication v.s. Ground truth", fontsize=24)
    plt.xlabel("ground truth price(unit:$1000)", fontsize=14)
    plt.ylabel("predict price", fontsize=14)
    plt.scatter(ground, pred, alpha=0.5)  #  scatter:散点图,alpha:"透明度"
    plt.plot(ground, ground, c='red')
    plt.show()

plot_pred_ground(fetch_list, infer_labels_np)