线性回归

1. 配置

导入模块。

查看代码

#general
import io

# data
import numpy as np
import pandas as pd

# machine learning
import keras

# data visualization
import plotly.express as px
from plotly.subplots import make_subplots
import plotly.graph_objects as go
import seaborn as sns

# 博客园引流
from Keras备忘录 import build_model

加载数据集

 查看代码

chicago_taxi_dataset = pd.read_csv("https://download.mlcc.google.com/mledu-datasets/chicago_taxi_train.csv")

读取数据集

Read dataset

# Updates dataframe to use specific columns.
training_df = chicago_taxi_dataset[['TRIP_MILES', 'TRIP_SECONDS', 'FARE', 'COMPANY', 'PAYMENT_TYPE', 'TIP_RATE']]

print('Read dataset completed successfully.')
print('Total number of rows: {0}\n\n'.format(len(training_df.index)))
training_df.head(200)

2. 训练和预测，结果可视化

定义绘图函数（注意：此处plot_model函数对输入特征为二维时的绘制方法似乎是错的，有奖请读者斧正）

可视化plotting functions

def make_plots(df, feature_names, label_name, model_output, sample_size=200):

  random_sample = df.sample(n=sample_size).copy()
  random_sample.reset_index()
  weights, bias, epochs, rmse = model_output

  is_2d_plot = len(feature_names) == 1
  model_plot_type = "scatter" if is_2d_plot else "surface"
  fig = make_subplots(rows=1, cols=2,
                      subplot_titles=("Loss Curve", "Model Plot"),
                      specs=[[{"type": "scatter"}, {"type": model_plot_type}]])

  plot_data(random_sample, feature_names, label_name, fig)
  plot_model(random_sample, feature_names, weights, bias, fig)
  plot_loss_curve(epochs, rmse, fig)

  fig.show()
  return

def plot_loss_curve(epochs, rmse, fig):
  curve = px.line(x=epochs, y=rmse)
  curve.update_traces(line_color='#ff0000', line_width=3)

  fig.append_trace(curve.data[0], row=1, col=1)
  fig.update_xaxes(title_text="Epoch", row=1, col=1)
  fig.update_yaxes(title_text="Root Mean Squared Error", row=1, col=1, range=[rmse.min()*0.8, rmse.max()])

  return

def plot_data(df, features, label, fig):
  if len(features) == 1:
    scatter = px.scatter(df, x=features[0], y=label)
  else:
    scatter = px.scatter_3d(df, x=features[0], y=features[1], z=label)

  fig.append_trace(scatter.data[0], row=1, col=2)
  if len(features) == 1:
    fig.update_xaxes(title_text=features[0], row=1, col=2)
    fig.update_yaxes(title_text=label, row=1, col=2)
  else:
    fig.update_layout(scene1=dict(xaxis_title=features[0], yaxis_title=features[1], zaxis_title=label))

  return

def plot_model(df, features, weights, bias, fig):
  df['FARE_PREDICTED'] = bias[0]

  for index, feature in enumerate(features):
    df['FARE_PREDICTED'] = df['FARE_PREDICTED'] + weights[index][0] * df[feature]

  if len(features) == 1:
    model = px.line(df, x=features[0], y='FARE_PREDICTED')
    model.update_traces(line_color='#ff0000', line_width=3)
  else:
    z_name, y_name = "FARE_PREDICTED", features[1]
    z = [df[z_name].min(), (df[z_name].max() - df[z_name].min()) / 2, df[z_name].max()]
    y = [df[y_name].min(), (df[y_name].max() - df[y_name].min()) / 2, df[y_name].max()]
    x = []
    for i in range(len(y)):
      x.append((z[i] - weights[1][0] * y[i] - bias[0]) / weights[0][0])

    plane=pd.DataFrame({'x':x, 'y':y, 'z':[z] * 3})

    light_yellow = [[0, '#89CFF0'], [1, '#FFDB58']]
    model = go.Figure(data=go.Surface(x=plane['x'], y=plane['y'], z=plane['z'],
                                      colorscale=light_yellow))

  fig.add_trace(model.data[0], row=1, col=2)

  return

def model_info(feature_names, label_name, model_output):
  weights = model_output[0]
  bias = model_output[1]

  nl = "\n"
  header = "-" * 80
  banner = header + nl + "|" + "MODEL INFO".center(78) + "|" + nl + header

  info = ""
  equation = label_name + " = "

  for index, feature in enumerate(feature_names):
    info = info + "Weight for feature[{}]: {:.3f}\n".format(feature, weights[index][0])
    equation = equation + "{:.3f} * {} + ".format(weights[index][0], feature)

  info = info + "Bias: {:.3f}\n".format(bias[0])
  equation = equation + "{:.3f}\n".format(bias[0])

  return banner + nl + info + nl + equation

print("SUCCESS: defining plotting functions complete.")

定义训练函数

训练

def train_model(model, df, features, label, epochs, batch_size):
  """Train the model by feeding it data."""

  # Feed the model the feature and the label.
  # The model will train for the specified number of epochs.
  # input_x = df.iloc[:,1:3].values
  # df[feature]
  history = model.fit(x=features,
                      y=label,
                      batch_size=batch_size,
                      epochs=epochs)

  # Gather the trained model's weight and bias.
  trained_weight = model.get_weights()[0]
  trained_bias = model.get_weights()[1]

  # The list of epochs is stored separately from the rest of history.
  epochs = history.epoch

  # Isolate the error for each epoch.
  hist = pd.DataFrame(history.history)

  # To track the progression of training, we're going to take a snapshot
  # of the model's root mean squared error at each epoch.
  rmse = hist["root_mean_squared_error"]

  return trained_weight, trained_bias, epochs, rmse

定义实验函数，也可直接作为主函数。

实验

def run_experiment(df, feature_names, label_name, learning_rate, epochs, batch_size):

  print('INFO: starting training experiment with features={} and label={}\n'.format(feature_names, label_name))

  num_features = len(feature_names)

  features = df.loc[:, feature_names].values
  label = df[label_name].values

  model = build_model(learning_rate, num_features)
  model_output = train_model(model, df, features, label, epochs, batch_size)

  print('\nSUCCESS: training experiment complete\n')
  print('{}'.format(model_info(feature_names, label_name, model_output)))
  make_plots(df, feature_names, label_name, model_output)

  return model

3. 开展实验

先用一种特征：

单特征

# The following variables are the hyperparameters.
learning_rate = 0.001
epochs = 10
batch_size = 50

# Specify the feature and the label.
features = ['TRIP_MILES']
label = 'FARE'

model_1 = run_experiment(training_df, features, label, learning_rate, epochs, batch_size)

此时可以修改学习率到1或原来的一成或，或批次大小为原来的十倍，查看超参数的调整的影响。

再尝试用两种特征'TRIP_MILES'和'TRIP_MINUTES'（注意：若使用两种特征，则它们大小最好在同一量级，所以此处将训练集原始的特征'TRIP_SECONDS'转换成分钟数作为新特征训练），只需修改上述程序的部分：

修改部分

training_df['TRIP_MINUTES'] = training_df['TRIP_SECONDS']/60

features = ['TRIP_MILES', 'TRIP_MINUTES']

训练完后，采用训练集的随即部分样本（非标准操作，仅供学习模型预测步骤使用）做出预测。先定义预测函数

预测函数

def format_currency(x):
  return "${:.2f}".format(x)

def build_batch(df, batch_size):
  batch = df.sample(n=batch_size).copy()
  batch.set_index(np.arange(batch_size), inplace=True)
  return batch

def predict_fare(model, df, features, label, batch_size=50):
  batch = build_batch(df, batch_size)
  predicted_values = model.predict_on_batch(x=batch.loc[:, features].values)

  data = {"PREDICTED_FARE": [], "OBSERVED_FARE": [], "L1_LOSS": [],
          features[0]: [], features[1]: []}
  for i in range(batch_size):
    predicted = predicted_values[i][0]
    observed = batch.at[i, label]
    data["PREDICTED_FARE"].append(format_currency(predicted))
    data["OBSERVED_FARE"].append(format_currency(observed))
    data["L1_LOSS"].append(format_currency(abs(observed - predicted)))
    data[features[0]].append(batch.at[i, features[0]])
    data[features[1]].append("{:.2f}".format(batch.at[i, features[1]]))

  output_df = pd.DataFrame(data)
  return output_df

def show_predictions(output):
  header = "-" * 80
  banner = header + "\n" + "|" + "PREDICTIONS".center(78) + "|" + "\n" + header
  print(banner)
  print(output)
  return

然后作出预测：

output = predict_fare(model_2, training_df, features, label)
show_predictions(output)

4. 鸣谢

Google开发者中心。