In [212]:

    

import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline

# import data
dataframe = pd.read_csv('turnstile_data_master_with_weather.csv', nrows=1000)


    

In [213]:

    

import numpy as np
import pandas as pd
from ggplot import *

"""
In this question, you need to:
1) implement the compute_cost() and gradient_descent() procedures
2) Select features (in the predictions procedure) and make predictions.

"""

def normalize_features(array):
   """
   Normalize the features in the data set.
   """
   array_normalized = (array-array.mean())/array.std()
   mu = array.mean()
   sigma = array.std()

   return array_normalized, mu, sigma

def compute_cost(X, y, theta):
    """
    Compute the cost function given a set of features / values, 
    and the values for our thetas.
    
    This can be the same code as the compute_cost function in the lesson #3 exercises,
    but feel free to implement your own.
    """
    m = len(y)
    
    cost = (1.0/(2.0*m)) * (((X.dot(theta)) - y).T).dot(X.dot(theta) - y)

    return cost

# delta-vector function for derivatives
def deltas(X, y, theta):
    m = len(y)
    delta = np.zeros(((171+1),1))

    delta = ((1.0/m) * (X.dot(theta) - y).T.dot(X)).T
    return delta

def gradient_descent(X, y, theta, alpha, iterations):
    """
    Perform gradient descent given a data set with an arbitrary number of features.
    
    This can be the same gradient descent code as in the lesson #3 exercises,
    but feel free to implement your own.
    """

    # store cost function values for plotting
    J_values = np.zeros((iterations,1))

    # gradient descent
    for iteration in xrange(0,iterations):
        theta = theta - (alpha[7] * deltas(X, y, theta))
 
    return theta

def predictions(dataframe):
    '''
    The NYC turnstile data is stored in a pandas dataframe called weather_turnstile.
    Using the information stored in the dataframe, let's predict the ridership of
    the NYC subway using linear regression with gradient descent.
    
    You can download the complete turnstile weather dataframe here:
    https://www.dropbox.com/s/meyki2wl9xfa7yk/turnstile_data_master_with_weather.csv    
    
    Your prediction should have a R^2 value of 0.20 or better.
    You need to experiment using various input features contained in the dataframe. 
    We recommend that you don't use the EXITSn_hourly feature as an input to the 
    linear model because we cannot use it as a predictor: we cannot use exits 
    counts as a way to predict entry counts. 
    
    Note: Due to the memory and CPU limitation of our Amazon EC2 instance, we will
    give you a random subet (~15%) of the data contained in 
    turnstile_data_master_with_weather.csv. You are encouraged to experiment with 
    this computer on your own computer, locally. 
    
    
    If you'd like to view a plot of your cost history, uncomment the call to 
    plot_cost_history below. The slowdown from plotting is significant, so if you 
    are timing out, the first thing to do is to comment out the plot command again.
    
    If you receive a "server has encountered an error" message, that means you are 
    hitting the 30-second limit that's placed on running your program. Try using a 
    smaller number for num_iterations if that's the case.
    
    If you are using your own algorithm/models, see if you can optimize your code so 
    that it runs faster.
    '''
    # initial data vectors
    x = dataframe[['Hour', 'maxpressurei', 'maxdewpti', 'mindewpti', 'meandewpti', 'meanpressurei', 'mintempi', 'maxtempi']]
    y = dataframe['ENTRIESn_hourly'].values

    # training sample size
    m = len(y)

    # proper vector shape
    y.shape = (m,1)

    # Add UNIT to features using dummy variables
    dummy_units = pd.get_dummies(dataframe['UNIT'], prefix='unit')
    x = x.join(dummy_units)
    x = x.values

    # number of features
    n = len(x[0,:])

    # design matrix
    X = np.hstack((np.ones((m,1)),x))

    # theta parameters 
    theta = np.zeros(((n+1),1))

    #gradient descent, number of iterations
    iterations = 500

    # learning rates to try
    alpha = [-0.3, -0.1, -0.03, -0.01, -0.003, -0.001, 0, 0.0001, 0.0003, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3]
    a_index = 7

    theta = gradient_descent(X, y, theta, alpha, iterations)
    
    plot = None
    # -------------------------------------------------
    # Uncomment the next line to see your cost history
    # -------------------------------------------------
    # plot = plot_cost_history(alpha, cost_history)
    # 
    # Please note, there is a possibility that plotting
    # this in addition to your calculation will exceed 
    # the 30 second limit on the compute servers.
    
    predictions = np.dot(X, theta)
    return predictions, plot


def plot_cost_history(alpha, cost_history):
   """This function is for viewing the plot of your cost history.
   You can run it by uncommenting this

       plot_cost_history(alpha, cost_history) 

   call in predictions.
   
   If you want to run this locally, you should print the return value
   from this function.
   """
   cost_df = pd.DataFrame({
      'Cost_History': cost_history,
      'Iteration': range(len(cost_history))
   })
   return ggplot(cost_df, aes('Iteration', 'Cost_History')) + \
      geom_point() + ggtitle('Cost History for alpha = %.3f' % alpha )


    

In [214]:

    

predictions = predictions(dataframe)


    

In [215]:

    

import numpy as np
import pandas as pd
from ggplot import *

"""
In this question, you need to:
1) implement the compute_cost() and gradient_descent() procedures
2) Select features (in the predictions procedure) and make predictions.

"""
def normalize_features(array):
   """
   Normalize the features in the data set.
   """
   array_normalized = (array-array.mean())/array.std()
   mu = array.mean()
   sigma = array.std()

   return array_normalized, mu, sigma

def compute_cost(X, y, theta):
    """
    Compute the cost function given a set of features / values, 
    and the values for our thetas.
    
    This can be the same code as the compute_cost function in the lesson #3 exercises,
    but feel free to implement your own.
    """
    m = len(y)
    
    cost = (1.0/(2.0*m)) * (((X.dot(theta)) - y).T).dot(X.dot(theta) - y)

    return cost

def gradient_descent(X, y, theta, alpha, iterations):
    """
    Perform gradient descent given a data set with an arbitrary number of features.
    
    This can be the same gradient descent code as in the lesson #3 exercises,
    but feel free to implement your own.
    """

    # delta-vector function for derivatives
    def deltas(X, y, theta):
        m = len(y)
        delta = np.zeros(((171+1),1))

        delta = ((1.0/m) * (X.dot(theta) - y).T.dot(X)).T
        return delta

    # store cost function values for plotting
    J_values = np.zeros((iterations,1))

    # gradient descent
    for iteration in xrange(0,iterations):
        theta = theta - (alpha * deltas(X, y, theta))
 
    return theta

def predictions(dataframe):
    '''
    The NYC turnstile data is stored in a pandas dataframe called weather_turnstile.
    Using the information stored in the dataframe, let's predict the ridership of
    the NYC subway using linear regression with gradient descent.
    
    You can download the complete turnstile weather dataframe here:
    https://www.dropbox.com/s/meyki2wl9xfa7yk/turnstile_data_master_with_weather.csv    
    
    Your prediction should have a R^2 value of 0.20 or better.
    You need to experiment using various input features contained in the dataframe. 
    We recommend that you don't use the EXITSn_hourly feature as an input to the 
    linear model because we cannot use it as a predictor: we cannot use exits 
    counts as a way to predict entry counts. 
    
    Note: Due to the memory and CPU limitation of our Amazon EC2 instance, we will
    give you a random subet (~15%) of the data contained in 
    turnstile_data_master_with_weather.csv. You are encouraged to experiment with 
    this computer on your own computer, locally. 
    
    
    If you'd like to view a plot of your cost history, uncomment the call to 
    plot_cost_history below. The slowdown from plotting is significant, so if you 
    are timing out, the first thing to do is to comment out the plot command again.
    
    If you receive a "server has encountered an error" message, that means you are 
    hitting the 30-second limit that's placed on running your program. Try using a 
    smaller number for num_iterations if that's the case.
    
    If you are using your own algorithm/models, see if you can optimize your code so 
    that it runs faster.
    '''
    # initial data vectors
    x = dataframe[['Hour', 'maxpressurei', 'maxdewpti', 'mindewpti', 'meandewpti', 'meanpressurei', 'mintempi', 'maxtempi']]
    y = dataframe['ENTRIESn_hourly'].values

    # training sample size
    m = len(y)

    # proper vector shape
    y.shape = (m,1)

    # Add UNIT to features using dummy variables
    dummy_units = pd.get_dummies(dataframe['UNIT'], prefix='unit')
    x = x.join(dummy_units)
    x = x.values

    # number of features
    n = len(x[0,:])

    # design matrix
    X = np.hstack((np.ones((m,1)),x))

    # theta parameters 
    theta = np.zeros(((n+1),1))

    #gradient descent, number of iterations
    iterations = 500

    # learning rates to try
    alpha = [-0.3, -0.1, -0.03, -0.01, -0.003, -0.001, 0, 0.0001, 0.0003, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3]
    a_index = 7

    theta = gradient_descent(X, y, theta, alpha, iterations)
    
    predictions = np.dot(X, theta)
    return predictions

def plot_cost_history(alpha, cost_history):
   """This function is for viewing the plot of your cost history.
   You can run it by uncommenting this

       plot_cost_history(alpha, cost_history) 

   call in predictions.
   
   If you want to run this locally, you should print the return value
   from this function.
   """
   cost_df = pd.DataFrame({
      'Cost_History': cost_history,
      'Iteration': range(len(cost_history))
   })
   return ggplot(cost_df, aes('Iteration', 'Cost_History')) + \
      geom_point() + ggtitle('Cost History for alpha = %.3f' % alpha )


    

In [216]:

    

predictions = predictions(dataframe)


    

In [217]:

    

import numpy as np
import pandas as pd
from ggplot import *

"""
In this question, you need to:
1) implement the compute_cost() and gradient_descent() procedures
2) Select features (in the predictions procedure) and make predictions.

"""
def normalize_features(array):
   """
   Normalize the features in the data set.
   """
   array_normalized = (array-array.mean())/array.std()
   mu = array.mean()
   sigma = array.std()

   return array_normalized, mu, sigma

def compute_cost(features, values, theta):
    """
    Compute the cost function given a set of features / values, 
    and the values for our thetas.
    
    This can be the same code as the compute_cost function in the lesson #3 exercises,
    but feel free to implement your own.
    """
    m = len(values)
    
    cost = (1.0/(2.0*m)) * (((features.dot(theta)) - values).T).dot(features.dot(theta) - values)

    return cost

def gradient_descent(features, values, theta, alpha, num_iterations):
    """
    Perform gradient descent given a data set with an arbitrary number of features.
    
    This can be the same gradient descent code as in the lesson #3 exercises,
    but feel free to implement your own.
    """

    m = len(values)
    cost_history = []

    # gradient descent
    for iteration in xrange(0,num_iterations):
        theta = theta - (alpha * (((1.0/m) * (features.dot(theta) - values).T.dot(features)).T))
        cost_history.append(compute_cost(features, values, theta))
 
    return theta

def predictions(dataframe):
    '''
    The NYC turnstile data is stored in a pandas dataframe called weather_turnstile.
    Using the information stored in the dataframe, let's predict the ridership of
    the NYC subway using linear regression with gradient descent.
    
    You can download the complete turnstile weather dataframe here:
    https://www.dropbox.com/s/meyki2wl9xfa7yk/turnstile_data_master_with_weather.csv    
    
    Your prediction should have a R^2 value of 0.20 or better.
    You need to experiment using various input features contained in the dataframe. 
    We recommend that you don't use the EXITSn_hourly feature as an input to the 
    linear model because we cannot use it as a predictor: we cannot use exits 
    counts as a way to predict entry counts. 
    
    Note: Due to the memory and CPU limitation of our Amazon EC2 instance, we will
    give you a random subet (~15%) of the data contained in 
    turnstile_data_master_with_weather.csv. You are encouraged to experiment with 
    this computer on your own computer, locally. 
    
    
    If you'd like to view a plot of your cost history, uncomment the call to 
    plot_cost_history below. The slowdown from plotting is significant, so if you 
    are timing out, the first thing to do is to comment out the plot command again.
    
    If you receive a "server has encountered an error" message, that means you are 
    hitting the 30-second limit that's placed on running your program. Try using a 
    smaller number for num_iterations if that's the case.
    
    If you are using your own algorithm/models, see if you can optimize your code so 
    that it runs faster.
    '''
    # initial data vectors
    x = dataframe[['Hour', 'maxpressurei', 'maxdewpti', 'mindewpti', 'meandewpti', 'meanpressurei', 'mintempi', 'maxtempi']]
    values = dataframe['ENTRIESn_hourly'].values

    # training sample size
    m = len(values)

    # proper vector shape
    values.shape = (m,1)

    # Add UNIT to features using dummy variables
    dummy_units = pd.get_dummies(dataframe['UNIT'], prefix='unit')
    x = x.join(dummy_units)
    x = x.values

    # number of features
    n = len(x[0,:])

    # design matrix
    features = np.hstack((x,np.ones((m,1))))
    print features
    # theta parameters 
    theta = np.zeros(((n+1),1))

    #gradient descent, number of iterations
    iterations = 400

    # learning rates to try
    alpha = 0.0001

    theta = gradient_descent(features, values, theta, alpha, iterations)

    # calculate r^2 (after gradient descent) 
    r_squared = 1 - np.sum((np.square(values - np.dot(features, theta))))/np.sum(np.square(values - np.mean(values)))
    print r_squared
    
    plot = None
    
    predictions = np.dot(features, theta)
    return predictions, plot

def plot_cost_history(alpha, cost_history):
   """This function is for viewing the plot of your cost history.
   You can run it by uncommenting this

       plot_cost_history(alpha, cost_history) 

   call in predictions.
   
   If you want to run this locally, you should print the return value
   from this function.
   """
   cost_df = pd.DataFrame({
      'Cost_History': cost_history,
      'Iteration': range(len(cost_history))
   })
   return ggplot(cost_df, aes('Iteration', 'Cost_History')) + \
      geom_point() + ggtitle('Cost History for alpha = %.3f' % alpha )


    

In [218]:

    

predictions = predictions(dataframe)
predictions


    

    




[[  1.    30.31  42.   ...,   0.     0.     1.  ]
 [  5.    30.31  42.   ...,   0.     0.     1.  ]
 [  9.    30.31  42.   ...,   0.     0.     1.  ]
 ..., 
 [  1.    30.31  42.   ...,   0.     1.     1.  ]
 [  5.    30.31  42.   ...,   0.     1.     1.  ]
 [  9.    30.31  42.   ...,   0.     1.     1.  ]]
0.202824343075






    
Out[218]:





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        [ 1924.33067788],
        [ 2357.99278763],
        [  187.70383568],
        [  621.36594544],
        [ 1055.02805519],
        [ 1488.69016495],
        [ 1922.3522747 ],
        [ 2356.01438446],
        [   79.34999599],
        [  513.01210574],
        [  946.6742155 ],
        [ 1380.33632525],
        [ 1813.998435  ],
        [ 2247.66054476],
        [  187.75842003],
        [  621.42052979],
        [ 1055.08263954]]), None)

In [219]:

    

import numpy as np
import pandas
from ggplot import *

"""
In this question, you need to:
1) implement the compute_cost() and gradient_descent() procedures
2) Select features (in the predictions procedure) and make predictions.

"""

def normalize_features(array):
   """
   Normalize the features in the data set.
   """
   array_normalized = (array-array.mean())/array.std()
   mu = array.mean()
   sigma = array.std()

   return array_normalized, mu, sigma

def compute_cost(features, values, theta):
    """
    Compute the cost function given a set of features / values, 
    and the values for our thetas.
    
    This can be the same code as the compute_cost function in the lesson #3 exercises,
    but feel free to implement your own.
    """
    
    m = len(values)
    
    cost = (1.0/(2.0*m)) * (((features.dot(theta)) - values).T).dot(features.dot(theta) - values)

    return cost

def gradient_descent(features, values, theta, alpha, num_iterations):
    """
    Perform gradient descent given a data set with an arbitrary number of features.
    
    This can be the same gradient descent code as in the lesson #3 exercises,
    but feel free to implement your own.
    """
    
    m = len(values)
    cost_history = []
    
    for iteration in xrange(0,num_iterations):
        theta = theta - (alpha * (((1.0/m) * (features.dot(theta) - values).T.dot(features)).T))
        cost_history.append(compute_cost(features, values, theta))
    
    return theta, pandas.Series(cost_history)

def predictions(dataframe):
    '''
    The NYC turnstile data is stored in a pandas dataframe called weather_turnstile.
    Using the information stored in the dataframe, let's predict the ridership of
    the NYC subway using linear regression with gradient descent.
    
    You can download the complete turnstile weather dataframe here:
    https://www.dropbox.com/s/meyki2wl9xfa7yk/turnstile_data_master_with_weather.csv    
    
    Your prediction should have a R^2 value of 0.20 or better.
    You need to experiment using various input features contained in the dataframe. 
    We recommend that you don't use the EXITSn_hourly feature as an input to the 
    linear model because we cannot use it as a predictor: we cannot use exits 
    counts as a way to predict entry counts. 
    
    Note: Due to the memory and CPU limitation of our Amazon EC2 instance, we will
    give you a random subet (~15%) of the data contained in 
    turnstile_data_master_with_weather.csv. You are encouraged to experiment with 
    this computer on your own computer, locally. 
    
    
    If you'd like to view a plot of your cost history, uncomment the call to 
    plot_cost_history below. The slowdown from plotting is significant, so if you 
    are timing out, the first thing to do is to comment out the plot command again.
    
    If you receive a "server has encountered an error" message, that means you are 
    hitting the 30-second limit that's placed on running your program. Try using a 
    smaller number for num_iterations if that's the case.
    
    If you are using your own algorithm/models, see if you can optimize your code so 
    that it runs faster.
    '''
    # Select Features (try different features!)
    features = dataframe[['rain', 'precipi', 'Hour', 'meantempi']]
    
    # Add UNIT to features using dummy variables
    dummy_units = pandas.get_dummies(dataframe['UNIT'], prefix='unit')
    features = features.join(dummy_units)
    
    # Values
    values = dataframe[['ENTRIESn_hourly']]
    m = len(values)

    features, mu, sigma = normalize_features(features)
    features['ones'] = np.ones(m) # Add a column of 1s (y intercept)
    
    # Convert features and values to numpy arrays
    features_array = np.array(features)
    values_array = np.array(values).flatten()

    # Set values for alpha, number of iterations.
    alpha = 0.1 # please feel free to change this value
    num_iterations = 75 # please feel free to change this value

    # Initialize theta, perform gradient descent
    theta_gradient_descent = np.zeros(len(features.columns))
    theta_gradient_descent, cost_history = gradient_descent(features_array, 
                                                            values_array, 
                                                            theta_gradient_descent, 
                                                            alpha, 
                                                            num_iterations)
    
    plot = None
    # -------------------------------------------------
    # Uncomment the next line to see your cost history
    # -------------------------------------------------
    # plot = plot_cost_history(alpha, cost_history)
    # 
    # Please note, there is a possibility that plotting
    # this in addition to your calculation will exceed 
    # the 30 second limit on the compute servers.

    # calculate r^2 (after gradient descent) 
    r_squared = 1 - np.sum((np.square(values_array - np.dot(features_array, theta_gradient_descent))))/np.sum(np.square(values_array - np.mean(values_array)))
    print r_squared
    
    predictions = np.dot(features_array, theta_gradient_descent)
    return predictions, plot


def plot_cost_history(alpha, cost_history):
   """This function is for viewing the plot of your cost history.
   You can run it by uncommenting this

       plot_cost_history(alpha, cost_history) 

   call in predictions.
   
   If you want to run this locally, you should print the return value
   from this function.
   """
   cost_df = pandas.DataFrame({
      'Cost_History': cost_history,
      'Iteration': range(len(cost_history))
   })
   return ggplot(cost_df, aes('Iteration', 'Cost_History')) + \
      geom_point() + ggtitle('Cost History for alpha = %.3f' % alpha )