Day 31: 60 days of Data Science and Machine Learning Series
Regression Project 1..
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In this post we will cover univariate linear regression with a project.
Linear Regression is used to model the relationship between two variables by fitting a linear equation to given data where one variable is explanatory variable and the other is a dependent variable.
Data for this project can be accessed here :
Let’s dive in!
Import necessary Libraries
import matplotlib.pyplot as plt
plt.style.use('ggplot')
%matplotlib inline
import numpy as np
import pandas as pd
import seaborn as sns
plt.rcParams['figure.figsize'] = (15, 10)
from mpl_toolkits.mplot3d import Axes3DLoad the Data
data = pd.read_csv('data.txt')data.info()Output —
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 97 entries, 0 to 96
Data columns (total 2 columns):
Population 97 non-null float64
Profit 97 non-null float64
dtypes: float64(2)
memory usage: 1.6 KBVisualize the Data
A scatterplot is used to determine the strength of the relationship between two variables in the given data.
ax=sns.scatterplot(x='Population', y = 'Profit',data=data)
ax.set_title('Profit vs population')Output —
Compute the Cost 𝐽(𝜃)
The objective of linear regression is to minimize the cost function
def cost_function(X,y,theta):
m=len(y)
y_pred=X.dot(theta)
error =( y_pred - y) **2
return 1/(2*m) * np.sum(error)m= data.Population.values.size
X = np.append(np.ones((m,1)),data.Population.values.reshape(m,1),axis=1)
y= data.Profit.values.reshape(m,1)
theta =np.zeros((2,1))cost_function(X,y,theta)Output —
32.072733877455676Implement Gradient Descent
Minimize the cost function 𝐽(𝜃)J(θ) by updating the below equation and repeat until convergence
def gradient_descent(X,y,theta,alpha,iterations):
m=len(y)
costs=[]
for i in range(iterations):
y_pred = X.dot(theta)
error = np.dot(X.transpose(),(y_pred-y))
theta -= alpha * 1/m *error
costs.append(cost_function(X,y,theta))
return theta,coststheta, costs = gradient_descent(X,y,theta,alpha=0.01,iterations=2000)
print("h(x) = {} + {}x1".format(str(round(theta[0,0],2)),
str(round(theta[1,0],2))))Output —
h(x) = -3.79 + 1.18x1Visualizing the Cost Function J(𝜃)
theta_0 = np.linspace(-10,10,100)
theta_1 = np.linspace(-1,4,100)cost_values = np.zeros((len(theta_0),len(theta_1)))for i in range(len(theta_0)):
for j in range(len(theta_1)):
t=np.array([theta_0[i],theta_1[j]])
cost_values[i,j]= cost_function(X,y,t)fig = plt.figure(figsize=(15,10))ax= fig.gca(projection='3d')
surf = ax.plot_surface(theta_0,theta_1,cost_values,cmap='viridis')
fig.colorbar(surf,shrink=0.5, aspect =5)plt.xlabel('$\ Theta_0$')
plt.ylabel('$\ Theta_1$')
ax.set_zlabel('$J(\Theta)$')
ax.view_init(32,32)plt.show()Plotting the Convergence
plt.plot(costs)
plt.xlabel('Iterations')
plt.ylabel('$J(\Theta)$')
Training Data with Univariate Linear Regression Fit
theta = np.squeeze(theta)
sns.scatterplot(x='Population',y='Profit',data=data)x_value = [x for x in range(5,25)]
y_value = [(x* theta[1] + theta[0]) for x in x_value]
sns.lineplot(x_value,y_value)plt.xlabel('Population')
plt.ylabel('Profit')
plt.title('Linear Regression Fit')
ML Regression Project 2: Coming soon
Follow and Stay tuned. Keep coding :)
For other projects, tune to —
Build Machine Learning Pipelines( With Code)
Recurrent Neural Network with Keras
Clustering Geolocation Data in Python using DBSCAN and K-Means
Facial Expression Recognition using Keras
Hyperparameter Tuning with Keras Tuner
Custom Layers in Keras
That’s it fellas. Peace out and keep coding :)
Stay Tuned and of-course let me end this post with a quote by Steve Jobs ;)
“Remembering that you are going to die is the best way I know to avoid the trap of thinking you have something to lose. You are already naked. There is no reason not to follow your heart.”
