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gradient_descent.py
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gradient_descent.py
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# -*- coding: utf-8 -*-
"""Assignment-1 Part-1.ipynb
Automatically generated by Colaboratory.
Original file is located at
https://colab.research.google.com/drive/12h3ecus-lYs_Pq6C10NoDHG0CdUnE2DM
"""
import pandas as pd
import matplotlib.pyplot as plt
import seaborn
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import mean_absolute_error, mean_squared_error
from sklearn.metrics import r2_score, explained_variance_score
from sklearn.linear_model import LinearRegression, SGDRegressor
import warnings
warnings.filterwarnings('ignore')
## Loading the dataset.
#Read csv file data into a dataframe and peek top 5 rows.
cols = ['FREQUENCY', 'ANGLE_OF_ATTACK', 'CHORD_LEN', 'FREE_STREAM_VELOCITY', 'SUCTION_SIDE_DISP_THICKNESS',
'SCALED_SOUND_PRESSURE']
df = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/00291/airfoil_self_noise.dat', sep='\t', names=cols)
df.head()
## Pre-processing Step
#detect and remove fields with duplicated, None, NaN, or empty '' values.
pd.options.mode.use_inf_as_na = True
print(df.isnull().sum())
print(df.duplicated().sum())
df.dropna(inplace=True)
df.drop_duplicates()
## Exploratory Data Analysis
#information about the attributes.
df.info()
#exploring the dataset
df.describe()
#exploring the target variable
df['SCALED_SOUND_PRESSURE'].describe()
## Feature Engineering
###Histogram
df.hist(color='blue', edgecolor='black', grid=False)
plt.tight_layout(rect=(0,0,1.2,1.2))
#computing pairwise correlations in the dataset
corrs = df.corr()
print(corrs)
#Correlations consist of redundancies. Removing using a boolean mask:
mask = np.triu(np.ones_like(corrs, dtype=bool))
### Heatmap
#plot heatmap to visualize the magnitude of correlation between each pair
seaborn.heatmap(corrs, mask=mask, cmap="Blues", annot=True, linewidth=0.5)
plt.show()
### Pairplot
#checking pair-wise correlationships in the dataset.
seaborn.pairplot(df, height=3)
plt.show()
## Part-1: Implementing an SGD Regressor Without Libraries
### Splitting data into dependent and independent variables - x&y
x = df.iloc[:,:-1]
y = df.iloc[:,-1]
#Splitting data into 70/30 train/test samples
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.3, shuffle=True)
x_train.shape, x_test.shape, y_train.shape, y_test.shape
#Resizing the distribution of values so that the mean of the observed values is 0 and the standard deviation is 1
sc = StandardScaler()
x_train_trans = sc.fit_transform(x_train)
x_test_trans = sc.transform(x_test)
class ManualSGD:
def __init__(self, learning_rate=0.001, epochs=500, threshold=None):
self.learning_rate=learning_rate
self.epochs=epochs
self.threshold=threshold
#predicting values using our model
def predict(self, x_test_trans):
x = np.insert(x_test_trans.T,0,np.ones(x_test_trans.shape[0]),axis=0)
dot_prod = np.dot(self.weights, x)
return dot_prod
def Rsquared(self,x,y):
return 1-(((y - self.predict(x))**2).sum()/((y - y.mean())**2).sum())
def loss_function(self,x,y,category='mse'):
if category == 'mse':
loss=np.sum(np.square(x.reshape(-1, 1) - y.reshape(-1, 1)))/(2*x.shape[0])
return np.round(loss,3)
def fit(self,x,y):
self.losses=[] #list to track the losses
self.x=x
self.y=y
self.weights = np.random.rand(self.x.shape[1]+1).reshape(1,-1)
self.feature_vector = np.insert(self.x.T, 0,np.ones(self.x.shape[0]), axis=0)
dw=0
while self.epochs>=0:
self.hyp = np.dot(self.weights,self.feature_vector)
self.losses.append(self.loss_function(self.hyp,y))
# @ is matrix multiplication
dw = (self.feature_vector@(self.hyp-self.y).T)
dw /= self.x.shape[0] #average it
self.weights -= (self.learning_rate*dw.reshape(1,-1))
#update weights
self.epochs -= 1 #decrement iterations count by 1
#Optimum Learning Rate and Iterations
lr, itrs = 0.003, 15000
#create object of class
model = ManualSGD(learning_rate=lr,epochs=itrs)
#fit the training data on the model
model.fit(x_train_trans,np.array(y_train))
#predict
y_pred=model.predict(x_test_trans)
loss=list(model.losses)
#visualize loss
plt.plot(loss)
plt.xlabel("Epochs/Max_iterations")
plt.ylabel("Loss")
plt.show()
r2 = model.Rsquared(x_train_trans,np.array(y_train))
mae = mean_absolute_error(y_train, model.hyp[0])
rmse = mean_squared_error(y_train, model.hyp[0], squared=False)
evs = explained_variance_score(y_train, model.hyp[0])
print("Training Error for Learning Rate: "+str(lr)+", Iterations= "+str(itrs))
print("======================================")
print("R2 Score: ", r2)
print("Mean absolute error: ", mae)
print("Root Mean squared error: ", rmse)
print("Explained Variance Score: ", evs)
r2 = model.Rsquared(x_test_trans,np.array(y_test))
mae = mean_absolute_error(y_test, y_pred[0])
rmse = mean_squared_error(y_test, y_pred[0], squared=False)
evs = explained_variance_score(y_test, y_pred[0])
print("Test Error for Learning Rate: "+str(lr)+", Iterations= "+str(itrs))
print("======================================")
print("R2 Score: ", r2)
print("Mean absolute error: ", mae)
print("Root Mean squared error: ", rmse)
print("Explained Variance Score: ", evs)
lr_list = [0.001, 0.003, 0.01, 0.1, 0.25]
epoch_list = [7000, 10000, 15000, 25000, 40000]
for lr in lr_list:
for itrs in epoch_list:
model = ManualSGD(learning_rate=lr,epochs=itrs)
model.fit(x_train_trans,np.array(y_train))
r2 = model.Rsquared(x_train_trans,np.array(y_train))
mae = mean_absolute_error(y_train, model.hyp[0])
rmse = mean_squared_error(y_train, model.hyp[0], squared=False)
evs = explained_variance_score(y_train, model.hyp[0])
print("Training Error for Learning Rate: "+str(lr)+", Iterations= "+str(itrs))
print("======================================")
print("R2 Score: ", r2)
print("Mean absolute error: ", mae)
print("Root Mean squared error: ", rmse)
print("Explained Variance Score: ", evs)
file = open("Manual_SGD_log.txt","a")
file.write("LR = " + str(lr) + ", max_iterations = " + str(itrs) +
", R^2 = "+str(r2) + ", MAE = "+str(mae) + ", RMSE = " + str(rmse) +
", Explained-Variance = " + str(evs) + " \n")
file.close()
print("Wrote to file sucessfully.")
"""# **From the above set of experiments, the best performance was exhibited by the combination of learning rate=0.003 and epochs=7,000.** """
#Optimum Learning Rate and Iterations
lr, itrs = 0.003, 7000
#create object of class
model = ManualSGD(learning_rate=lr,epochs=itrs)
#fit the training data on the model
model.fit(x_train_trans,np.array(y_train))
#predict
y_pred=model.predict(x_test_trans)
loss=list(model.losses)
#visualize loss
plt.plot(loss)
plt.xlabel("Epochs/Max_iterations")
plt.ylabel("Loss")
plt.show()
r2 = model.Rsquared(x_train_trans,np.array(y_train))
mae = mean_absolute_error(y_train, model.hyp[0])
rmse = mean_squared_error(y_train, model.hyp[0], squared=False)
evs = explained_variance_score(y_train, model.hyp[0])
print("Training Error for Learning Rate: "+str(lr)+", Iterations= "+str(itrs))
print("======================================")
print("R2 Score: ", r2)
print("Mean absolute error: ", mae)
print("Root Mean squared error: ", rmse)
print("Explained Variance Score: ", evs)
r2 = model.Rsquared(x_test_trans,np.array(y_test))
mae = mean_absolute_error(y_test, y_pred[0])
rmse = mean_squared_error(y_test, y_pred[0], squared=False)
evs = explained_variance_score(y_test, y_pred[0])
print("Test Error for Learning Rate: "+str(lr)+", Iterations= "+str(itrs))
print("======================================")
print("R2 Score: ", r2)
print("Mean absolute error: ", mae)
print("Root Mean squared error: ", rmse)
print("Explained Variance Score: ", evs)