17 minute readCreated on December 16, 2019Last modified on June 1, 2020

Polynomial Regression Using TensorFlow

In this tutorial you will learn about polynomial regression and how you can implement it in Tensorflow.

In this, we will be performing polynomial regression using 5 types of equations -

Linear
Quadratic
Cubic
Quartic
Quintic

Regression

What is Regression?

Regression is a statistical measurement that is used to try to determine the relationship between a dependent variable (often denoted by Y), and series of varying variables (called independent variables, often denoted by X ).

What is Polynomial Regression

This is a form of Regression Analysis where the relationship between Y and X is denoted as the nth degree/power of X. Polynomial regression even fits a non-linear relationship (e.g when the points don't form a straight line).

Imports

import tensorflow.compat.v1 as tf
+Polynomial Regression Using TensorFlow | Navan ChauhanNavan ChauhanAbout Me
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17 minute readCreated on December 16, 2019Last modified on September 15, 2020Polynomial Regression Using TensorFlow
In this tutorial you will learn about polynomial regression and how you can implement it in Tensorflow.
In this, we will be performing polynomial regression using 5 types of equations -
Linear
Quadratic
Cubic
Quartic
Quintic
Regression
What is Regression?
Regression is a statistical measurement that is used to try to determine the relationship between a dependent variable (often denoted by Y), and series of varying variables (called independent variables, often denoted by X ).
What is Polynomial Regression
This is a form of Regression Analysis where the relationship between Y and X is denoted as the nth degree/power of X. Polynomial regression even fits a non-linear relationship (e.g when the points don't form a straight line).
Imports
import tensorflow.compat.v1 as tf
 tf.disable_v2_behavior()
 import matplotlib.pyplot as plt
 import numpy as np
 import pandas as pd
-
Dataset
Creating Random Data
Even though in this tutorial we will use a Position Vs Salary datasset, it is important to know how to create synthetic data
To create 50 values spaced evenly between 0 and 50, we use NumPy's linspace funtion
linspace(lower_limit, upper_limit, no_of_observations)
x = np.linspace(0, 50, 50)
+
Dataset
Creating Random Data
Even though in this tutorial we will use a Position Vs Salary dataset, it is important to know how to create synthetic data
To create 50 values spaced evenly between 0 and 50, we use NumPy's linspace function
linspace(lower_limit, upper_limit, no_of_observations)
x = np.linspace(0, 50, 50)
 y = np.linspace(0, 50, 50)
 
We use the following function to add noise to the data, so that our values
x += np.random.uniform(-4, 4, 50)
 y += np.random.uniform(-4, 4, 50)
@@ -22,7 +22,7 @@
 | Senior Partner    | 8     | 300000  |
 | C-level           | 9     | 500000  |
 | CEO               | 10    | 1000000 |
-
We convert the salary column as the ordinate (y-cordinate) and level column as the abscissa
abscissa = df["Level"].to_list() # abscissa = [1,2,3,4,5,6,7,8,9,10]
+
We convert the salary column as the ordinate (y-coordinate) and level column as the abscissa
abscissa = df["Level"].to_list() # abscissa = [1,2,3,4,5,6,7,8,9,10]
 ordinate = df["Salary"].to_list() # ordinate = [45000,50000,60000,80000,110000,150000,200000,300000,500000,1000000]
 
n = len(abscissa) # no of observations
 plt.scatter(abscissa, ordinate)
@@ -32,7 +32,7 @@
 plt.show()
 
Defining Stuff
X = tf.placeholder("float")
 Y = tf.placeholder("float")
-
Defining Variables
We first define all the coefficients and constant as tensorflow variables haveing a random intitial value
a = tf.Variable(np.random.randn(), name = "a")
+
Defining Variables
We first define all the coefficients and constant as tensorflow variables having a random initial value
a = tf.Variable(np.random.randn(), name = "a")
 b = tf.Variable(np.random.randn(), name = "b")
 c = tf.Variable(np.random.randn(), name = "c")
 d = tf.Variable(np.random.randn(), name = "d")
@@ -304,4 +304,4 @@
 plt.title('Quintic Regression Result')
 plt.legend()
 plt.show()
-
Results and Conclusion
You just learnt Polynomial Regression using TensorFlow!
Notes
Overfitting
> Overfitting refers to a model that models the training data too well.Overfitting happens when a model learns the detail and noise in the training data to the extent that it negatively impacts the performance of the model on new data. This means that the noise or random fluctuations in the training data is picked up and learned as concepts by the model. The problem is that these concepts do not apply to new data and negatively impact the models ability to generalize.
Source: Machine Learning Mastery
Basically if you train your machine learning model on a small dataset for a really large number of epochs, the model will learn all the deformities/noise in the data and will actually think that it is a normal part. Therefore when it will see some new data, it will discard that new data as noise and will impact the accuracy of the model in a negative manner
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Results and Conclusion

You just learnt Polynomial Regression using TensorFlow!

Notes

Overfitting

> Overfitting refers to a model that models the training data too well.Overfitting happens when a model learns the detail and noise in the training data to the extent that it negatively impacts the performance of the model on new data. This means that the noise or random fluctuations in the training data is picked up and learned as concepts by the model. The problem is that these concepts do not apply to new data and negatively impact the models ability to generalise.

Source: Machine Learning Mastery

Basically if you train your machine learning model on a small dataset for a really large number of epochs, the model will learn all the deformities/noise in the data and will actually think that it is a normal part. Therefore when it will see some new data, it will discard that new data as noise and will impact the accuracy of the model in a negative manner

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