Gradient Descent with Tensorflow-GradientTape()

TensorFlow’s GradientTape API is used to record operations for automatic differentiation. It allows developers to compute the gradients of a target tensor with respect to one or more input tensors, which can then be used to optimize the parameters of a model using gradient descent.

Implementation:

Here is an example of how to use GradientTape() to compute gradients and optimize a model:

import tensorflow as tf
# Define the model
x = tf.constant(3.0)
with tf.GradientTape() as tape:
    tape.watch(x) 
    y = x ** 2
dy_dx = tape.gradient(y, x)
print(dy_dx)

In this example, we defined a simple model with a single variable x and a quadratic loss function y. We used GradientTape() to record the operations for automatic differentiation and then computed the gradients of the loss function with respect to x. Finally, we used the optimizer to update the value of x using the computed gradients.

To deploy a second order derivative with GradientTape() in TensorFlow, you can use the following code:

x = tf.constant(4.0)
with tf.GradientTape() as t2:
    t2.watch(x)
    with tf.GradientTape() as t:
        t.watch(x)
        y = x ** 3
    dy_dx = t.gradient(y, x)
d2y_dx = t2.gradient(dy_dx, x)
print(d2y_dx)

This will print the second-order derivative of the function y with respect to x. In this case, since y = x^3, the second order derivative will be 24. Note that, the second order derivative could be a tensor and need to be evaluated with sess.run if it is not a constant value.

Simple Gradient Descent for Linear regression:

Here, we will examine the process of constructing a basic linear regression model, represented by the equation Y = aX + b. The parameters of this model are represented by a and b, and the goal is to determine the optimal values for these parameters so that the model can effectively generalize the relationship between X and Y.

1. Creating dataset of 1000 samples with random values where 800 will be considered as a training set and 200 will be considered as a testing set:

import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt
%matplotlib inline
no_samples = 1000
a =…