
TensorFlow Machine Learning Cookbook
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In this recipe, we will use TensorFlow to solve two dimensional linear regressions with the matrix inverse method.
Linear regression can be represented as a set of matrix equations, say . Here we are interested in solving the coefficients in matrix x. We have to be careful if our observation matrix (design matrix) A is not square. The solution to solving x can be expressed as
. To show this is indeed the case, we will generate two-dimensional data, solve it in TensorFlow, and plot the result.
First we load the necessary libraries, initialize the graph, and create the data, as follows:
import matplotlib.pyplot as plt import numpy as np import tensorflow as tf sess = tf.Session() x_vals = np.linspace(0, 10, 100) y_vals = x_vals + np.random.normal(0, 1, 100)
Next we create the matrices to use in the inverse method. We create the A
matrix first, which will be a column of x-data and a column of 1s. Then we create the b
matrix from the y-data...