Implementing a Decomposition Method

For this recipe, we will implement a matrix decomposition method for linear regression. Specifically we will use the Cholesky decomposition, for which relevant functions exist in TensorFlow.

Getting ready

Implementing inverse methods in the previous recipe can be numerically inefficient in most cases, especially when the matrices get very large. Another approach is to decompose the A matrix and perform matrix operations on the decompositions instead. One such approach is to use the built-in Cholesky decomposition method in TensorFlow. One reason people are so interested in decomposing a matrix into more matrices is because the resulting matrices will have assured properties that allow us to use certain methods efficiently. The Cholesky decomposition decomposes a matrix into a lower and upper triangular matrix, say and , such that these matrices are transpositions of each other. For further information on the properties of this decomposition, there are many...