HPC Posts

I can’t think of of trending field of scientific research that has ever been better suited for “beginners” than Machine Learning and AI. Even though the field has been around for decades it feels like day one. There is now a perfect convergence of resources to facilitate the learning and doing of Machine Learning.

The post will implement Multinomial Logistic Regression. The multiclass approach used will be one-vs-rest. The Jupyter notebook contains a full collection of Python functions for the implementation. An example problem done showing image classification using the MNIST digits dataset.

This post will be mostly Python code with implementation and examples of the Logistic Regression theory we have been discussing in the last few posts. Examples include fitting to 2 feature data using an arbitrary order multinomial model and a simple 2 class image classification problem using the MNIST digits data.

In this post I’ll discuss evaluating the “goodness of fit” for a Logistic Regression model and do an implementation of the formulas in Python using numpy. We’ll look at an example to check the validity of the code.

In this post I will look at “Regularization” in order to address an important problem that is common with implementations, namely over-fitting. We’ll go through for logistic regression and linear regression. After getting the equations for regularization worked out we’ll look at an example in Python showing how this can be used for a badly over-fit linear regression model.

Logistic regression is a widely used Machine Learning method for binary classification. It is also a good stepping stone for understanding Neural Networks. In this post I will present the theory behind it including a derivation of the Logistic Regression Cost Function gradient.

This will be the last post in the Linear Regression series. We will look at the problems of over or under fitting data along with non-linear feature variables.

In this post I will present the matrix/vector form of the Linear Regression problem and derive the “exact” solution for the parameters.