Deriving

Using Principal Component Analysis with Real-life dataPhoto by Vista Wei on UnsplashMotivationThere exist publicly accessible data which describe the socio-economic characteristics of a geographic location. In Australia where I reside, the Government through the Australian Bureau of Statistics (ABS) collects and publishes individual and household data on a regular basis in respect of income, occupation, education, employment and housing at an area level. Some examples of the published data points include:Percentage of…

Integrating a function using a neural network (with code)Photo by Jack Anstey on Unsplash1. IntroductionThis article presents a method for training a neural network to derive the integral of a function. The technique works not only with analytically-solvable integrals but also with integrals that do not have a closed-form solution and are typically solved by numerical methods. An example is the normal distribution’s cumulative density function (CDF). Equation 1 is this distribution’s probability density function (PDF),…

Credit: Kryshtofor Volodymyr/Shutterstock Researchers at the University of Tsukuba have created a new method for deriving approximate linear equations to complicated nonlinear problems. Using simulation results, they show that the model derived using their proposed pseudo-linearization approach yields responses that are closer to those of the well-known alternative method. This work can help scientists and engineers predict…

Deriving Bayesian Linear Regression from first principles using PythonPhoto by Klim Musalimov on UnsplashLinear Regression is the most well known algorithm in Data Science, however there is more than one version of it. The version most people use comes from the Frequentist interpretation of statistics, but there is another that comes from the Bayesian school of thought.In this article, we will go over Bayes’ theorem, the difference between Frequentist and Bayesian statistics and finally carry out Bayesian Linear…