Linear

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…

Theoretical foundations on how MILP is defined and how its solution space looks like visuallyPhoto by Ivan Bandura on UnsplashThis post is a continuation of the series (previous post) on the theory and applications of Mixed Integer Linear Programming (MILP). Today, we look atthe formal, general definition of MILP,how its space of feasible solutions looks like.The first part describes how MILP models look in general, what are and are not valid MILP expressions. The second part shows a little bit of theory behind MILP,…

Photo by Michael Dziedzic on UnsplashMaster elements of linear algebra, start with simple and visual explanations of basic conceptsOften the main difficulty one faces when one wants to begin one’s journey into the world of machine learning is having to understand math concepts. Sometimes this can be difficult if you do not have a solid background in subjects such as linear algebra, statistics, probability, optimization theory, or others. 🤔💭🔢✖️🧮In this article then, I would like to start by giving intuitive explanations of…

An Interactive Visualisation for You to Experiment WithImage created by Arus Nazaryan using Midjourney. Prompt: “Drone footage of two flocks of sheep, bright blue and deep red, divided by a fence which separates the flocks in the middle, clean, realistic sheep, on green grass, photorealistic”Classification is a central topic in machine learning. However, it can be challenging to understand how the different algorithms work. In this article, we will make linear discriminant analysis come alive with an interactive plot that…

Welcome to the second part of our Back To Basics series. In the first part, we covered how to use Linear Regression and Cost Function to find the best-fitting line for our house prices data. However, we also saw that testing multiple intercept values can be tedious and inefficient. In this second part, we’ll delve deeper into Gradient Descent, a powerful technique that can help us find the perfect intercept and optimize our model. We’ll explore the math behind it and see how it can be applied to our linear regression…

An accessible perspective on essential machine learning conceptsToday, we will delve into three crucial concepts in Machine Learning: Linear Regression, Cost Function, and Gradient Descent. These concepts form the foundation of many Machine Learning algorithms. Initially, I decided against writing an article on these topics because they are so widely covered. However, I have changed my mind because understanding these concepts is essential for understanding more advanced topics like Neural Networks (that I plan on…

Part 4: A comprehensive step-by-step guide to solving a linear system with LU DecompositionPhoto by Andry Roby on UnsplashThe first article of this Linear Algebra series has introduced how to solve a linear system using Gaussian elimination and the previous article also explained how to find an inverse matrix and also how to use the inverse matrix to solve the linear system. This article will introduce another way to solve the linear system using LU decomposition.Lower-Upper (LU) decomposition is a way to factorize a…

How to solve complex constrained optimisation problems having discrete variablesPhoto by Mitchell Luo on UnsplashDesigning and implementing algorithms for complex problems is hard. Fun, but hard. What if I told that you can solve certain optimisation problems using only their mathematical specification? Join me on the journey to the wonderful world of Mixed Integer Linear Programming, which has its applications in nurse rostering, kidney exchange programs, production scheduling, robotic cells energy optimisation,…

Photo by Nicholas Cappello on UnsplashLong-Term Forecasting using Transformers may not be the way to goIn recent years, Transformer-based solutions have been gaining incredible popularity. With the success of BERT, GTP, and other language transformers researchers started to apply this architecture to other sequential-modeling problems, specifically in the area of time series forecasting (also known as Long-Term Time Series Forecasting or LTSF). The attention mechanism seemed to be a perfect method to extract some of the…

Part 3: A comprehensive step-by-step guide to finding the inverse matrix using elementary row operations and determinants of the matrixPhoto by Raimond Klavins on UnsplashThe previous article explained the different matrix operations and corresponding operations. This article will dive deep into two different methods on how to get the inverse matrix using elementary row operations and using determinants of the matrix.An inverse matrix is similar to the reciprocal of a number such that the multiplication of a number by its…