Beyond the Margins exploring mathematics & machine learning
Regularized (Penalized) Regression
In this article, we will explore regularized (penalized) regression methods that help prevent overfitting and address issues such as multicollinearity, which can make $X^TX$ ill-conditioned or even non-invertible. OLS Limitations: As mentioned in this article Read more 03 Oct 2025 - less than 1 minute read
The Complex Beauty of the Mandelbrot Set
In this article, we will explore the artistic component of mathematics. Specifically, we will look at the Mandelbrot set– a set of complex numbers that exhibits artistic beauty. What Constitutes the Mandelbrot Set? The Mandelbrot set is a mathematical set of complex numbers. When we plot the points inside and outside this set we can observ... Read more 10 Jul 2023 - 4 minute read
Multiple Linear Regression (Part 3)
In this article, we will look at another technique to calculate the regression coefficients $\beta$ called Gradient Descent. This is an optimization technique that involves taking the gradient to find the optimal $\beta$ values that minimize the loss function. Optimization and Linear Regression In the previous post, we looked at how the nor... Read more 28 Jun 2023 - 6 minute read
NLP-Driven Predictive Modeling of Clinical Trial Status
Introduction/ Motivation Clinical trials are research studies conducted to evaluate the safety and effectiveness of new medical interventions, such as drugs, treatments, or medical devices. These trials involve the participation of human volunteers who may benefit from innovative healthcare solutions. However, not all clinical trials proceed as ... Read more 15 Jun 2023 - 14 minute read
Multiple Linear Regression (Part 2)
In this article, we will explore the common metrics that help us assess the performance of our linear regression model. We will also look at an implementation of linear regression using the scikit-learn library in Python. Additionally, we will discuss the assumptions underlying linear regression and discuss when linear regression is useful in... Read more 30 May 2023 - 7 minute read