An intuitive and comprehensive guide to probability distributions — A probability distribution describes the probabilities of the values that a random variable can take. It is an important concept in statistics and probability theory, and every book on this topic discusses probability distributions along with their properties. However, they emphasize the mathematical properties of these distributions rather than the…

Learn how the SHAP library works under the hood — SHAP is a mathematical method to explain the predictions of machine learning models. It is based on the concepts of game theory and can be used to explain the predictions of any machine learning model by calculating the contribution of each feature to the prediction. SHAP can determine the most…

A comprehensive guide to Spark datasets and DataFrames — Preliminary Apache Spark is an open source distributed data processing engine that can be used for big data analysis. It has built-in libraries for streaming, graph processing, and machine learning, and data scientists can use Spark to rapidly analyze data at scale. …

Learn the mathematical intuition behind PCA — In the first part of this article, I introduced the covariance matrix and discussed the mathematical foundation of PCA. In this part first, we discuss the application of singular value decomposition (SVD) in SVD and then we see a case study of PCA for the MNIST dataset. Finally, we discuss…

Learn the mathematical intuition behind PCA — Principal Component Analysis (PCA), is a method used to reduce the dimensionality of large datasets. We will also study the covariance matrix and the multivariate normal distribution in detail since understanding them will result in a better understanding of PCA. …

Learn about different weight initialization methods in neural networks — Weight and bias are the adjustable parameters of a neural network, and during the training phase, they are changed using the gradient descent algorithm to minimize the cost function of the network. However, they must be initialized before one can start training the network, and this initialization step has an…

The mathematical foundation of feedforward neural nets — The feedforward neural network is the simplest type of artificial neural network which has lots of applications in machine learning. It was the first type of neural network ever created, and a firm understanding of this network can help you understand the more complicated architectures like convolutional or recurrent neural…

Avoiding stack overflow in Python using tail-recursion — Recursion in computer science is a method of problem-solving in which a function calls itself from within its own code. This method is very useful and can be applied to many types of problems, however, it has a limitation. Functions use the stack to keep their local variables, and the…

Learn about disassembling Python bytecode — The source code of a programming language can be executed using an interpreter or a compiler. In a compiled language, a compiler will translate the source code directly into binary machine code. This machine code is specific to that target machine since each machine can have a different operating system…