This tutorial is an extension of Method Of Lagrange Multipliers: The Theory Behind Support Vector Machines (Part 1: The Separable Case)) and explains the non-separable case. In real life problems positive and negative training examples may not be completely separable by a linear decision boundary. This tutorial explains how a soft margin can be built […]
This tutorial is designed for anyone looking for a deeper understanding of how Lagrange multipliers are used in building up the model for support vector machines (SVMs). SVMs were initially designed to solve binary classification problems and later extended and applied to regression and unsupervised learning. They have shown their success in solving many complex machine […]
Whether you implement a neural network yourself or you use a built in library for neural network learning, it is of paramount importance to understand the significance of a sigmoid function. The sigmoid function is the key to understanding how a neural network learns complex problems. This function also served as a basis for discovering […]
A Gentle Introduction to Taylor Series Taylor series expansion is an awesome concept, not only the world of mathematics, but also in optimization theory, function approximation and machine learning. It is widely applied in numerical computations when estimates of a function’s values at different points are required. In this tutorial, you will discover Taylor series […]
When it comes to machine learning tasks such as classification or regression, approximation techniques play a key role in learning from the data. Many machine learning methods approximate a function or a mapping between the inputs and outputs via a learning algorithm. In this tutorial, you will discover what is approximation and its importance in […]
The method of Lagrange multipliers is a simple and elegant method of finding the local minima or local maxima of a function subject to equality or inequality constraints. Lagrange multipliers are also called undetermined multipliers. In this tutorial we’ll talk about this method when given equality constraints. In this tutorial, you will discover the method […]
Whether it is a supervised learning problem or an unsupervised problem, there will be some optimization algorithm working in the background. Almost any classification, regression or clustering problem can be cast as an optimization problem. In this tutorial, you will discover what is optimization and concepts related to it. After completing this tutorial, you will […]
Hessian matrices belong to a class of mathematical structures that involve second order derivatives. They are often used in machine learning and data science algorithms for optimizing a function of interest. In this tutorial, you will discover Hessian matrices, their corresponding discriminants, and their significance. All concepts are illustrated via an example. After completing this […]
Gradient descent procedure is a method that holds paramount importance in machine learning. It is often used for minimizing error functions in classification and regression problems. It is also used in training neural networks, and deep learning architectures. In this tutorial, you will discover the gradient descent procedure. After completing this tutorial, you will know: […]
Partial derivatives and gradient vectors are used very often in machine learning algorithms for finding the minimum or maximum of a function. Gradient vectors are used in the training of neural networks, logistic regression, and many other classification and regression problems. In this tutorial, you will discover partial derivatives and the gradient vector. After completing […]
