Archive | Calculus

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Calculus for Machine Learning (7-day mini-course)

Calculus for Machine Learning Crash Course. Get familiar with the calculus techniques in machine learning in 7 days. Calculus is an important mathematics technique behind many machine learning algorithms. You don’t always need to know it to use the algorithms. When you go deeper, you will see it is ubiquitous in every discussion on the […]

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Method of Lagrange Multipliers: The Theory Behind Support Vector Machines (Part 3: Implementing An SVM From Scratch In Python)

The mathematics that powers a support vector machine (SVM) classifier is beautiful. It is important to not only learn the basic model of an SVM but also know how you can implement the entire model from scratch. This is a continuation of our series of tutorials on SVMs. In part1 and part2 of this series we […]

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Method of Lagrange Multipliers: The Theory Behind Support Vector Machines (Part 2: The Non-Separable Case)

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 […]

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Application of differentiations in neural networks

Differential calculus is an important tool in machine learning algorithms. Neural networks in particular, the gradient descent algorithm depends on the gradient, which is a quantity computed by differentiation. In this tutorial, we will see how the back-propagation technique is used in finding the gradients in neural networks. After completing this tutorial, you will know […]

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Method of Lagrange Multipliers: The Theory Behind Support Vector Machines (Part 1: The Separable Case)

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 […]

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Lagrange Multiplier Approach with Inequality Constraints

Lagrange Multiplier Approach with Inequality Constraints

In a previous post, we introduced the method of Lagrange multipliers to find local minima or local maxima of a function with equality constraints. The same method can be applied to those with inequality constraints as well. In this tutorial, you will discover the method of Lagrange multipliers applied to find the local minimum or […]

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Calculus in Action: Neural Networks

An artificial neural network is a computational model that approximates a mapping between inputs and outputs.  It is inspired by the structure of the human brain, in that it is similarly composed of a network of interconnected neurons that propagate information upon receiving sets of stimuli from neighbouring neurons. Training a neural network involves a […]

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Muhammad Khubaib Sarfraz

A Gentle Introduction to Taylor Series

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 […]

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A Gentle Introduction To Approximation

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 […]

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The Chain Rule of Calculus – Even More Functions

The chain rule is an important derivative rule that allows us to work with composite functions. It is essential in understanding the workings of the backpropagation algorithm, which applies the chain rule extensively in order to calculate the error gradient of the loss function with respect to each weight of a neural network. We will […]

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