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 […]
Vector valued functions are often encountered in machine learning, computer graphics and computer vision algorithms. They are particularly useful for defining the parametric equations of space curves. It is important to gain a basic understanding of vector valued functions to grasp more complex concepts. In this tutorial, you will discover what vector valued functions are, […]
Integral calculus was one of the greatest discoveries of Newton and Leibniz. Their work independently led to the proof, and recognition of the importance of the fundamental theorem of calculus, which linked integrals to derivatives. With the discovery of integrals, areas and volumes could thereafter be studied. Integral calculus is the second half of the […]
It is often desirable to study functions that depend on many variables. Multivariate calculus provides us with the tools to do so by extending the concepts that we find in calculus, such as the computation of the rate of change, to multiple variables. It plays an essential role in the process of training a neural […]
The derivative defines the rate at which one variable changes with respect to another. It is an important concept that comes in extremely useful in many applications: in everyday life, the derivative can tell you at which speed you are driving, or help you predict fluctuations on the stock market; in machine learning, derivatives are […]
Many areas of calculus require an understanding of continuous functions. The characteristics of continuous functions, and the study of points of discontinuity are of great interest to the mathematical community. Because of their important properties, continuous functions have practical applications in machine learning algorithms and optimization methods. In this tutorial, you will discover what continuous […]
Indeterminate forms are often encountered when evaluating limits of functions, and limits in turn play an important role in mathematics and calculus. They are essential for learning about derivatives, gradients, Hessians, and a lot more. In this tutorial, you will discover how to evaluate the limits of indeterminate forms and the L’Hospital’s rule for solving […]
Optimization, as one of the core processes in many machine learning algorithms, relies on the use of derivatives in order to decide in which manner to update a model’s parameter values, to maximize or minimize an objective function. This tutorial will continue exploring the different techniques by which we can find the derivatives of functions. […]
Many machine learning algorithms involve an optimization process for different purposes. Optimization refers to the problem of minimizing or maximizing an objective function by altering the value of its inputs. Optimization algorithms rely on the use of derivatives in order to understand how to alter (increase or decrease) the input values to the objective function, […]
