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 […]
In the literature, the term Jacobian is often interchangeably used to refer to both the Jacobian matrix or its determinant. Both the matrix and the determinant have useful and important applications: in machine learning, the Jacobian matrix aggregates the partial derivatives that are necessary for backpropagation; the determinant is useful in the process of changing […]
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: […]
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 […]
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. […]
We have previously seen that calculus is one of the core mathematical concepts in machine learning that permits us to understand the internal workings of different machine learning algorithms. Calculus, in turn, builds on several fundamental concepts that derive from algebra and geometry. The importance of having these fundamentals at hand will become even more […]
The measurement of the rate of change is an integral concept in differential calculus, which concerns the mathematics of change and infinitesimals. It allows us to find the relationship between two changing variables and how these affect one another. The measurement of the rate of change is also essential for machine learning, such as in […]
Calculus is the mathematical study of change. The effectiveness of calculus to solve a complicated but continuous problem lies in its ability to slice the problem into infinitely simpler parts, solve them separately, and subsequently rebuild them into the original whole. This strategy can be applied to study all continuous elements that can be sliced […]
