Calculus, more appropriately called analysis, is the branch of mathematics studying the rate of change of quantities and the volume, area, and length of objects. The calculus is divided into differential calculus and integral calculus.
Calculus is an intrinsic field of maths, especially in many machine learning algorithms that you cannot expect of skipping this course to study the essence of Data Science.
- Differential Calculus cuts something into tiny pieces to find how it changes.
- Integral Calculus integrates the small elements to see how much there is.
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A gradient descent measures how much the output of a function changes if you change the inputs a little bit.
Gradient descent finds the rate of change of the variables and adjusts to move towards the minimum point. The minimum point, in this case, is the values of the input variables, which will give us the minimum value for the cost function.
Suppose you have a ball and a bowl. Whether you slide the ball in the bowl, it will eventually land in the bottom of the bowl.
Gradient Descent in Machine Learning
In our machine learning model, our focus is to reduce the cost of our input data. The cost function is used to observe the error in predictions of an ML model. So minimising this means getting to the least error value possible or growing the accuracy of the model. In short, We increase the accuracy by iterating over a training data set while tweaking the parameters(the biases and weights) of our model.
We are often faced with issues whereby we are attempting to predict a variable dependent on multiple variables. For instance, we might want to predict the price of a stock, and its cost can depend on several factors such as company growth, inflation rate, interest rate, and so on.
Therefore, for us to better quantify and predict the price accurately, the field of Machine Learning utilises multivariate calculus to understand the relationships.
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What Is Multivariate Calculus?
Multivariate implies that there are multiple variables. Therefore multivariate calculus is a field of calculus that involves various variables.
Multivariate Calculus Uses
Multivariate calculus is a field that assists us in the explanation of the relationships between input variables and output variables.
It contributes to us with the tools to build an accurate predictive model. Moreover, multivariate calculus can explain the change in our target variable concerning the rate of difference in the input variables
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How Is Multivariate Calculus Used In Machine Learning?
Multivariate calculus is used in machine learning
- In a support vector algorithm, multivariate calculus is used to find the maximal margin.
- In the EM algorithm, it is used to find the maxima.
- The optimisation problems rely on multivariate calculus.
- In gradient descent, it is used to find the local and global maxima.
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Coming from a non-technical background, it is really hard to learn Machine Learning and Python. However, this blog truly enlightened me about the importance of calculus for this field. I have to learn from the basics to master this subject. Great blog!